Case 1
- Inner radius
- 3
- Outer radius
- 5
- Angle
- 90°
12.566371
Open with these valuesAnnular Sector Area Calculator
12.566371units²
Result: 12.566371 units²An annular sector is a slice of a ring: the full annulus π(R² − r²) kept in the proportion θ ÷ 360. Both radii go in with the same length unit and the area comes back squared in that unit. A washer cut open, a lane of a curved running track.
The numbers at a glance
Held fixed: Inner radius 3.000, Outer radius 5.000.
| Angle (°) | Result |
|---|---|
| 0.00 | 0.000000 |
| 25.00 | 3.490659 |
| 50.00 | 6.981317 |
| 75.00 | 10.471976 |
| 90.00Your value | 12.566371 |
| 100.00 | 13.962634 |
| 125.00 | 17.453293 |
| 150.00 | 20.943951 |
| 175.00 | 24.434610 |
Worked examples
Case 2
- Inner radius
- 2
- Outer radius
- 4
- Angle
- 60°
6.283185
Open with these valuesCase 3
- Inner radius
- 1
- Outer radius
- 10
- Angle
- 180°
155.508836
Open with these valuesHow it's calculated
A = π × (R² − r²) × θ ÷ 360
- StepMeasure the outer radius R and the inner radius r of the ring.
- StepEnter the opening angle of the slice, in degrees.
- ResultRead the area in the square of the unit you entered.
Reference table
| Inner, outer, angle | Exact | Area |
|---|---|---|
| 2, 4, 60 | 2π | 6.283185 |
| 3, 5, 90 | 4π | 12.566371 |
| 4, 7, 120 | 11π | 34.557519 |
| 3, 5, 360 | 16π | 50.265482 |
| 1, 10, 180 | 49.5π | 155.508836 |
Questions
How do you calculate the area of an annular sector?
Square both radii, subtract the inner from the outer, multiply by π, then keep the fraction θ ÷ 360. From 3 to 5 over 90° gives 4π, about 12.57 square units.
What happens at 360 degrees?
The fraction becomes one and the result is the whole annulus, π(R² − r²). From 3 to 5 that is 16π, about 50.27.
Is this the same as a circular sector?
Only when the inner radius is zero. Otherwise the hole in the middle is cut away and the piece is smaller.
Which units does the answer use?
The square of whatever you entered. Both radii must use the same length unit; the angle is always in degrees.
Sources and last check
Information, not professional advice.