Arc Length Calculator
A 90-degree arc on a circle with radius 5 has an arc length of about 7.85. This arc length calculator finds the arc length and sector area from the radius and the central angle, in degrees or radians.
Quick answer
Arc length is the distance along the curved edge of a circle section.
What this tells you
- •Arc length is the distance along the curved edge of a circle section.
- •The formula is arc length = radius x angle in radians.
- •Sector area is half the radius squared times the angle in radians.
How to Use
- 1Enter the radius of the circle.
- 2Enter the central angle.
- 3Choose whether the angle is in degrees or radians.
- 4Click Calculate to get the arc length, sector area, and full circle values.
How It Works
Formula
Arc length = r x theta (theta in radians). Sector area = 0.5 x r squared x theta.Arc length is the product of the radius and the central angle measured in radians. If the angle is in degrees, it is converted to radians by multiplying by pi and dividing by 180. The sector area is half of the radius squared times the angle in radians.
Calculation note: values are processed in the order shown above, using the current input units.
Worked Examples
90-degree arc with radius 5
Convert 90 degrees to pi/2 radians. Arc length = 5 x pi/2 = 7.854. Sector area = 0.5 x 25 x pi/2 = 19.635.
1 radian arc with radius 10
With a radius of 10 and an angle of exactly 1 radian, the arc length is simply 10. The sector area is 0.5 x 100 x 1 = 50.
Arc Length for Common Angles at Radius 1
Arc length and sector area for a unit circle (radius 1).
| Angle (deg) | Arc Length | Sector Area |
|---|---|---|
| 30 | 0.5236 | 0.2618 |
| 45 | 0.7854 | 0.3927 |
| 60 | 1.0472 | 0.5236 |
| 90 | 1.5708 | 0.7854 |
| 180 | 3.1416 | 1.5708 |
| 360 | 6.2832 | 3.1416 |
Common mistakes
- Using degrees directly in the formula without converting to radians. Multiply degrees by pi and divide by 180 first.
- Confusing arc length with chord length. Arc length measures along the curve, while chord length is the straight-line distance between the two endpoints.
- Entering the diameter instead of the radius. The formula uses the radius, so divide the diameter by 2 first.