Interlocking Resection Calculator
Calculate an unknown station's coordinates from angle observations to three known points using interlocking resection, free online.
Known points & observed bearings
| Use | Name | Easting | Northing | Bearing (point→unknown) | Wt | |
|---|---|---|---|---|---|---|
Enter the bearing from each trig/control point to the unknown position (e.g. a join or plan bearing). Keep every point in the same coordinate system and units. 2 points minimum; 3+ recommended.
Estimated position
InvalidEnter at least two active known points with valid coordinates and bearings to estimate a position.
Geometry notes
- Add at least two active known points to compute a position.
For education, planning and field-note checking only. It does not replace a licensed surveyor, approved survey software, calibrated instruments, GNSS control or legal cadastral procedures. Always check coordinate systems, datums, magnetic declination and field observations. Calculations run entirely in your browser.
How to use this calculator
- Add at least two known points — name, Easting and Northing — and the bearing to each (three or more is recommended).
- Choose the Bearing direction: point→unknown (default) if your bearings are quoted from each control point to the unknown (e.g. a join/plan bearing), or unknown→point if you observed the bearing standing at your setup. The solved position is the same either way.
- Set a bearing correction if your bearings are magnetic rather than grid (use 0 for grid bearings), and choose decimal-degree or DMS display.
- Read the estimated Easting/Northing, the forward and reverse bearings, the residual table, the geometry quality badge and the diagram. Use Load example to see a worked case.
How it works
Resection finds an unknown position from bearings to two or more known points. Each bearing defines a line of position running through the known point in the point→unknown direction; where the lines meet is your estimated position. Because a line is bidirectional, it makes no difference to the answer whether you enter the unknown→point bearing you observed or the point→unknown bearing — the calculator reverses as needed and the Bearing-direction toggle just labels the columns to match your data.
With exactly two active observations the calculator solves the direct intersection of the two lines. With three or more it uses a weighted least-squares line solution (normal equations, solved with a guarded 2×2 inverse) because the lines rarely meet at a single point. It then reports the perpendicular residual of each line, the RMS and maximum residual, every pairwise crossing angle, and a geometry rating so you can judge how strong the fix is.
Worked example
Three trig stations around E5000, N5000. Trig A (4800, 5300), Trig B (5300, 5200) and Trig C (5150, 4700) with point→unknown bearings 146.31°, 236.31° and 333.43° (from each trig to the unknown) resolve to E 5000.000, N 5000.000 with an RMS residual of about 0 — a strong, well-conditioned fix. (These are the back-bearings of the observed 326.31°/56.31°/153.43°; the fix is the same either way.) Press Load example to try it.
Tips
- Keep every known point in the same coordinate system and units — never mix a local grid with MGA/UTM.
- Aim for known points that surround you with wide angular spread; shallow crossings make the fix very sensitive to bearing error.
- This is an estimating, checking and training tool, not certified survey output.
Frequently asked questions
What is resection in surveying?
Resection determines the position of the point you are standing on (the unknown) by observing bearings or angles to two or more points of known coordinates. It is the opposite of intersection, where the instrument sits on a known point and observes to unknown points.
Is this the same as triangulation?
Not quite. Using three bearing lines is often loosely called triangulation, but the correct term here is resection because your position is unknown and you sight outward to known points. This tool intersects the reverse bearing lines to fix that unknown position.
How many trig stations do I need?
Two known points give a direct intersection, but three or more are strongly recommended. With three or more the calculator can compute residuals, which reveal field mistakes and weak geometry that two points cannot expose.
Why do three bearing lines form a small triangle?
Because every observed bearing carries a little error, three lines rarely cross at one exact point — they form a small 'triangle of error'. The least-squares solution finds the best single point, and the residuals tell you how big that triangle is.
What is a reverse bearing or back bearing?
The bearing observed from your unknown position to a known point and the bearing from that point back to you differ by exactly 180°. The line of position is the same line regardless of which direction you quote, so the calculator accepts either — use the Bearing-direction toggle to tell it whether your entered bearings are unknown→point or point→unknown, and it displays both.
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Cite this tool
Zerdly. (2026). Interlocking Resection Calculator. Retrieved from https://www.zerdly.com/tools/interlocking-resection-calculator/
Tip: Enter any known values to calculate the remaining results.
All calculations run in your browser. Your inputs are never saved or transmitted.