Calculator Inputs
Example Data Table
These sample rows show how sector perimeter changes with different radius, angle, and arc-length combinations.
| Example | Radius | Angle (°) | Arc Length | Perimeter |
|---|---|---|---|---|
| Radius + Angle | 5 | 60 | 5.236 | 15.236 |
| Radius + Angle | 7.5 | 120 | 15.708 | 30.708 |
| Diameter + Angle | 6 | 90 | 9.4248 | 21.4248 |
| Radius + Arc | 10 | 45.8366 | 8 | 28 |
Formula Used
Sector Perimeter
P = 2r + s
Where P is perimeter, r is radius, and s is arc length.
Arc Length from Degrees
s = (θ / 360) × 2πr
Use this when the central angle θ is entered in degrees.
Arc Length from Radians
s = rθ
Use this when the central angle θ is already in radians.
Helpful Related Values
Chord Length: c = 2r sin(θ/2)
Sector Area: A = ½r²θ or A = ½rs
Diameter: d = 2r
How to Use This Calculator
Frequently Asked Questions
1. What is the perimeter of a sector?
A sector perimeter is the total boundary length of the sector. It includes the curved arc and the two straight radii, so it is not the same as arc length alone.
2. Why does the calculator need radius or diameter?
The sector perimeter depends on the straight sides and the curved arc. Radius or diameter is necessary because both the arc length and the two side lengths come from the circle size.
3. Can I use radians instead of degrees?
Yes. Choose the radians option when your angle is already in radian measure. The calculator converts and uses the correct arc-length formula automatically.
4. What if I already know the arc length?
Select a method that uses arc length. Then enter radius or diameter and the known arc length. The calculator will derive the angle and compute the perimeter directly.
5. Is chord length part of sector perimeter?
No. The perimeter uses the two radii and the arc. Chord length is still useful because it describes the straight segment joining the arc endpoints, but it is a separate measurement.
6. Can this calculator help with school geometry?
Yes. It is useful for homework, exam practice, tutoring, and classroom demonstrations because it shows the main result, related values, formulas, and a graph together.
7. Why is my input rejected above 360 degrees?
This page treats a sector as part of one full circle. Because of that, the angle is limited to 360 degrees, or 2π radians, for standard sector calculations.
8. What does the graph show?
The graph shows how sector perimeter changes as the central angle increases while the current radius stays fixed. It makes the relationship between angle growth and perimeter easier to see.