Arc Length Calculator
Find the length of a circular arc from the central angle and the radius or diameter, with the sector area and chord.
Change the values and press Calculate to work out your own figures.
Enter the central angle and either the radius or the diameter.
Show the working
- θ = 60°
- Sector area = ½ r² θ (θ in radians) = θ/360 × π r²
- Arc length = r θ
- Arc length = 10.47197551 cm
How to use it
Enter the central angle and either the radius or the diameter.
Enter the measurements (decimals, fractions such as 3/4, or mixed numbers such as 1 1/2) and, if you like, their unit; the answer is then also given in other units. Show the working gives the formula.
Key facts
s = r θ (θ in radians) = θ/360 × 2πr
Radians
An angle in radians is the arc length divided by the radius, so s = r θ; 360° is 2π radians.
Questions
What is the arc length for 60° on a radius of 10?
10π/3 ≈ 10.47197551.
What is a radian?
The angle whose arc equals the radius, about 57.3°.
Formulas
s = r θ (θ in radians) = θ/360 × 2πr
Sources
Limitations
- All measurements in one calculation use the same unit; the answer is also given in other units.
- Measurements up to 10¹⁵.