Circular Segment Chord and Area Calculator
Find a circular segment’s area, chord, arc and boundary length from radius and segment height, including major segments.
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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
Recover the central angle from perpendicular segment height. Use the circular-sector area minus its signed triangle area, keeping the major arc when height exceeds radius.
θ=2acos(1−h/r); area=r²(θ−sinθ)/2; chord=2√(h(2r−h)); arc=rθ
Worked example
For radius 2 m and height 2 m, the segment is a semicircle: area 2π m², chord 4 m and arc 2π m.
Assumptions and input details
Height is perpendicular chord-to-arc distance for the selected region, from zero through twice the radius. It is not chord length. Height above the radius selects a major segment. Zero and full-circle endpoints are supported. Small angles use a series to avoid subtracting nearly equal terms. This tool describes planar geometry; tank lengths and liquid volumes are handled by Tank Liquid Volume.
References: Wolfram Research: circular segment
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Choose from 23 length definitions, including explicitly labelled regional measures. Area conversions square the length factor; geometric volumes cube it.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
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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