COGO Inverse (Two Points to Bearing and Distance)
From two known points, the straight-line distance and the azimuth of the line between them.
Example
You enter
- Start northing N1 (ft) 5000
- Start easting E1 (ft) 5000
- End northing N2 (ft) 5141.42
- End easting E2 (ft) 5141.42
You get
- Distance 200 ft
- Azimuth (clockwise from north) 45 deg
Checked against published worked examples from: Coordinate geometry (Ghilani & Wolf, FM 5-233).
Details, formula, and sources
Scopedistance = sqrt(dN^2 + dE^2), azimuth = atan2(dE, dN) clockwise from north; dN = N2-N1, dE = E2-E1. From N5000/E5000 to N5141.42/E5141.42 the line runs 200.00 ft at azimuth 45.00 deg. Read it as a quadrant bearing by converting the azimuth. Plane geometry - no curvature or grid scale factor; the project control governs.
Formula or tabledN = N2 - N1; dE = E2 - E1; distance = sqrt(dN^2 + dE^2); azimuth = atan2(dE, dN) x 180/pi, normalized to 0-360 deg (clockwise from north).
Source and editionFirst-principles coordinate geometry (the COGO inverse) as compiled in the standard route-surveying references (Ghilani & Wolf, Elementary Surveying; FM 5-233), by name.
Free accessThe point-to-point inverse (distance and azimuth from two coordinates) is a public surveying result.
What governsEstimate. AHJ and licensed professional govern.
API field namesstart_n, start_e, end_n, end_e, distance_ft, azimuth_deg
- Azimuth basis atan2(dE, dN) clockwise from north, 0-360 degsurveying convention
- Plane geometry flat-earth distance and azimuth; no curvature or grid scale factorplane-survey assumption
- Distinct points the two points must differ; a zero-length line has no bearingscope of this tile