Survey Formula Sheet Builder

Height of collimation

HI = RL_known + BS; RL_new = HI − FS; ΔRL = BS − FS

HI

height of the line of sight (collimation) (m)

BS / FS

backsight / foresight staff readings (m)

RL

reduced level (m)

Assumes: Level line of sight (collimation error removed or balanced); upright staff. Sign: A positive BS − FS is a rise from the known point to the new point. Example: RL 100, BS 1.25, FS 0.88 → HI 101.25, RL 100.37, ΔRL +0.37 · open the tool

Arithmetic check

ΣBS − ΣFS = RL_last − RL_first

ΣBS, ΣFS

sums of backsights and foresights (not intermediate sights) (m)

Assumes: Checks the arithmetic only — not the field readings. Sign: Both sides carry the same sign. Example: Two-setup booking BS 1.5, 1.4; FS 0.8, 2.1 → ΣBS − ΣFS = 0 = last − first RL · open the tool

Join (inverse)

ΔE = E₂ − E₁; ΔN = N₂ − N₁; d = √(ΔE² + ΔN²); bearing = atan2(ΔE, ΔN)

E, N

easting, northing in one projected grid (m)

d

grid distance (m)

bearing

grid bearing clockwise from grid north, 0–360° (°)

Assumes: Plane grid coordinates in one CRS; not a geodesic or ground distance. Sign: atan2 takes ΔE first; a zero-length line has no bearing. Example: ΔE = 3 m, ΔN = 4 m → d = 5 m, bearing 36.8699° · open the tool

Radiation (polar to coordinates)

E = E₀ + d·sin(A); N = N₀ + d·cos(A)

A

grid bearing (°)

d

horizontal grid distance (m)

Assumes: Horizontal grid distance; bearing from grid north. Sign: Bearings increase clockwise. Example: From (1000, 2000), 60°, 100 m → E 1086.6025, N 2050 · open the tool

Interior angle closure

Σ_expected = (n − 2) × 180°; misclose = Σ_measured − Σ_expected; c = −misclose ÷ n

n

number of interior angles

c

equal correction per angle (″)

Assumes: Closed polygon, interior angles, equal weights. Sign: The correction has the opposite sign to the misclose. Example: n = 5, Σ = 540.05° → misclose +180″, -36″ each · open the tool

Area by coordinates

A = ½ |Σ (Eᵢ·Nᵢ₊₁ − Eᵢ₊₁·Nᵢ)|

Eᵢ, Nᵢ

corner coordinates in order around the boundary (m)

A

plane area (m²)

Assumes: Simple (non-crossing) polygon on a plane grid. Sign: Signed sum is positive anticlockwise; the area is its magnitude. Example: Rectangle 40 m × 25 m → A = 1000 m² (0.1 ha) · open the tool

Vertical difference

V = d·sin(v); H = d·cos(v); v = 90° − z

d

slope distance (m)

v / z

vertical angle from horizontal / zenith angle (°)

Assumes: No curvature or refraction correction (short sights). Sign: A depression (negative v) gives a negative V. Example: d = 50 m, v = 6° → V = 5.2264 m, H = 49.7261 m · open the tool

Ellipsoidal to orthometric height

H = h − N

h

ellipsoidal height (from GNSS) (m)

N

geoid separation from a named geoid model (m)

H

orthometric (sea-level style) height (m)

Assumes: N comes from a named geoid model for the same datum as h. Sign: N is negative where the geoid lies below the ellipsoid. Example: h = 45.200 m, N = −30.500 m → H = 75.7 m · open the tool

Vertical photo scale

scale = f ÷ H; 1 : n with n = H ÷ f (same units)

f

calibrated focal length (mm)

H

flying height above the ground (m)

Assumes: Vertical photo over flat ground; no tilt or relief displacement. Sign: Higher ground is closer to the camera, so its scale is larger. Example: f = 152 mm, H = 1520 m → 1 : 10000 · open the tool

Map scale

ground distance = map distance × n (scale 1 : n, same units)

n

scale denominator

map distance

distance measured on the plan (mm)

Assumes: A true-to-scale printed plan; a screen or photocopy may not be. Sign: Always positive. Example: 40 mm at 1 : 2500 → 100 m on the ground · open the tool