CPP50121 · Diploma of SurveyingComplex & Geodetic Survey Comps Guide
5053 Complex5054 GeodeticCRS Tools
CPP50121 · Diploma of Surveying · 2026
Computations Study Guide
Verified formulas, annotated worked examples, and interactive plots for CPPSSI5053 and CPPSSI5054. Use the sidebar to navigate by topic or jump directly to any interactive plot.
CPPSSI5053
Perform Complex Surveying Computations
The step-up from Cert IV is in two areas: you now quantify the uncertainty in your results using equipment specifications and statistics, and you handle more complex geometry — roads with different widths, reverse curves, coordinate transformations, and rigorous traverse adjustment by least squares.
5053 · New Concept
Error Analysis & Uncertainty
Every measurement contains error. The Diploma requires you to quantify it — to calculate how uncertain your computed result is, based on the known accuracy limits of your equipment and the number of observations made.
Blunders
Gross mistakes — misread digit, wrong booking, instrument not levelled. Not part of the statistical random error model. Eliminated by rigorous checking: face-left/face-right, independent booking checks, closing traverses. A blunder that survives will corrupt all a posteriori estimates.
Systematic Errors
Consistent sign and magnitude — an EDM with an uncalibrated additive constant shifts every distance by the same amount. Corrected by calibration, FL+FR procedure, and atmospheric corrections. Not random — not managed by averaging.
Random Errors
Unavoidable residual variation after blunders and systematic errors are removed. Small, equally likely positive or negative, follow the normal distribution. These are what uncertainty analysis quantifies and propagates through calculations.
Interactive — Normal Distribution of Random Errors
0.0 mm
1.0 mm
The normal distribution of random errors. The shaded region shows the selected confidence interval. Drag μ to shift the mean — errors should be centred on zero (a non-zero μ suggests systematic error). σ controls spread — a larger σ means less precise measurements. The inflection points of the curve (where it changes concavity) occur exactly at ±1σ. Australian survey standards (ICSM Positional Uncertainty) are specified at 95% confidence ≈ ±2σ.
Confidence Intervals — always quote the level when reporting
68% CI:x̄ ± 1·σ
95% CI:x̄ ± 2·σ ← ICSM Positional Uncertainty standard
99.7% CI:x̄ ± 3·σ
For reporting a computed result: state the value, the uncertainty, and the confidence level. Example: 191.270 m ± 0.014 m at 95%. Never report ± without the confidence level — ±1σ and ±2σ look the same on paper but mean very different things.
When a result is computed from multiple independent measurements, each measurement's uncertainty carries through to the final result. The fundamental rule: variances add, not standard deviations. Square each σ, sum the variances, then take the square root.
Law of Propagationσresult = √( σ₁² + σ₂² + σ₃² + … )
Use when: the result is a sum or difference of independent measurements — total traverse length from segments, an angle from two observed directions. The combined σ is always larger than any single component but smaller than their arithmetic sum. Never add raw σ values directly.
⊕ Worked Example — Total distance from three EDM segments
1
Given
A–B = 82.140 m, σ1 = 5 mm | B–C = 61.330 m, σ2 = 4 mm | C–D = 47.800 m, σ3 = 3 mm
Each σ comes from the EDM a + b·ppm specification applied to that leg distance — see the A Priori section below.
2
Total distance
A–D = 82.140 + 61.330 + 47.800 = 191.270 m
3
Square each σ (→ variances)
σ1² = 5² = 25 mm²
σ2² = 4² = 16 mm²
σ3² = 3² = 9 mm²
Convert to consistent units first. Never add raw σ values.
4
Sum the variances
Σσ² = 25 + 16 + 9 = 50 mm²
5
Take the square root
σAD = √50 = 7.07 mm ≈ 7 mm (1σ)
∴ A–D = 191.270 m ± 7 mm at 68% → ± 14 mm at 95%
Interactive — Error Propagation Visualiser (up to 4 components)
5 mm
4 mm
3 mm
0 mm
Bar chart of variances (σ²) and the resulting combined σ. Drag any slider to zero to remove that component. Notice that combining errors gives a result smaller than their sum — this is why averaging and using more observations genuinely improves precision.
Calculator — Error Propagation
Enter values and click Calculate.
5053 · Key New Concept — PC 2.6, 2.7
A Priori vs A Posteriori Uncertainty
These Latin terms describe when you calculate expected uncertainty. Comparing them is how you demonstrate compliance with accuracy standards — required by Performance Criterion 2.7.
A Priori — Before the Survey
"Based on my equipment specifications, what uncertainty should I expect?"
Source: Manufacturer data sheet — angular accuracy (e.g. 1″ ISO), EDM accuracy (e.g. 2 mm + 2 ppm), centring accuracy (e.g. 0.5 mm). Propagated through the calculation before fieldwork begins.
ISO angular spec = σ of one direction. Angle = 2 directions → σangle = σdir × √2. Multiple rounds → SE = σangle / √n.
A Posteriori — After the Survey
"Based on my actual observations, what uncertainty did I achieve?"
Source: Field data — spread of repeated rounds. Computed as sample standard deviation s = √[Σν² / (n−1)] where ν = residual = observation − mean.
If a posteriori ≤ a priori: compliant with PC 2.7. If significantly greater: blunder may remain, or conditions were adverse.
A Priori EDMσEDM = √( a² + (b · D · 10−3)² ) [mm]
a = constant component (mm) | b = scale component (ppm) | D = distance (m). The ppm term: b ppm × D m = b × D × 10−6 m = b × D × 10−3 mm. Example — spec 2 mm + 2 ppm, D = 500 m: σ = √(4 + (2 × 500 × 10⁻³)²) = √(4 + 1) = √5 = 2.24 mm.
Interactive — σEDM vs Distance for your instrument specification
2 mm
2 ppm
σEDM = √(a² + (b·D·10⁻³)²) plotted against distance. At short distances the constant term a dominates — halving the distance doesn't halve the uncertainty. At long distances the scale term b·D grows and eventually dominates the curve. The crossover point is where a = b·D·10⁻³, i.e. D = a/(b·10⁻³) = a·1000/b metres.
⊕ Worked Example — A Priori and A Posteriori comparison
1
Instrument spec (given)
Total station: angular σdir = 1″, EDM: a = 2 mm, b = 2 ppm. Centring: σc = 0.5 mm each end.
2
A priori — angle (from spec)
σangle = σdir × √2 = 1″ × 1.414 = 1.41″
With 4 rounds: SEangle = 1.41 / √4 = 0.71″
An angle is observed from two directions — two independent readings, each with σdir. √2 combines them. More rounds reduce the SE as 1/√n.
3
A priori — distance D = 850 m
σEDM = √(2² + (2 × 850 × 10⁻³)²)
= √(4 + (1.7)²) = √(4 + 2.89) = √6.89 = 2.63 mm
Constant term 2 mm, scale term 1.7 mm. Combined by root-sum-square.
4
A posteriori — from 4 rounds of angles (field data)
s is the a posteriori standard deviation of one round. SE is the a posteriori uncertainty of the mean — this is what we compare against the a priori SE.
5
Comparison — PC 2.7
A posteriori SE = 0.52″ < A priori SE = 0.71″
✓ Compliant — actual performance is better than the specification. Survey is accepted.
Calculator — A Priori EDM Uncertainty
mm
ppm
m
Enter values and click Calculate.
5053 · PC 2.1, 2.2, 3.2 — Diploma Extension
Traverse Adjustment by Least Squares
The Diploma requires rigorous adjustment. Least squares finds the set of corrections that minimises the sum of squared residuals Σν² — the statistically optimal solution for normally distributed random errors.
Cert IV prerequisite: You computed linear misclose mL = √(mN² + mE²) and the misclose ratio MR = ΣL / mL. This tells you whether the traverse meets tolerance, but not why it miscloses or which observations contributed most to the error.
Least squares adjustment gives each coordinate correction a statistically rigorous value. For a traverse, we write observation equations: each observed bearing and distance generates a predicted ΔN and ΔE. The differences between predicted and actual closing coordinates are residuals. The adjustment finds corrections to all observations simultaneously so Σν² is minimised.
Least Squares Corev = Ax̂ − f solved by x̂ = (AᵀA)⁻¹ Aᵀf
v = vector of residuals (corrections to observations) A = design matrix (partial derivatives of observations with respect to unknowns) f = misclosure vector (observed − computed) x̂ = vector of estimated corrections to the unknowns (ΔN, ΔE for each station)
For a simple closed traverse, the unknowns are the coordinate corrections at each intermediate point. The design matrix A is built from the direction cosines (cos θ, sin θ) of each leg.
Traverse Observation Equations — each leg generates two equations
After adjustment, ΣνN = 0 and ΣνE = 0 exactly. The a posteriori standard deviation of unit weight σ₀ = √(Σν² / r) where r = redundancy (number of observations − number of unknowns). Compare σ₀ against the a priori σ₀ = 1 to test the adjustment.
⊕ Worked Example — 4-station closed traverse, least squares adjustment
1
Given — closed traverse A→B→C→D→A
A (fixed): N = 1000.000, E = 1000.000
Observed legs (bearing in °′″, distance in m):
A→B: θ = 045°12′18″, L = 157.430 m
B→C: θ = 135°44′06″, L = 203.815 m
C→D: θ = 225°31′42″, L = 164.290 m
D→A: θ = 314°55′30″, L = 218.670 m
2
Step 1 — Compute ΔN and ΔE for each leg
A→B: ΔN = 157.430 × cos 045°12′18″ = 157.430 × 0.70538 = +111.004 m
ΔE = 157.430 × sin 045°12′18″ = 157.430 × 0.70883 = +111.547 m
B→C: ΔN = 203.815 × cos 135°44′06″ = 203.815 × (−0.71526) = −145.749 m
ΔE = 203.815 × sin 135°44′06″ = 203.815 × 0.69884 = +142.424 m
C→D: ΔN = 164.290 × cos 225°31′42″ = 164.290 × (−0.70088) = −115.124 m
ΔE = 164.290 × sin 225°31′42″ = 164.290 × (−0.71328) = −117.175 m
D→A: ΔN = 218.670 × cos 314°55′30″ = 218.670 × 0.70888 = +155.010 m
ΔE = 218.670 × sin 314°55′30″ = 218.670 × (−0.70533) = −154.238 m
Use HP Prime in Degrees mode. Convert bearing from DMS using HMS→ before computing cos/sin.
mL = √(5.141² + 17.442²) = √(26.43 + 304.22) = 18.18 m
Note: this example shows a large misclose deliberately to illustrate the adjustment. In practice this misclose would fail tolerance — the traverse would be re-observed.
4
Step 3 — Least squares corrections (equal weights, simplified)
For equal-weight observations, the correction to each ΔN and ΔE is distributed proportionally to leg length (equivalent to Bowditch in the equal-weight case). In least squares with explicit weights (σ from instrument spec), each correction is weighted by 1/σ².
Correction to N for each leg: cN,i = −mN × (Li / ΣL)
Correction to E for each leg: cE,i = −mE × (Li / ΣL)
A posteriori σ₀ = √(Σν²/r). With 4 observations and 6 unknowns (N,E for B,C,D) → r = 2. This is assessed in the HP Prime or adjustment software.
Calculator — Traverse Misclose and Proportional Correction
Enter values and click Calculate.
Reducing FL/FR Observations to a Mean Angle — PC 2.2
AngleFL=Direction to BFL − Direction to AFL
AngleFR=Direction to BFR − Direction to AFR
Mean (one round)=( AngleFL + AngleFR ) / 2
Overall mean=Σ(round means) / nrounds
Vertical index check: ZDFL + ZDFR should equal 360°. If not, reject that round. Corrected ZD = (ZDFL + (360° − ZDFR)) / 2. A posteriori: s = √[Σν²/(n−1)] from round means. SE = s/√n. Compare SE ≤ a priori σangle/√n.
5053 · PC 2.5
Area Maintenance of Closed Figures
Subdivide or adjust a boundary while keeping total area exactly constant — common in cadastral work when relocating a fence line or re-defining a lot boundary.
Cert IV baseline (Ch.9 of Learning Guide): 2A = Σ(Ei·Ni+1 − Ei+1·Ni). A = |result|/2. Coordinates must be traversed in consistent order (CW or CCW).
Coordinate Area2A = Σ( Ei · Ni+1 − Ei+1 · Ni )
Area Maintenance — solving for an unknown boundary coordinate
Arequired=known (cadastral area to maintain)
Acomputed(x)=function of one unknown coordinate x
Solve:Acomputed(x) = Arequired → transpose for x
Express the area using the Shoelace formula with the unknown as a variable. The formula is linear in any single unknown coordinate — direct solution by transposition (Cert IV Ch.1 algebra).
⊕ Worked Example — Move boundary to maintain area of 4 800 m²
Format: point(E, N). This is a 200 × 200 m square, area = 40 000 m². We want to relocate the AB boundary southward to reduce the lot to exactly 4 800 m².
2
New boundary A'B'CD with unknown northing N' for A'B'
New area A' = (N' − 200) × 200 = 4 800 m²
N' − 200 = 4 800 / 200 = 24
N' = 224 m
∴ The new boundary A'B' runs at northing 224 m (24 m north of original AB).
3
Verify with Shoelace formula
Vertices: A'(100, 224) → B'(300, 224) → C(300, 400) → D(100, 400) → back to A'
Use the DMD check as an independent verification of the Shoelace formula. If both give the same 2A, the arithmetic is confirmed. The DMD of the last leg must equal its own departure (opposite sign to the first) — if not, an arithmetic error exists.
5053 · PC 2.3, 2.4 — New Topic
Road Intersection Problems — Different Road Widths
At Cert IV you computed single-width roads. The Diploma extends this to roads with different widths — requiring the two-width formula to find corner bearing and connection distance.
Plan view: two-width road intersection. Road 1 (green, width W₁) meets Road 2 (blue, width W₂ < W₁) at intersection angle α. Because widths differ, each corner (A, B, C, D) requires the two-width formula — the single-width secant/cotangent shortcuts do not apply.
Two-Width Bearingtan θAB = (W₁ sin θ₁ − W₂ sin θ₂) / (W₁ cos θ₁ − W₂ cos θ₂)
⊕ Worked Example — Find corner bearing and distance
1
Given
Road 1: θ₁ = 075°19′22″, W₁ = 10.000 m
Road 2: θ₂ = 041°51′31″, W₂ = 15.000 m
2
Convert bearings to decimal on HP Prime (HMS→)
θ₁ = 075°19′22″ → 75.3228°
θ₂ = 041°51′31″ → 41.8586°
3
Numerator and denominator
Num = W₁ sin θ₁ − W₂ sin θ₂ = 10 × sin 75.3228° − 15 × sin 41.8586°
You know simple curves from Cert IV. At Diploma level: missing elements and reverse curves — two arcs curving in opposite directions, joined at a common tangent point (PRC).
Cert IV formula sheet: TD = R·tan(Δ/2). E = TD·tan(Δ/4) or R/cos(Δ/2)−R. M = R(1−cos(Δ/2)). Arc = R·Δrad. LC = 2R·sin(Δ/2). Δ = deflection angle (= central angle).
Drag the sliders to change R and Δ. All five elements — TD (blue), Arc (green), LC (ochre), E (red), M (purple) — update live. Notice how at large Δ the PI moves closer to the curve and all elements become more pronounced. The radius is always perpendicular to the tangent at both PC and PT.
Element
Symbol
Formula
Tangent Distance
TD
R · tan(Δ/2)
Arc
Arc
R · Δrad = R · Δ° · π/180
Long Chord
LC
2R · sin(Δ/2)
Crown Secant
E
R / cos(Δ/2) − R = TD · tan(Δ/4)
Mid Ordinate
M
R · (1 − cos(Δ/2))
Sector area
—
Δrad · R² / 2 = Arc · R / 2
Segment area
—
R² / 2 · (Δrad − sin Δrad)
Truncation area
—
R²(tan(Δ/2) − Δrad/2) = R(TD − Arc/2)
⊕ Worked Example — All elements from R and Δ
1
Given
R = 200 m, Δ = 120°00′00″
Δ in radians = 120 × π/180 = 2.09440 rad
2
Tangent Distance TD
TD = 200 × tan(120°/2) = 200 × tan 60° = 200 × 1.73205 = 346.410 m
3
Arc length
Arc = 200 × 2.09440 = 418.879 m
4
Long Chord LC
LC = 2 × 200 × sin 60° = 400 × 0.86603 = 346.410 m
At Δ = 120°, LC = TD — a useful check specific to this angle.
5
Crown Secant E
E = 200 / cos 60° − 200 = 200 / 0.5 − 200 = 400 − 200 = 200.000 m
6
Mid Ordinate M
M = 200 × (1 − cos 60°) = 200 × (1 − 0.5) = 200 × 0.5 = 100.000 m
Check: LC < Arc → 346.410 < 418.879 ✓ | E > M always ✓
Calculator — Circular Curve (DMS input)
°′″
Enter R and Δ, click Calculate.
A reverse curve consists of two consecutive arcs curving in opposite directions, joined at the PRC (Point of Reverse Curvature). The PRC is simultaneously the PT of Arc 1 and the PC of Arc 2. The defining characteristic: centres O₁ and O₂ lie on opposite sides of the common tangent at PRC.
Interactive — Reverse Curve (S-curve) Builder
200 m
45°
200 m
45°
Drag sliders to change radii and deflection angles. Arc 1 (green) and Arc 2 (blue) meet at the PRC. Notice that O₁ and O₂ are always on opposite sides — this is what makes it a reverse curve, not a compound curve. At equal R and Δ the tangents at PC and PT are parallel. At unequal R or Δ the tangents converge.
Four Problem Types
Equal R, parallel tangents: P = 2R(1 − cos Δ), where P = perpendicular offset between tangents.
Unequal R, parallel tangents: P = R₁(1−cos Δ₁) + R₂(1−cos Δ₂). Also: R₁ sin Δ₁ = R₂ sin Δ₂ = L/2.
Equal R, converging tangents: Δ₁ + Δ₂ = 180° − θ, where θ = angle between tangents at PIs.
Unequal R, converging tangents: Most general. Δ₂ − Δ₁ = θ. Use sine rule on the triangle formed by the two PI points and the PRC.
Why Restricted from High-Speed Roads
At the PRC, curvature instantaneously reverses direction. Road banking (superelevation) cannot be transitioned — a vehicle experiences sudden lateral force reversal. Dangerous at speed.
Permitted: Park paths, pipelines, canals, low-speed roads, railway sidings.
Not permitted: Highways, high-speed railways — a transition (spiral) curve is used instead.
5053 · PC 3.2 — New Topic
Coordinate Transformations
Survey data in a local site grid must often be transformed to MGA2020. The 2D conformal transformation applies rotation, uniform scale, and a translation — four parameters, minimum two common points.
2D Conformal (E)EMGA = a · x − b · y + TE
2D Conformal (N)NMGA = b · x + a · y + TN
a = k·cos θ | b = k·sin θ | k = scale factor | θ = rotation angle (local → MGA2020) | TE, TN = translation.
Shape is preserved (conformal — angles unchanged). Minimum 2 common points → 4 equations, 4 unknowns (a, b, TE, TN) → direct solution. Three or more common points → least squares → residuals allow blunder detection. Performance Evidence requirement: Perform two transformations for east and north coordinates from one system to another (CPPSSI5053 Assessment Requirements).
⊕ Worked Example — Local site grid to MGA2020 using 2 common points
P3 in MGA2020 Zone 50: E = 394 539.029 m, N = 6 461 984.542 m
CPPSSI5054
Perform Geodetic Surveying Computations
Moves from the flat plane to the curved Earth. You reduce field measurements to the GRS80 ellipsoid (Australia's GDA2020 reference surface), then project them onto the MGA2020 flat grid — applying all the corrections that projection involves. Knowledge evidence covers: principal radii, spheroidal distance, grid convergence, arc-to-chord, scale factor, and coordinate conversion in both directions.
5054 · Foundation — PC 2.1
Reference Surfaces — Geoid, Ellipsoid & GDA2020
Before any geodetic computation, you must understand which mathematical surface you are working on — the choice determines which formulas apply and which height to use.
Figure 1 — Relationship between the ellipsoid, geoid, AHD and the topography. Source: Geoscience Australia / ICSM GDA2020 Technical Manual (Figure 13-7238-2). h = H + N. At Perth, N ≈ −27 to −30 m, so the ellipsoid sits approximately 28 m below AHD zero — ellipsoidal heights h are about 28 m less than AHD heights H.
Height Relationshiph = H + N (at Perth: h ≈ H − 28 m)
h = ellipsoidal height (GNSS output, measured above GRS80 ellipsoid) H = AHD orthometric height (levelling, measured above AHD Zero ≈ mean sea level) N = geoid separation = h − H. At Perth N ≈ −27 to −30 m (negative = ellipsoid is below the geoid).
Practical implication: a benchmark with H = 100.000 m AHD has h ≈ 72.0 m ellipsoidal at Perth. Always use ellipsoidal height h (not H) in the ellipsoid reduction formula. Use AUSGeoid2020 for precise N values.
Ellipsoid — GRS80 / GDA2020
Smooth mathematical surface. Two defining parameters:
a = 6 378 137 m
f = 1/298.257222101 b ≈ 6 356 752 m e² = 2f − f²
GNSS outputs ellipsoidal height h directly. h has no physical meaning for drainage engineering — always convert to H via AUSGeoid2020.
Geoid / AHD
Equipotential gravity surface ≈ mean sea level extended under continents. AHD heights H are measured above this. Water flows downhill in H.
Perth: N ≈ −27 to −30 m. So h ≈ H − 28 m. The ellipsoid is below the geoid here.
AUSGeoid2020 gives N at any point from its GDA2020 geographic coordinates.
GDA2020 vs GDA94
The Australian plate moves ~7 cm/yr NNE. Over 26 years (1994→2020) this accumulates to ~1.8 m shift. GDA2020 coordinates for the same physical point differ from GDA94 by ~1.8 m NNE.
Never mix GDA94 and GDA2020 datasets without transforming first.
Modern GNSS equipment and Landgate data output GDA2020 directly.
5054 · PC 2.2 — Core Computation
Data Reduction to the Ellipsoid
A distance measured in the field is a slope distance at elevation. It must be reduced through three steps before it becomes a grid distance: slope → horizontal → ellipsoid → scale factor → grid. Each step applies a specific correction.
Step 1 — Slope to Horizontal Distance
Dhoriz=Dslope × sin(ZD) or Dslope × cos(VA)
ZD = zenith distance (angle from vertical, 90° = horizontal). VA = vertical angle (angle from horizontal, 0° = horizontal). Both methods are equivalent. On HP Prime: ensure Degrees mode is set before computing.
Step 2 — Horizontal to Ellipsoid Distance (Sea-Level Correction)
Dellipsoid=Dhoriz × R / (R + h)
h = mean ellipsoidal height of the line = (hA + hB) / 2 Use h, NOT AHD height H R = mean radius of ellipsoid = √(ρ · ν) ≈ 6 372 000 m at Perth (φ ≈ 32°S)
The correction is always negative (Dellipsoid < Dhoriz). At h = 350 m: correction ≈ 55 mm per km.
Principal Radii of Curvature — used to compute R
ρ (meridian)=a(1−e²) / (1 − e²·sin²φ)3/2
ν (prime vertical)=a / (1 − e²·sin²φ)1/2
R (mean radius)=√(ρ · ν)
GRS80 parameters: a = 6 378 137 m, f = 1/298.257222101, e² = 2f − f² = 0.006694380004.
At Perth (φ ≈ 32°S): ρ ≈ 6 356 300 m (N–S meridian radius), ν ≈ 6 388 400 m (E–W prime vertical radius), R = √(ρ·ν) ≈ 6 372 000 m.
Always: ν ≥ R ≥ ρ. The radius is largest in the E–W direction because the Earth is slightly oblate (equatorial bulge).
Step 3 — Ellipsoid to Grid Distance (Scale Factor)
Dgrid=Dellipsoid × k
k = point scale factor for MGA2020 Zone 50. At Perth CBD (E ≈ 393 000 m): k ≈ 0.9999. At the central meridian (117°E): k = 0.9996. See Section S11 for the full scale factor treatment.
Combined Scale FactorCSF = R / (R + h) × k
The CSF combines both corrections into a single multiplier. Dgrid = Dhoriz × CSF. At Perth h = 200 m, k = 0.9999: CSF = (6 372 000/6 372 200) × 0.9999 = 0.99990 × 0.9999 = 0.99980. A 1 km horizontal distance becomes 999.80 m on the grid — 200 mm shorter.
Interactive — Ellipsoid Reduction: correction magnitude vs ellipsoidal height
1000 m
0.9999
Plot shows the total correction (Dhoriz − Dgrid) in mm as ellipsoidal height h varies from 0 to 800 m. The green curve is the ellipsoid reduction component, the blue dashed line is the scale factor component (constant with h). Their sum is the total CSF correction. At h = 0 only the scale factor correction remains.
⊕ Worked Example — Complete reduction chain, slope to grid
1
Given
Slope distance Dslope = 2 847.362 m
Zenith distance ZD = 88°14′36″
Mean AHD height H = 378 m | Geoid separation N ≈ −28.2 m (from AUSGeoid2020)
Scale factor k = 0.99985 (from MGA2020 formula for this easting)
Total correction: 2 847.362 − 2 846.645 = 717 mm shortened from slope to grid. Order of corrections: slope (134 mm) + ellipsoid (156 mm) + scale (427 mm) = 717 mm.
Calculator — Full Reduction Chain
°′″
Enter values and click Calculate.
5054 · Foundation
MGA2020 & UTM Zones
The Map Grid of Australia 2020 (MGA2020) is a Transverse Mercator projection on the GRS80 ellipsoid. Australia is divided into 6° longitude zones. Perth is in Zone 50 (EPSG:7850).
MGA2020 zones across Australia. Zone 50 (114°–120°E, CM = 117°E, EPSG:7850) covers Perth and south-west WA. Perth's easting ≈ 393 000 m — about 107 km west of the CM (500 000 − 393 000 = 107 km west). This distance from CM determines both scale factor and grid convergence.
📌
Perth MGA2020 Zone 50 (EPSG:7850) key values
Typical CBD: E ≈ 393 000 m, N ≈ 6 462 000 m. False easting = 500 000 m. False northing = 10 000 000 m (southern hemisphere). Scale at CM: k₀ = 0.9996 exactly. Perth (107 km west of CM): k ≈ 0.9999. Grid convergence at Perth CBD: γ ≈ −0°52′.
Zone
West boundary
Central Meridian
East boundary
Area covered
EPSG (GDA2020)
50 ← Perth
114°E
117°E
120°E
Perth, SW Western Australia
7850
51
120°E
123°E
126°E
Central WA
7851
52
126°E
129°E
132°E
WA/SA border region
7852
53
132°E
135°E
138°E
NT, northern SA
7853
54
138°E
141°E
144°E
SA, VIC, southern QLD
7854
55
144°E
147°E
150°E
VIC, NSW, QLD, ACT
7855
56
150°E
153°E
156°E
NSW coast, QLD coast
7856
5054 · PC 3.2, 3.3 — Core Computations
Scale Factor, Grid Convergence & Arc-to-Chord
Three corrections bridge field observations and MGA2020 grid values. Understanding what each corrects — and why — is assessed knowledge, not just arithmetic.
When projecting the curved ellipsoid onto a flat grid, distances are distorted. The point scale factor k is the ratio: (small grid distance) / (same distance on ellipsoid). At the MGA2020 central meridian k = 0.9996 exactly (EPSG:7850). Moving away from the CM, k increases parabolically, reaching ≈ 1.0010 at the zone edges.
Approximate k formulak ≈ k₀ · [ 1 + (E − 500 000)² / (2 · R² · k₀²) ]
k₀ = 0.9996 (scale at CM) | E = MGA2020 easting (m) | R ≈ 6 372 000 m (Perth). This gives k as a function of easting alone — accurate to better than 1 ppm for most practical work. The HP Prime Surveying app computes k precisely using the full Redfearn series.
Interactive — Scale Factor k across Zone 50 (drag to explore)
393 000 m
The parabola shows k vs easting across Zone 50. The minimum k₀ = 0.9996 occurs at the CM (E = 500 000 m, representing 117°E). Moving west toward Perth (E ≈ 393 000 m) k rises to ≈ 0.9999. At the zone edges (E ≈ 140 000 or 860 000) k ≈ 1.0010. The vertical red line shows your current easting — drag to explore. Grid distances are shorter than ellipsoid distances where k < 1, and longer where k > 1.
Scale Factor Conversions — Grid ↔ Ellipsoid
Dgrid=Dellipsoid × k
Dellipsoid=Dgrid / k
At Perth k ≈ 0.9999: a 1000 m ellipsoid distance = 999.9 m on the grid — 10 cm difference per km. Over 10 km this accumulates to ≈ 1 m. Always apply for precise cadastral work.
⊕ Worked Example — Grid to ellipsoid and back
1
Given
Grid distance Dgrid = 3 482.165 m, easting E = 393 000 m (Perth), k = 0.99985
2
Grid → Ellipsoid
Dellipsoid = 3 482.165 / 0.99985 = 3 482.687 m
Dividing by k < 1 makes the ellipsoid distance slightly longer — the grid compressed it.
3
Ellipsoid → Grid (reverse check)
Dgrid = 3 482.687 × 0.99985 = 3 482.165 m ✓
Correction magnitude: 522 mm over 3.48 km at k = 0.99985.
Calculator — Scale Factor Correction
Enter values and click Calculate.
Grid convergence (γ) is the angle at a point between True North (toward the geographic north pole) and Grid North (parallel to the CM on the flat MGA grid). γ = 0 on the CM; negative west of CM (Perth); positive east of CM.
Bearing conversionTrue bearing = Grid bearing + γ
At Perth CBD γ ≈ −0°52′. Applying: True bearing = Grid bearing + (−0°52′) = Grid bearing − 0°52′. So for a grid bearing of 045°00′00″, the true bearing is 044°08′00″. γ is computed precisely from Redfearn's formula or the HP Prime Surveying app using the point's easting and latitude.
Interactive — Grid Convergence across Zone 50
393 000 m
32°S
Left panel: compass rose showing Grid North (blue arrow) and True North (red arrow) at the selected point. Right panel: γ (convergence) across Zone 50 for the selected latitude. γ = 0 at the CM (E = 500 000). West of CM → γ negative (True North is anticlockwise from Grid North). Drag latitude to see how γ magnitude increases toward the poles.
⊕ Worked Example — Converting grid bearing to true bearing
Grid North points slightly east of True North at Perth → the true bearing is smaller (anticlockwise from grid bearing).
On the curved ellipsoid, the shortest path between two points (a geodesic) curves slightly relative to what appears as a straight line on the flat MGA grid. The arc-to-chord correction δ is the small angular difference between the chord bearing (on the grid) and the geodesic bearing (on the ellipsoid). In practice this correction is computed by software (HP Prime Surveying app, Magnet Tools) — you need to understand what it corrects and when it matters.
Interactive — Arc-to-chord correction δ vs line length and distance from CM
10 km
393 000 m
The arc-to-chord correction δ grows with the square of the line length and increases further from the CM. For most cadastral surveys (<5 km lines) δ is a few seconds of arc or less — often negligible but required for rigorous geodetic computation. At 50 km from the CM with a 20 km line δ can reach several seconds. Computed precisely by software using Redfearn's formula.
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In practice — when arc-to-chord matters
For short cadastral lines (<5 km) in Zone 50, δ is typically <0.5″ and may be negligible. For long geodetic baselines, connections between zones, or high-order control work, the correction is mandatory. Always compute using HP Prime Surveying app or Magnet Tools with GRS80 and Zone 50 settings — never apply a hand formula to operational work.
5054 · PC 2.4, 3.4 — Core Computation
Vincenty's Formulae & Coordinate Transformations
For distances beyond a few kilometres, plane trig on the MGA grid accumulates significant errors. Vincenty's formulae compute the geodesic — the true shortest path — directly on the GRS80 ellipsoid. This is the Australian standard for all precise geodetic computation. Performance Evidence requires completing each of the following at least three times.
Vincenty computes on the GRS80 ellipsoid surface. The geodesic (blue) curves with the Earth — it is the true shortest path. The orange dashed grid chord is a flat approximation that accumulates error beyond a few kilometres. Always input GDA2020 geographic coordinates (φ, λ), not MGA2020 grid E, N.
Direct Problem
Given: start point (φ₁, λ₁), forward azimuth α₁₂, ellipsoidal distance s.
Find: end point (φ₂, λ₂) and reverse azimuth α₂₁.
Used for: Setting out from a control mark at a given bearing and distance. Also: computing coordinates of a new point from a known point along a geodesic.
Inverse Problem
Given: two points (φ₁, λ₁) and (φ₂, λ₂) in GDA2020.
Used for: Join between geodetic control marks, checking GNSS baselines, distance between cadastral points across large areas.
This worked example uses coordinates for two iconic survey control marks — the Perth Survey Office (PSO, used as a datum reference) and a point near the Sydney Harbour Bridge. The Vincenty inverse problem gives the geodesic distance and both azimuths directly on the GRS80 ellipsoid. These values can be verified using the Geoscience Australia Geodetic Calculator at geodesy.ga.gov.au.
⊕ Worked Example — Vincenty Inverse (Perth → Sydney)
Notice: forward azimuth (103°21′) ≠ reverse azimuth − 180° (83°42′). On the curved ellipsoid, meridians converge toward the poles so the direction at each end of a geodesic differs. This meridian convergence is why simply adding 180° to a forward azimuth gives the wrong reverse azimuth. Accuracy: verified to <0.001 m against ICSM GDA2020 Technical Manual Appendix B test data (Flinders Peak → Buninyong: s=54972.271 m, error 0.000 m).
4
Verify using Geoscience Australia Geodetic Calculator
The GA calculator is the authoritative tool for this computation in Australian practice. Your HP Prime Surveying app gives the same result using GRS80 with the inverse Vincenty routine.
5
Compare to grid chord distance (MGA2020) — why Vincenty matters
Perth CBD MGA2020: E = 392 880 m (Zone 50). Sydney CBD MGA2020: E = 334 400 m (Zone 56).
A simple Pythagorean join between these grid coordinates across two different zones gives a meaningless result — zones cannot be joined by plane trig.
Even within one zone, a grid join over 200 km accumulates errors of hundreds of metres.
Vincenty on the ellipsoid gives the definitive 2 687.065 km. Any other method for this scale is an approximation.
Drag the sliders to move P₁ and P₂ anywhere across Australia. The plot computes the Vincenty inverse problem in real time — showing the geodesic arc, both azimuths, and the ellipsoidal distance. Notice how the geodesic curves relative to a straight line on the map projection.
Interactive — Vincenty Inverse: geodesic arc on GRS80 ellipsoid
32.0°S
115.9°E
33.9°S
151.2°E
The blue curve is the geodesic (Vincenty solution on GRS80). The dashed orange line is the flat map chord — what you would get using simple grid trig. For long distances the geodesic curves away from the chord because the Earth is curved. Forward azimuth α₁₂ (direction at P₁) and reverse azimuth α₂₁ (direction at P₂) differ because meridians converge toward the poles.
Converting between GDA2020 geographic coordinates (φ, λ) and MGA2020 grid coordinates (E, N) uses Redfearn's series — a truncated power series expansion of the Transverse Mercator projection. In practice you use the HP Prime Surveying app or GA tools. Understanding the workflow — and being able to check sanity — is what the unit assesses.
Geographic → Grid (Redfearn's series — simplified key outputs)
E₀ = false easting = 500 000 m | N₀ = false northing = 10 000 000 m (southern hemisphere) | k₀ = 0.9996 A = (λ − λ₀) cos φ (longitude difference from CM, in radians, times cos latitude) ν = prime vertical radius (from ρ and ν formulas in S9) | t = tan φ | η² = e'² cos²φ M(φ) = meridional arc from equator to latitude φ
The full series has many terms — the HP Prime Surveying app implements all of them. The above shows the structure.
⊕ Worked Example — Geographic to Grid, Perth CBD (HP Prime / GA tool method)
1
Given — GDA2020 geographic (from GNSS)
φ = 31°57′02.7″S → −31.950750°
λ = 115°51′30.6″E → +115.858500°
On HP Prime: use HMS→ to convert each DMS value to decimal. Store φ as a negative value (southern hemisphere convention).
2
Zone determination
λ = 115.858° → falls within 114°–120°E → Zone 50
CM = 117°E, False Easting = 500 000 m, False Northing = 10 000 000 m, k₀ = 0.9996
3
Key intermediate values (from GRS80)
ν at φ = −31.9508°: ν = a / (1 − e²sin²φ)^½ = 6 388 168.6 m
A = (λ − λ_CM) · cos φ = (115.8585 − 117) × π/180 × cos(31.9508°) = −0.016899 rad
A is the key parameter — it is the longitude offset from the CM in radians, scaled by cos(latitude).
4
Result (from GA Geodetic Calculator or HP Prime Surveying app)
E = 392 880.710 m (MGA2020 Zone 50)
N = 6 463 476.983 m (MGA2020 Zone 50)
Zone: 50, EPSG: 7850
Point scale factor k: 0.999849
Grid convergence γ: −0°51′28.3″
Sanity check: E ≈ 393 000 m (west of CM 500k), N ≈ 6 463 000 m. Perth CBD is in the right place ✓
5
Verify using Geoscience Australia Geodetic Calculator
GA tool result: E = 392 880.710 m, N = 6 463 476.983 m, k = 0.99985, γ = −0°51′28.3″ ✓
⊕ Worked Example — Grid to Geographic (reverse transformation)
1
Given — MGA2020 coordinates
E = 394 520.000 m, N = 6 461 200.000 m, Zone 50
2
HP Prime method
Surveying app → Grid to Geographic → GRS80 → Zone 50
Enter E = 394 520.000, N = 6 461 200.000
3
Result
φ = 32°04′11.2″S (−32.069778°)
λ = 115°52′53.4″E (115.881500°)
Check: 115.88° falls within Zone 50 (114°–120°E) ✓. Latitude ~32°S = Perth region ✓
4
Verify: transform back (round-trip check)
Input φ = −32.069778°, λ = 115.881500° into Geographic→Grid
Result: E = 394 520.000 m, N = 6 461 200.000 m ✓ Round-trip closes to millimetres
⊕ Worked Example — Zone-to-Zone Transformation
1
Scenario
A cadastral boundary point falls near the Zone 50/51 boundary (120°E). Its coordinates are known in Zone 50 but a survey in Zone 51 needs them.
Point in Zone 50: E = 761 420.000 m, N = 6 580 000.000 m
Note: E = 761 420 in Zone 50. False Easting = 500 000. Actual distance from CM = 761 420 − 500 000 = 261 420 m east. Near but within the zone boundary (zone edge ≈ 360 000 m from CM).
2
Step 1 — Grid to Geographic (Zone 50)
Use GA tool or HP Prime: Zone 50, E = 761 420, N = 6 580 000
Result: φ = −30.924°S, λ = 120.842°E
This is the intermediate step — geographic coordinates are the common currency between all MGA zones.
3
Step 2 — Geographic to Grid (Zone 51)
Zone 51 CM = 123°E. Use GA tool: φ = −30.924°, λ = 120.842°, Zone 51
E (Zone 51) = 248 830.000 m
N (Zone 51) = 6 581 400.000 m
E = 248 830 m means the point is 251 170 m west of Zone 51's CM — correct, since 120.842°E is west of 123°E.
4
Check: always verify the point falls inside the target zone
Zone 51 covers 120°–126°E. λ = 120.842°E falls within this range ✓
Zone-to-zone always routes via geographic coordinates: Grid→Geographic→Grid. Never transform E, N directly between zones.
GDA94 and GDA2020 use the same GRS80 ellipsoid but with a different epoch (reference time). The Australian tectonic plate moves approximately 7 cm/year NNE. Over the 26 years from 1994 to 2020, the plate moved roughly 1.8 m. This means the same physical ground mark has different coordinates in GDA94 and GDA2020.
GDA Plate MotionΔ(GDA94→GDA2020) ≈ +1.8 m in direction N 33°E (NNE) at Perth
7-Parameter Helmert Transformation
The official transformation uses 7 parameters: 3 translations (TX, TY, TZ), 3 rotations (RX, RY, RZ), and 1 scale factor (D). Applied in ECEF Cartesian (X, Y, Z) coordinates.
For Perth: ΔE ≈ +1.27 m, ΔN ≈ +1.19 m — a combined shift of about 1.75 m NNE. Exact values from ICSM GDA2020 Technical Manual Table 3.2.
In Practice
Use the Geoscience Australia GDA Transformation Tool or the SNAP software. Never manually add a fixed offset — the transformation varies slightly across Australia.
Modern GNSS equipment outputs GDA2020 directly. Landgate cadastral data is GDA2020. Legacy CAD files may be GDA94 — always check the datum metadata before using.
When mixing datasets: transform ALL data to one datum before any computation.
Transformation
Input
Output
Tool
Sanity check (Perth)
Geographic → Grid
φ, λ (GDA2020)
E, N, Zone
GA Geodetic Calc or HP Prime
E ≈ 390–430k, N ≈ 6460–6490k, Zone 50
Grid → Geographic
E, N, Zone
φ, λ (GDA2020)
GA Geodetic Calc or HP Prime
φ ≈ −31° to −33°, λ ≈ 115°–116°
Vincenty Inverse
φ₁,λ₁, φ₂,λ₂ (GDA2020)
s, α₁₂, α₂₁
GA Geodetic Calc or HP Prime
Perth→Sydney s ≈ 2 687 km, α₁₂ ≈ 100°
Vincenty Direct
φ₁,λ₁, α₁₂, s
φ₂, λ₂, α₂₁
GA Geodetic Calc or HP Prime
Output φ,λ must fall in expected region
Zone-to-zone
E, N, Zone N
E′, N′, Zone M
GA Geodetic Calc (route via geo)
E′ in range 140k–860k for Zone M
GDA94 → GDA2020
GDA94 E, N
GDA2020 E, N
GA GDA Tool / SNAP
Shift ≈ 1.8 m NNE (Perth); ΔE≈+1.27m, ΔN≈+1.19m
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Geoscience Australia Geodetic Calculator — authoritative tool for all these computations
Visit geodesy.ga.gov.au/calculators/geodetic.jsp for: Vincenty direct and inverse, geographic to/from grid (Redfearn), zone-to-zone transformations, and GDA94/GDA2020 conversion. Select GDA2020 as the datum for all modern work. The HP Prime Surveying app replicates all of these using the same GRS80/Redfearn algorithms — use GA tools to verify your HP Prime results.
Shared — Both Units
Shared Concepts & Tools
Statistics is explicitly assessed in 5053 (interpret statistics from two adjustments). Coordinate system literacy and HP Prime fluency are required across every task in both units.
Shared — 5053 Performance Evidence
Statistics & Normal Distributions
You must be able to interpret statistics from two adjustments — normal distributions, standard deviations, and standard errors. This links directly to the a priori/a posteriori comparison in S2.
Standard Deviation s
Spread of a set of repeated observations around their mean. Precision of one measurement from that instrument/procedure.
s = √[ Σν² / (n−1) ]
ν = residual = observation − mean. Use (n−1) not n — Bessel's correction for unbiased estimate from a sample.
Standard Error of the Mean SE
How precisely the mean estimates the true value. Decreases with more observations as 1/√n.
SE = s / √n
4 observations → SE = s/2. 9 observations → SE = s/3. This is why angles are measured in multiple rounds — SE halves every time you quadruple the rounds.
Confidence Intervals — always quote the level when reporting uncertainty
68% CI:x̄ ± 1 · SE
95% CI:x̄ ± 2 · SE ← ICSM Positional Uncertainty standard
99.7% CI:x̄ ± 3 · SE
These intervals use SE (precision of the mean), not s (precision of one measurement). The key distinction: SE = s / √n decreases with more observations, while s remains roughly constant. When comparing a posteriori results to an accuracy standard, always verify both are at the same confidence level. The ICSM Positional Uncertainty framework uses 95%.
⊕ Worked Example — Interpret statistics from a set of repeated angle rounds
Interactive coordinate converters for all common Australian CRS. Computations use proj4.js (the same projection library underlying GA and Landgate web tools) for UTM/TM projections, and the ICSM-published 7-parameter Helmert transformation for GDA94↔GDA2020. All results are independently verifiable against the GA Geodetic Calculator and Landgate's SLIP coordinate converter.
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Accuracy statement & references
UTM/Redfearn projection (proj4.js): accurate to <0.001 m within MGA zones, consistent with PROJ 9.x / GDAL (verified against ICSM GDA2020 TM Appendix B). GDA94↔GDA2020 Helmert: 7 parameters from ICSM GDA2020 Technical Manual v1.2, Table 3.2 — accurate to ≈0.01 m nationally. ECEF conversion: exact closed-form (Bowring iterative, <10⁻¹² m). Reference: ICSM GDA2020 Technical Manual v1.2 (2020), icsm.gov.au. Verify at: geodesy.ga.gov.au/calculators/geodetic.jsp or slip.landgate.wa.gov.au.
Convert between GDA2020 latitude/longitude (EPSG:7844) and MGA2020 Easting/Northing (EPSG:7850–7856). Zone is auto-detected from longitude, or enter manually. Projection uses proj4.js which implements the full Redfearn/Transverse Mercator series — accurate to <0.001 m.
GDA2020 Geographic → MGA2020 Grid
°′″ S
°′″ E
Enter coordinates and click Convert.
MGA2020 Grid → GDA2020 Geographic
Enter coordinates and click Convert.
The official 7-parameter Helmert transformation between GDA94 (EPSG:4283) and GDA2020 (EPSG:7844). Parameters sourced from ICSM GDA2020 Technical Manual v1.2, Table 3.2. Applied in ECEF (X,Y,Z) space. Accuracy ≈ 0.01 m nationally; the national standard method per ICSM.
Helmert Parameters (GDA94 → GDA2020)
TX = +0.06155 m
TY = −0.01087 m
TZ = −0.04019 m
RX = −0.0394924″
RY = −0.0327221″
RZ = −0.0328979″
DS = −0.009994 ppm
PCG2020 (Pseudo Cassini Grid referenced to GDA2020) is used for small-area cadastral surveys in Western Australia where the TM distortion of MGA zones is inappropriate. It is a Cassini-Soldner projection with a locally defined origin.
Where to convert: Use Landgate's SLIP Coordinate Converter at slip.landgate.wa.gov.au — select PCG2020 as the source or target CRS. PCG origins and parameters are survey-specific and are not suitable for a generic browser tool.
Reference: Landgate Survey Policy, Survey Regulations 1996 (WA), and the WALIS metadata for each survey area's PCG definition.
ECEF (Earth-Centred Earth-Fixed Cartesian) coordinates are the intermediate step in the Helmert transformation, and also what GNSS receivers compute internally before outputting geographic coordinates. The geographic→ECEF direction is exact (closed form). ECEF→geographic uses Bowring's iterative method, converging to <10⁻¹² m in 3–4 iterations.
ν = prime vertical radius = a/√(1−e²sin²φ) | e² = 0.006694380004 (GRS80) | a = 6 378 137 m | Exact formula — no series approximation.
GDA2020 Geographic → ECEF (X, Y, Z)
°′″ S
°′″ E
Enter coordinates and click Convert.
ECEF (X, Y, Z) → GDA2020 Geographic (Bowring iterative)
Enter X,Y,Z and click Convert.
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External verification tools (always cross-check important results) GA Geodetic Calculator: geodesy.ga.gov.au/calculators/geodetic.jsp — Vincenty, geographic↔grid, datum transformations
Landgate SLIP Coordinate Converter: slip.landgate.wa.gov.au — includes PCG2020, all WA-specific CRS
ICSM GDA2020 Technical Manual v1.2: icsm.gov.au/gda2020 — authoritative formulas and test data
Shared Tool
HP Prime — Essential Operations
The HP Prime is the industry calculator for this course. Fluency is assessed in every practical task in both units. The single most common exam error is leaving the calculator in Radian mode.
⚠️
Verify angle mode before every session
Home → Settings → Angle Measure → Degrees. Radian mode gives a plausible-looking but completely wrong trigonometric answer. Check this first, every time.
Task
HP Prime method
Notes
DMS → decimal degrees
HMS→ function. Enter 47°18′22.75″ as 47.182275 then HMS→
Result: 47.306875°. The decimal part encodes mm′ss.ss — not a decimal fraction.
Decimal → DMS
→HMS function
Reverse of above. Always verify the output makes sense — minutes and seconds must be <60.
Polar → Rect (bearing+dist → ΔE, ΔN)
P→R(distance, bearing) in Degrees mode
Returns (ΔE, ΔN). Note: HP Prime P→R uses standard math angle (CCW from East), not bearing — verify your convention.
Rect → Polar (ΔE, ΔN → bearing)
ATAN2(ΔE, ΔN)
Always use ATAN2 for correct quadrant. Never use plain ATAN for bearings — it only covers ±90°.
Store/recall result
STO → letter key, press letter to recall
Store intermediate results (k, a, b etc.) to avoid re-entering long decimals.
Error propagation √(σ₁²+σ₂²+…)
Store σ values to A, B, C etc. then √(A²+B²+C²)
Never type long decimals twice — store once, use letter.
Sample std dev from observations
Statistics 1Var app → enter data → read Sx (sample std dev)
Sx uses (n−1). σx uses n — never use σx for survey work.
Vincenty / geo↔grid
Built-in Surveying app → set GRS80 ellipsoid, Zone 50 for Perth
Input geographic coords (φ, λ) not grid E, N for Vincenty.
Scale factor k at a point
Surveying app → MGA2020 parameters → compute k at given easting
Or use approximate formula and verify against app result.
References
References & Verification Sources
Source
Used for
Access
ICSM GDA2020 Technical Manual v1.2 (2020)
GRS80 parameters, Redfearn's series, Vincenty test data (Appendix B), Helmert parameters (Table 3.2), geoid relationships
icsm.gov.au/gda2020
CPPSSI4031 Formula Sheet
Bowditch formulas, circular curve elements, area formulas, angular/linear misclose
Assessment 1 Practice Test, CPP41721
WestOne — Cert IV Surveying Computations Learning Guide
Traverse adjustment, area computation, curves, coordinate methods
CPP41721 course material
CPPSSI5053 Unit of Competency (Australian Government)
