Bearing Mean Circular Statistics Calculator
Averages compass bearings using circular statistics, reporting the mean whole-circle direction, resultant vector and spread.
Bearings
- Brg 1°′″
- Brg 2°′″
- Brg 3°′″
- Brg 4°′″
Mean bearing
The mean is the direction of the summed unit vectors (atan2 of ΣsinB, ΣcosB), so it wraps correctly around north. R near 1 means tightly grouped bearings; near 0 means widely scattered.
How to use this calculator
- Pick your angle format (DD, DMS or DDM).
- Enter each whole-circle bearing — add as many as you like.
- Read the mean bearing, the spread, and the resultant length R.
How it works
Bearings are directions, so you can't just average the numbers — 359° and 001° must mean 000°, not 180°.
The tool sums each bearing's unit vector and takes the direction of the total (atan2 of ΣsinB, ΣcosB). R near 1 means tightly grouped; near 0 means scattered.
Worked example
Either side of north. Bearings 359.5°, 000.3°, 001.1°, 000.7° give a mean near 000.4° — the wrap is handled correctly.
Frequently asked questions
Why not just average the degrees?
Because of the 360°/0° wrap. A plain average of 359° and 1° gives 180° — the opposite direction. Circular statistics fix that.
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.
Related tools
- Repeated Observation Mean and Spread Calculator
- Bearing Conversion Practice Generator
- Standard Error of the Mean Calculator
- Weighted Average RL Calculator
- Intersection by Bearings Solver
- Azimuth to Bearing Converter
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Cite this tool
Zerdly. (2026). Bearing Mean Circular Statistics Calculator. Retrieved from https://www.zerdly.com/tools/bearing-mean-circular-statistics-calculator/
Tip: Enter any known values to calculate the remaining results.
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