The “pizza slice” area question — a portion of a circle defined by an angle.
How it works
Multiplying a full circle’s area by the fraction of 360 degrees the angle represents gives the sector area; the same fraction applied to the circumference gives the arc length.
What this does not include
This does not include a fixed 180-degree special case — for that, use this site’s semicircle area calculator instead, which is optimized for that specific angle.
How to use this calculator
- Enter the radius and the sector’s angle in degrees.
A worked example
A sector with radius 5 and a 90° angle: area = (angle/360) × πr² = 19.634954.
Radius 5 with a full 360° angle (the whole circle): area = 78.539816 — matching the plain circle-area formula exactly, as it should.
What the variables mean
| Variable | Meaning |
|---|---|
| Radius | Distance from the circle’s center to its edge |
| Angle | The sector’s central angle, in degrees |
Edge cases worth knowing
A 360° sector is just the full circle — the formula naturally reduces to the standard πr² area formula at that angle, confirming the sector formula is a generalization of it, not a separate rule.
A radius of zero collapses the sector to a point regardless of angle, so the calculator declines to show a result.
Frequently asked questions
What happens at exactly 360 degrees?
The sector becomes the full circle, and the area equals the standard πr² formula.
What’s the difference between sector area and arc length?
Area measures the 2D region enclosed by the sector; arc length measures just the curved boundary distance, a 1D measurement.
What’s a practical use for this?
Calculating material for a curved architectural feature, or working out a pie chart’s slice area.
