Case 1
- Radius
- 5
- Angle
- 90°
19.634954
Open with these valuesSector Area Calculator
19.634954units²
Result: 19.634954 units²A sector is a slice of pie: the whole circle πr² kept in the proportion θ ÷ 360. Unlike arc length, the radius enters squared, so doubling the radius quadruples the slice while the same angle still cuts the same fraction.
The numbers at a glance
Held fixed: Radius 5.000.
| Angle (°) | Result |
|---|---|
| 0.00 | 0.000000 |
| 25.00 | 5.454154 |
| 50.00 | 10.908308 |
| 75.00 | 16.362462 |
| 90.00Your value | 19.634954 |
| 100.00 | 21.816616 |
| 125.00 | 27.270770 |
| 150.00 | 32.724923 |
| 175.00 | 38.179077 |
Worked examples
Case 2
- Radius
- 3
- Angle
- 60°
4.712389
Open with these valuesCase 3
- Radius
- 10
- Angle
- 360°
314.159265
Open with these valuesHow it's calculated
A = π × r² × θ ÷ 360
- StepEnter the radius in any length unit.
- StepEnter the angle of the slice, in degrees.
- ResultRead the area in the square of that unit.
What this number means
The angle goes in as degrees
The field runs from 0 to 360 and the formula divides by 360, so a quarter slice is entered as 90. An angle given in radians has to be converted to degrees first.
360 degrees is the whole circle
The fraction becomes one and the formula falls back to πr². A radius of 10 then gives 100π, about 314.16 square units.
The radius counts double, the angle once
Twice the angle is twice the slice, but twice the radius is four times the slice. Radius 5 at 90° covers 19.63 square units; radius 10 at the same 90° covers 78.54.
A sector is not a segment
A segment is the sector with the triangle back to the centre cut away, so it is always smaller. It also needs the chord, which this calculator does not ask for.
Commonly misread
The angle can be entered in radians.
This field is in degrees and stops at 360. Convert a radian angle to degrees before entering it.
Twice the radius means twice the sector area.
The area grows with the radius squared: at 90°, radius 5 gives 19.63 and radius 10 gives 78.54 square units.
Arc length and sector area scale the same way with the radius.
The arc is a length and grows with the radius, the sector is an area and grows with its square. Doubling the radius doubles the arc but quadruples the slice.
Reference table
| Radius, angle | Exact | Area |
|---|---|---|
| 1, 90 | π ÷ 4 | 0.785398 |
| 3, 60 | 1.5π | 4.712389 |
| 5, 90 | 6.25π | 19.634954 |
| 5, 180 | 12.5π | 39.269908 |
| 10, 360 | 100π | 314.159265 |
Questions
How do you find the area of a sector?
Multiply the full circle area πr² by the angle over 360. Radius 5 at 90° gives 6.25π, about 19.63 square units.
How is this different from arc length?
The arc is a length and grows with the radius; the sector is an area and grows with the radius squared. Doubling the radius doubles the arc but quadruples the slice.
What about a segment rather than a sector?
A segment is the sector minus the triangle back to the centre. It is always smaller, and it needs the chord as well as the angle.
Does 360 degrees give the whole circle?
Yes — the fraction becomes one and the formula reduces to πr². Radius 10 gives 100π, about 314.16.
Sources and last check
Information, not professional advice.