Sector Area Calculator
Enter radius and central angle to calculate the area of a sector instantly.
What is the area of a sector of a circle?
A sector is the “slice” of a circle formed by two radii and the arc between them. If you imagine cutting a pizza, each slice is a sector. The area of a sector tells you how much surface is inside that slice.
This area of a sector of a circle calculator helps you compute that value quickly, whether your angle is given in degrees or radians. It is useful for geometry homework, engineering sketches, architecture layouts, and many practical measurement problems.
Sector area formulas
When angle is in degrees
If the central angle is in degrees, the formula is:
Area = (θ / 360) × πr²
- θ = central angle in degrees
- r = radius of the circle
When angle is in radians
If the central angle is in radians, use:
Area = (1/2) × r² × θ
- θ = central angle in radians
- r = radius of the circle
How to use this calculator
- Enter the radius of the circle.
- Enter the central angle.
- Select whether the angle is in degrees or radians.
- Choose how many decimal places you want.
- Click Calculate to see the area, arc length, and sector fraction.
Worked examples
Example 1: Degrees
Suppose r = 8 and θ = 60°. Sector area = (60/360) × π × 8² = (1/6) × π × 64 ≈ 33.5103 square units.
Example 2: Radians
Suppose r = 5 and θ = 1.2 rad. Sector area = 0.5 × 5² × 1.2 = 0.5 × 25 × 1.2 = 15 square units.
Common mistakes to avoid
- Using degree formula when angle is in radians (or vice versa).
- Entering diameter instead of radius. Radius is half of diameter.
- Forgetting units in final answer (square cm, square m, etc.).
- Rounding too early during intermediate steps.
Why this calculator is helpful
Manual calculations are fine for one problem, but when you have many values, a calculator saves time and reduces errors. This tool also provides extra outputs like arc length and percentage of the full circle, giving you a better geometric understanding.
Quick FAQ
Can the angle be more than 360°?
Yes. The calculator can still compute a value. An angle larger than 360° means a sector spanning more than one full rotation.
Can the angle be negative?
For geometric area, use a positive angle. Negative angles represent direction, but area itself should be non-negative.
What unit is the result in?
The area is in square units based on your radius unit. If radius is in meters, area is in square meters.