Circular Mean and Dispersion Calculator
Calculate circular mean direction and resultant length for equally weighted angles in degrees.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Average unit vectors instead of ordinary degree values so directions close across the 0°/360° boundary.
C=mean(cos θ); S=mean(sin θ); R=√(C²+S²); mean direction=atan2(S,C)
Worked example
Angles 350°,0°,10° have mean direction 0°, not 120°, and resultant length about 0.989871835.
Assumptions and input details
Equally weighted circular directions, not axial orientations (where 0° and 180° are equivalent). Near-zero resultant leaves direction undefined. Circular SD uses √(−2ln R) radians and can exceed a full turn; no inferential test.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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