Arc Length and Sector Area Calculator
Calculate a circular arc, sector area and chord from radius and central angle. Mix angle and length units and view a sector diagram plus unit equivalents.
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
Convert the central angle to radians. Multiply radius by that angle for arc length and half the squared radius by the angle for sector area. The chord joins the two arc endpoints and has length 2r sin(θ/2).
arc length = rθ; sector area = ½r²θ; chord = 2r sin(θ/2), with θ in radians
Worked example
With radius 5 cm and angle 90° = π/2 radians, the arc is 2.5π ≈ 7.85398163 cm, the sector area is 6.25π ≈ 19.6349541 cm², and the chord is about 7.07106781 cm.
Assumptions and input details
Use a positive radius and a single sector angle between 0 and a full turn, including endpoints. Enter radians numerically rather than as an expression containing π. Arc length differs from the straight chord. For angles greater than 180° the sector is the major sector. At a full turn, the chord is zero and the sector is a full disk. Squared-length units use the square of the length conversion factor.
References: OpenStax: angles, arcs and sectors
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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