Surveying Calculator — Plane Coordinates
Solve local plane survey coordinates from a distance and azimuth, or find horizontal distance and azimuth between two easting/northing points.
Solve forward or inverse coordinate geometry in a local survey plane. Forward mode finds an endpoint from a start coordinate, horizontal distance and azimuth. Inverse mode finds the distance and direction between two points expressed in the same easting/northing reference.
How to use this tool
- Choose forward or inverse calculation.
- Enter start easting and northing in one common length unit.
- For forward mode enter horizontal distance and decimal-degree azimuth; for inverse mode enter the endpoint coordinates.
- Check the coordinate changes and forward/back directions before using the result.
Formula
ΔE = d sin A; ΔN = d cos A; d = √(ΔE² + ΔN²); A = atan2(ΔE, ΔN)
Azimuth A is measured clockwise from north: 0° north, 90° east, 180° south and 270° west. Forward coordinates add the two changes to the start. Inverse azimuth is normalized to the interval from 0° inclusive to 360° exclusive.
Example
Start at E = 1,000 m, N = 1,000 m. A horizontal line of 100 m at azimuth 90° goes due east, so ΔE = 100 m and ΔN = 0. The endpoint is E = 1,100 m, N = 1,000 m, with back azimuth 270°.
Frequently asked questions
Can I enter GPS latitude and longitude?
No. These are planar distances and coordinates, not angular geographic coordinates. Ellipsoidal geodesics, map projections, convergence and grid-to-ground scale corrections require a different calculation.
Is distance measured along the slope?
No. Enter a distance already reduced to the horizontal plane and compatible with the coordinate reference. Instrument, prism, atmospheric and elevation reductions are not performed here.
What if the points coincide?
The distance is zero and the line’s azimuth is undefined. The tool displays that explicitly rather than assigning a meaningful north direction to a zero-length line.
Which feet and numeric limits apply?
Feet are international feet, exactly 0.3048 m. Coordinates must stay within ±1 billion selected units and forward distance at most one billion. Those are numeric limits, not a guarantee that a plane approximation is suitable at that scale.
Sources
Last updated: 2026-10-30