Arc Length & Sector Area Calculator
Arc length calculator: length of a circular arc from radius and central angle, plus sector area and chord length.
s = r · θ
How to use this calculator
- Choose the quantity you want under “Solve for”.
- Type the known values and pick their units: any combination works.
- The result updates as you type. Open “Show the steps” to see the substitution.
Arc length = radius × angle in radians. In degrees: s = 2πr × θ/360. Sector area = r² θ ÷ 2.
Formula
s = r · θ
| Symbol | Quantity | Units |
|---|---|---|
| r | Radius | m, km, cm, mm, µm, nm, pm, Å, in, ft, yd, mi, nmi, au, ly |
| θ | Central angle | °, rad, gon, turn, ′, ″, mrad |
| s | Arc length | m, km, cm, mm, µm, nm, pm, Å, in, ft, yd, mi, nmi, au, ly |
Worked example
Given: r = 10 cm · θ = 60 °
s = r θ
Result: s = 10.472 cm
Arc length for different values of Radius
| r · Radius | s · Arc length |
|---|---|
| 5 cm | 5.236 cm |
| 7.5 cm | 7.854 cm |
| 9 cm | 9.4248 cm |
| 10 cm | 10.472 cm |
| 11 cm | 11.519 cm |
| 12.5 cm | 13.09 cm |
| 15 cm | 15.708 cm |
| 20 cm | 20.944 cm |
Other values as in the worked example.
Frequently asked questions
Radius 10 cm, angle 60°?
Arc ≈ 10.47 cm, sector area ≈ 52.36 cm², chord 10 cm.
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