Arc Circumference Calculator

Advanced arc length calculator for construction, engineering, and classrooms. Enter radius, diameter, angle, chord, or circle fraction values. Supports degrees or radians, multiple methods, and unit conversions. Instant results with formula steps and clear diagrams. Export CSV or PDF, save examples, share quick links.

Inputs

Unit: m
Pick how you want to define the arc.
Degrees or radians, as selected above.
Link updates as inputs change.

Results

Arc length
– m
Central angle
–° / – rad
Chord length
– m
Sector perimeter
– m
Sector area
– m²
Arc as % of circumference
–%
Circle circumference
– m
Circle area
– m²

Diagram

Simple circle sector diagram showing arc, radius, and angle. θ

Formula used

Let R be radius, θ the central angle in radians, and s the arc length.

  • Arc length: s = R · θ
  • Degrees to radians: θ = (π/180) · θ°
  • Chord: c = 2R · sin(θ/2)
  • Sector area: A = (1/2) · R² · θ
  • Sector perimeter: P = s + 2R
  • Circle circumference: C = 2πR, area: πR²
For inputs using chord c and radius R, the angle is θ = 2 · asin(c / (2R)). For percent of circle p, use θ = 2π · (p/100).

How to use this calculator

  1. Choose a calculation mode based on your known values.
  2. Enter values and pick the correct angle unit.
  3. Select a length unit and desired decimal precision.
  4. Click Calculate to update every result and the diagram.
  5. Use Download CSV or Download PDF for records.
  6. Copy the shareable link to save or send your setup.

Example data

Click Use to load values into the form, then calculate.

ModeUnitRadiusDiameterAngleAngle UnitPercentChordCircumf.
radius-anglem160deg
radius-anglem2.5120deg
diameter-anglein1090deg
chord-radiusm3deg4
radius-percentft1deg25
circumference-anglem1.2rad31.4159

Quick Angles Table (updates with radius)

Based on current radius and unit. Change radius, then calculate.

Angle (deg) Angle (rad) Arc length Chord length Sector area

Arc by Percent of Circle

Arc length and angle for common circle fractions at current radius.

Percent of circle Angle (deg) Angle (rad) Arc length

Unit Conversion Reference

Multipliers relative to one unit. Useful for manual checks.

Unit To meters To inches To feet

FAQs

It is the arc length of a circle segment, equal to s = R · θ when θ is in radians.

Choose degrees or radians. The calculator converts degrees to radians before applying the arc length formula.

Yes. With chord c and radius R, the angle is θ = 2 · asin(c/(2R)), then compute s = R · θ.

The sector perimeter is the arc length plus two radii: P = s + 2R.

All outputs use your chosen unit. Areas use squared units. You can switch units anytime and recalculate.

Results are exact to machine precision before rounding. Adjust the precision field to control displayed decimals.

Yes. Enter any positive angle. The calculator handles obtuse arcs and full circles consistently.