Inverse between two coordinates
The bearing, azimuth, and horizontal distance between two plane-survey coordinates (northing, easting).
Experimental: not yet fully verified. How results are checked
The bearing is N 45°00'00" E and the distance is 141.421 ft.
- Distance
- Azimuth
Provenance
- Computed by
- survey.cogo.inverse 1.0.0, core 0.1.0
- Model
- Plane coordinate geometry: azimuth = atan2(ΔE, ΔN), distance = √(ΔN² + ΔE²)
- Accuracy
- Exact for the plane (grid or assumed) coordinates given
- Notes
- 1 shown with the answer
- Cites
- Ghilani, C. D., and Wolf, P. R., Pearson, Elementary Surveying: An Introduction to Geomatics
Something look off?
How we got thisFormula, worked example, sources, and proof
Model: Plane coordinate geometry: azimuth = atan2(ΔE, ΔN), distance = √(ΔN² + ΔE²)
Accuracy: Exact for the plane (grid or assumed) coordinates given
Worked example: From (1,000, 1,000) to (1,100, 1,100). Source: add-survey-suite scenario: N 45°00'00" E, 141.421. It is golden test vector v001, and every build checks the tool still gives its answer within its tolerance.
You enter
- From easting
- 1000 ft
- To easting
- 1100 ft
- From northing
- 1000 ft
- To northing
- 1100 ft
You get
- Bearing
- N 45°00'00" E
- Distance
- 141.421 ft
- Azimuth
- 45°
Review: Not yet independently reviewed by a licensed surveyor.
Last verified: 2026-09-23, when a maintainer last confirmed this tool's sources at the issuer. See the sources ledger.
Status: version 1.0.0, core 0.1.0. See this tool in the verification report.
Checked against: 6 golden test vectors (download the test vectors, each with its source and tolerance). See how results are checked and every source.
Sources
- Elementary Surveying: An Introduction to Geomatics, Ghilani, C. D., and Wolf, P. R., Pearson, 16th edition. Chapters 10 (traverse computations), 12 (area), 24 (horizontal curves), 25 (vertical curves), 26 (volumes).
Experimental means this tool has not yet met the stable bar: at least 20 golden vectors, differential tests, and an independent worked example.
Learn the concept: Traverse closure and precision explained