Area Calculator FAQ
How do you calculate the area of a sector?
You can calculate sector area from radius and angle, from arc length and radius, or from arc length and angle. This calculator supports all three methods and can also solve for a missing radius, angle, or arc length when the area is known.
What is the formula for the area of a sector with radius and angle?
A common formula is A = πr² × θ / 360°. If the angle is in radians, the equivalent formula is A = r²θ / 2.
How do you find sector area from arc length and radius?
Use A = lr / 2, where l is the arc length and r is the radius.
How do you find sector area from arc length and angle?
If the angle is in radians, use A = l² / (2θ). If the angle is in degrees, use A = 90l² / (πθ). This calculator handles the unit conversion for the selected angle unit automatically.
Can I enter the angle in radians or full-circle units?
Yes. The angle unit selector supports degrees, radians, and full circle units.
How do you calculate the area of a semicircle?
A semicircle is a sector with an angle of 180°, π rad, or 0.5 full circle. You can use the same sector formulas, or the direct semicircle formula A = πr² / 2.
Can this sector calculator be used for a half circle or quarter circle?
Yes. Enter 180° for a half circle or 90° for a quarter circle. The same works in radians or full-circle units.
Can this calculator work backwards from the area?
Yes. Select radius, angle, or arc length as the target value, and the calculator will solve the chosen sector formula in reverse from the area. It also validates that the result still represents a real sector and can show the derived third value.
When is a sector area calculator useful?
It is useful for geometry homework, pie-slice shapes, circular plots, machine parts, fan blades, curved panels, and any design or measurement where only part of a circle is used.
