Circular Sector Area
A sector is a fraction of the circle, so multiply the full area by the angle over 360. The perimeter is the arc plus two radii.
Your numbers
Area
52.36cm²
Arc length
10.47cm
Perimeter
30.47cm
Formula
Area = π × Radius² × Angle (°) ÷ 360
Enter 360° and you get the whole circle. This is exactly how you size a slice of pizza.
What to enter
| Input | Default | Accepted range |
|---|---|---|
| Radius (cm)Centre to edge — half the diameter. | 10 | 0 and up |
| Angle (°) (°)An angle in degrees; a full turn is 360°. | 60 | 0 ~ 360 |
Step by step
Quick reference table
Results when only Radius (cm) changes and everything else stays put.
| Radius (cm) | Area (cm²) | Arc length (cm) | Perimeter (cm) |
|---|---|---|---|
| 5 | 13.09 | 5.24 | 15.24 |
| 7.5 | 29.45 | 7.85 | 22.85 |
| 10 | 52.36 | 10.47 | 30.47 |
| 15 | 117.81 | 15.71 | 45.71 |
| 20 | 209.44 | 20.94 | 60.94 |
What each result means
| Result | At default values |
|---|---|
| Area (cm²)The space a shape covers — length squared. | 52.36 |
| Arc length (cm)The length of the curved piece cut from a circle’s edge. | 10.47 |
| Perimeter (cm)The total length around the outside of a shape. | 30.47 |
Common mistakes
Enter 360° and you get the whole circle. This is exactly how you size a slice of pizza.
Glossary
- Radius
- Centre to edge — half the diameter.
- Angle (°)
- An angle in degrees; a full turn is 360°.
- Area
- The space a shape covers — length squared.
- Arc length
- The length of the curved piece cut from a circle’s edge.
- Perimeter
- The total length around the outside of a shape.
Frequently asked questions
Q. How is Circular Sector Area calculated?
Area = π × Radius² × Angle (°) ÷ 360 — A sector is a fraction of the circle, so multiply the full area by the angle over 360. The perimeter is the arc plus two radii.
Q. Can you walk through an example?
With Radius 10cm, Angle (°) 60°, the answer is Area 52.36cm².
Q. What do I need to enter?
Enter Radius, Angle (°). The result recalculates as you type, and an empty box counts as zero.
Q. How much does the answer move if I change a number?
Changing only Radius (cm) moves the answer to Radius (cm) 5 → Area (cm²) 13.09 and Radius (cm) 20 → Area (cm²) 209.44. The table below lays out five steps.
Q. How are the numbers rounded?
Money is shown to the nearest whole unit, percentages to one decimal place and everything else to two. What you see is rounded; the calculation itself carries the unrounded value forward.
Q. Anything to watch out for?
Enter 360° and you get the whole circle. This is exactly how you size a slice of pizza.
Related calculators
Keep your length units consistent across inputs — mixing centimetres and metres throws results far off.