Sector Perimeter
A sector’s perimeter is one curved arc plus two straight radii. Forgetting the radii is a common slip — when cutting fabric or trimming an edge, those two straight sides need finishing too.
Your numbers
Sector perimeter
32.566cm
Arc length
12.566cm
Area
62.832cm²
Formula
Sector perimeter = Radius × 2 + 2 × π × Radius × Angle (°) ÷ 360
At 360° the formula still adds two radii. Use the plain circumference formula for a full circle.
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°. | 72 | 0 ~ 360 |
Step by step
Quick reference table
Results when only Radius (cm) changes and everything else stays put.
| Radius (cm) | Sector perimeter (cm) | Arc length (cm) | Area (cm²) |
|---|---|---|---|
| 5 | 16.283 | 6.283 | 15.708 |
| 7.5 | 24.425 | 9.425 | 35.343 |
| 10 | 32.566 | 12.566 | 62.832 |
| 15 | 48.85 | 18.85 | 141.372 |
| 20 | 65.133 | 25.133 | 251.327 |
What each result means
| Result | At default values |
|---|---|
| Sector perimeter (cm)One arc plus two radii — the whole edge of a sector. | 32.566 |
| Arc length (cm)The length of the curved piece cut from a circle’s edge. | 12.566 |
| Area (cm²)The space a shape covers — length squared. | 62.832 |
Common mistakes
At 360° the formula still adds two radii. Use the plain circumference formula for a full circle.
Glossary
- Radius
- Centre to edge — half the diameter.
- Angle (°)
- An angle in degrees; a full turn is 360°.
- Sector perimeter
- One arc plus two radii — the whole edge of a sector.
- Arc length
- The length of the curved piece cut from a circle’s edge.
- Area
- The space a shape covers — length squared.
Frequently asked questions
Q. How is Sector Perimeter calculated?
Sector perimeter = Radius × 2 + 2 × π × Radius × Angle (°) ÷ 360 — A sector’s perimeter is one curved arc plus two straight radii. Forgetting the radii is a common slip — when cutting fabric or trimming an edge, those two straight sides need finishing too.
Q. Can you walk through an example?
With Radius 10cm, Angle (°) 72°, the answer is Sector perimeter 32.566cm.
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 → Sector perimeter (cm) 16.283 and Radius (cm) 20 → Sector perimeter (cm) 65.133. 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?
At 360° the formula still adds two radii. Use the plain circumference formula for a full circle.
Related calculators
Keep your length units consistent across inputs — mixing centimetres and metres throws results far off.