Intersection by Distances Solver
Solves point coordinates by trilateration from two known stations and radii, handling the two-solution ambiguity.
Known points
Point A
Point B
Two solutions are returned — one each side of line A→B. Runs in your browser.
Intersection point
Solution 1
Solution 2
Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.
How to use this calculator
- Enter the coordinates of the two known stations A and B.
- Enter the measured distance from each station to the unknown point.
- Read the two possible solutions — one each side of line A→B.
How it works
Each distance defines a circle around its station; the unknown point lies where the two circles cross. There are generally two intersections (mirror images across line A→B), so the tool returns both.
If the circles are too far apart, or one is wholly inside the other, they can't meet and the tool flags it.
Worked example
A(0,0) at 50 m, B(80,0) at 50 m. The two circles cross at E 40, N +30 and E 40, N −30.
Frequently asked questions
Which of the two solutions is correct?
Both are geometrically valid — you resolve the ambiguity from your sketch, an approximate bearing, or a third observation. Never just pick one without checking.
Is this official course material?
No. It is free study support mapped to surveying course levels — not official North Metropolitan TAFE content or advice. Always follow your lecturer and the official assessment brief, and check your own working.
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Cite this tool
Zerdly. (2026). Intersection by Distances Solver. Retrieved from https://www.zerdly.com/tools/intersection-by-distances-solver/
Tip: Enter any known values to calculate the remaining results.
All calculations run in your browser. Your inputs are never saved or transmitted.