Free tool
Grid to ground distance calculator
Turn an MGA grid distance into a ground distance, or the other way. Get the scale factors and grid convergence for the spot.
Eastings and northings are MGA2020 or MGA94. The height must be the height above the ellipsoid, not AHD. Use the height of the line, not of the instrument. Choose the zone your coordinates are in.
Method and limits
- Point scale factor k comes from the Transverse Mercator series for the Map Grid of Australia: GRS80, central scale factor 0.9996, false easting 500,000 m, false northing 10,000,000 m. The line scale factor uses Simpson's rule on the two ends and the middle: (k1 + 4 km + k2) / 6. With one point only, k at that point is used for the whole line.
- Elevation factor = R / (R + h), where R is the mean radius of curvature at the line (the geometric mean of the meridian and prime vertical radii) and h is the ellipsoidal height. Combined scale factor = line scale factor x elevation factor. Ground distance = grid distance / combined factor.
- Checked against PROJ: point scale factor within 1 part in 10^10, and grid convergence within 0.000000001 degrees, on 3,000 random points in zones 49 to 56. Line scale factors were checked against geodesic distances on the GRS80 ellipsoid for 2,000 random lines from 100 m to 20 km: the worst difference was 1.3 parts in 10^9 (0.03 mm on a 20 km line).
- "Ground" means the horizontal distance at the height you enter, reduced along the ellipsoid normal. It has no slope, atmospheric or geoid corrections. It does not replace the scale factor stated in a project's own control specification.
- This tool is a convenience, not a survey deliverable. Check results against your own work, and use certified methods for anything you sign off. Provided as is, in line with the terms. Nothing you enter is sent anywhere.