Intersection (bearings and distances)

Where two lines cross, a line meets a circle, or two circles meet: bearing–bearing, bearing–distance, and distance–distance intersections from two known points, every solution returned and labeled.

Experimental: not yet fully verified. How results are checked

Computing your own values needs JavaScript and WebAssembly. The worked example below was computed when this page was built, and the documentation under "How we got this" applies.

The two circles meet at 2 points.

Solutions
Solution	Northing	Easting
left of the baseline	1,187.265 ft	1,234.375 ft
right of the baseline	812.735 ft	1,234.375 ft

Intersection

Provenance

Computed by: survey.cogo.intersection 1.0.0, core 0.1.0
Model: Plane coordinate geometry: two lines by their directions, a line and a circle, or two circles about the known points (Ghilani & Wolf 2021, ch. 11)
Accuracy: Exact for the geometry; a shallow crossing or a near-tangent meeting magnifies small errors in the inputs
Notes: 1 shown with the answer
Cites: Ghilani, C. D., and Wolf, P. R., Pearson, Elementary Surveying: An Introduction to Geomatics

Something look off?

Your values

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First point northing Like 1000.00 ft · plain numbers mean ft First point easting Like 1000.00 ft · plain numbers mean ft Direction from the first pointoptional Bearing or azimuth, like N 45°00'00" E Distance from the first pointoptional Instead of a direction, like 300.00 ft · plain numbers mean ft Second point northing Like 1000.00 ft · plain numbers mean ft Second point easting Like 1400.00 ft · plain numbers mean ft

More options 2

Direction from the second pointoptional Bearing or azimuth, like N 30°00'00" W Distance from the second pointoptional Instead of a direction, like 250.00 ft · plain numbers mean ft

Run many at once from a CSV

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How we got thisFormula, worked example, sources, and proof

Model: Plane coordinate geometry: two lines by their directions, a line and a circle, or two circles about the known points (Ghilani & Wolf 2021, ch. 11)

Accuracy: Exact for the geometry; a shallow crossing or a near-tangent meeting magnifies small errors in the inputs

Worked example: Two distances from a 400 ft baseline. Source: add-survey-suite two-solution scenario. It is golden test vector v001, and every build checks the tool still gives its answer within its tolerance.

You enter

Distance from the first point: 300 ft
Distance from the second point: 250 ft
First point easting: 1000 ft
Second point easting: 1400 ft
First point northing: 1000 ft
Second point northing: 1000 ft

You get

Number of solutions: 2
Intersection: two circles

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.

Changes

2026-09-23, fixed: Survey tools cite Ghilani and Wolf's Elementary Surveying, 16th edition (2021), but their method notes said "Ghilani & Wolf 2018". The notes now give 2021, the edition cited. No results change. Changelog

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. Chapter 11 (coordinate geometry: intersections and three-point resection).

Experimental means this tool has not yet met the stable bar: at least 20 golden vectors, differential tests, and an independent worked example.

Your values

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You get

Changes

Sources

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