LifeTally
Circular sector area and arc length
How long is this circular arc, and what is the area of its sector?
Use a radius in centimetres and a central angle in degrees to calculate the curved arc length and sector area.
Radius and central angle
Enter the radius, not the diameter. Fractions are allowed. Both inputs must be valid, even when one is zero; an empty field is not zero. Enter 0.5 rather than 1/2.
How the estimate works
One circular sector in a flat Euclidean plane. The central angle selects the sweep: an angle above 180° selects the larger sector, and 360° means the whole circle, not zero. A zero radius or angle is an allowed limiting case and gives zero for both results.
s = π × r × θ ÷ 180
A = π × r² × θ ÷ 360
π ≈ 3.141592653589793This calculates the curved arc and sector area, not a chord, a circular segment bounded by a chord, sector perimeter, an annulus or a spherical region. It does not model cutting, material allowances, geography or actual physical fit. Check your own measurements.
OpenStax: angles, arc length and sector area ↗Check the filled example
Our chosen example: r = 6 cm and θ = 150°. The arc is 5π cm ≈ 15.708 cm, and the sector area is 15π cm² ≈ 47.1239 cm².
Accepted input values
- Radius r, cm
- 6
- Central angle θ, degrees
- 150
Plan the next step
Use the standard calculator to check another arithmetic expression.
Open the standard calculator →