Annular Sector Area Calculator
Take the outer sector and subtract the inner one. Multiply the difference of the squared radii by the angle’s share of the circle for the area; the perimeter adds both arcs plus the two straight edges.
Your numbers
Area
201.06cm²
Arc length
31.42cm
Perimeter
66.27cm
Formula
Area = π × (Radius² − Inner radius²) × Angle (°) ÷ 360
This is the shape of a circular border path, a spiral stair tread, or pipe insulation cut as a wedge.
What to enter
| Input | Default | Accepted range |
|---|---|---|
| Radius (cm)Centre to edge — half the diameter. | 20 | 0 and up |
| Inner radius (cm)The smaller of two radii when the ends differ. | 12 | 0 and up |
| Angle (°) (°)An angle in degrees; a full turn is 360°. | 90 | 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) |
|---|---|---|---|
| 10 | 34.56 | 15.71 | 38.56 |
| 15 | 63.62 | 23.56 | 48.41 |
| 20 | 201.06 | 31.42 | 66.27 |
| 30 | 593.76 | 47.12 | 101.97 |
| 40 | 1,143.54 | 62.83 | 137.68 |
What each result means
| Result | At default values |
|---|---|
| Area (cm²)The space a shape covers — length squared. | 201.06 |
| Arc length (cm)The length of the curved piece cut from a circle’s edge. | 31.42 |
| Perimeter (cm)The total length around the outside of a shape. | 66.27 |
Common mistakes
This is the shape of a circular border path, a spiral stair tread, or pipe insulation cut as a wedge.
Glossary
- Radius
- Centre to edge — half the diameter.
- Inner radius
- The smaller of two radii when the ends differ.
- 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 Annular Sector Area Calculator calculated?
Area = π × (Radius² − Inner radius²) × Angle (°) ÷ 360 — Take the outer sector and subtract the inner one. Multiply the difference of the squared radii by the angle’s share of the circle for the area; the perimeter adds both arcs plus the two straight edges.
Q. Can you walk through an example?
With Radius 20cm, Inner radius 12cm, Angle (°) 90°, the answer is Area 201.06cm².
Q. What do I need to enter?
Enter Radius, Inner 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) 10 → Area (cm²) 34.56 and Radius (cm) 40 → Area (cm²) 1,143.54. 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?
This is the shape of a circular border path, a spiral stair tread, or pipe insulation cut as a wedge.
Related calculators
Keep your length units consistent across inputs — mixing centimetres and metres throws results far off.