Logo of Abdullah Saud bin Abdulaziz Al-Abdulmughni Land Survey OfficeAbdullah Saud bin Abdulaziz Al-AbdulmughniLand Survey Office · Established 1984
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Technical Reference

Land Surveying Reference

The constants, UTM/EPSG zones and formulas implemented by this site — the exact values used in its calculations, verified by an automated geodetic test suite on every release.

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WGS84 Datum Constants

  • Semi-major axis: a = 6378137 m (defining value).
  • Flattening: f = 1 / 298.257223563.
  • Semi-minor axis: b = a(1 − f) ≈ 6356752.3142 m.
  • First eccentricity squared: e² ≈ 0.00669437999014.
  • Geographic coordinates on this datum: EPSG:4326.

UTM Zones for Saudi Arabia & the Gulf

Universal Transverse Mercator: 6° zones, central-meridian false easting 500000 m, central-meridian scale k₀ = 0.9996.

  • UTM 36N — 30°E to 36°E · CM 33° · EPSG:32636 (northwest KSA).
  • UTM 37N — 36°E to 42°E · CM 39° · EPSG:32637 (Madinah, Tabuk, western Makkah).
  • UTM 38N — 42°E to 48°E · CM 45° · EPSG:32638 (Riyadh, Qassim, Hail, Kuwait).
  • UTM 39N — 48°E to 54°E · CM 51° · EPSG:32639 (Eastern Province, Bahrain, Qatar, western UAE).
  • UTM 40N — 54°E to 60°E · CM 57° · EPSG:32640 (eastern UAE, Oman).

Core Plane-Surveying Formulas

  • Area (shoelace): A = ½ |Σ (xᵢ·yᵢ₊₁ − xᵢ₊₁·yᵢ)|.
  • Azimuth from deltas: az = atan2(ΔE, ΔN), clockwise from north.
  • Forward point: E₂ = E₁ + d·sin(az), N₂ = N₁ + d·cos(az).
  • Bowditch (compass-rule) adjustment: per-leg correction = − misclosure × (leg length ÷ total length).

Circular Curve Elements

  • Tangent: T = R·tan(Δ/2) · Arc length: L = R·Δrad.
  • Long chord: LC = 2R·sin(Δ/2) · External: E = R(sec(Δ/2) − 1) · Middle ordinate: M = R(1 − cos(Δ/2)).

Geodesic Distances (Vincenty)

Distance and azimuth between two points on the WGS84 ellipsoid are solved with Vincenty's iterative direct/inverse formulas, millimetre-accurate at ordinary ranges. A useful verification constant: one degree of longitude at the equator equals a·π/180 ≈ 111319.4908 m — one of the invariants this site's calculations are tested against automatically.

Unit Conversions

  • International foot: 1 ft = 0.3048 m (exact).
  • US survey foot: 1200/3937 ≈ 0.304800610 m.
  • Hectare: 1 ha = 10000 m² · 1 km² = 100 ha.
  • Acre: 4046.8564224 m² (exact).
  • Dunam: varies regionally (~900–1000 m²); confirm the definition adopted by your authority before converting.

Accuracy Notes

  • UTM scale is 0.9996 on the central meridian and grows away from it, so the grid area differs slightly from the geodesic ground area; the site reports both transparently.
  • When a polygon spans multiple UTM zones, the grid is computed on one stated zone and the report flags it.

This page is an aid; statutory work requires a certified field survey. Try these formulas live with the site surveying tools.