Circular Sector Area

A sector is a fraction of the circle, so multiply the full area by the angle over 360. The perimeter is the arc plus two radii.

Your numbers

Radius(cm)Angle (°)(°)

Area

52.36cm²

Arc length

10.47cm

Perimeter

30.47cm

Formula

Area = π × Radius² × Angle (°) ÷ 360

Enter 360° and you get the whole circle. This is exactly how you size a slice of pizza.

What to enter

Input	Default	Accepted range
Radius (cm)Centre to edge — half the diameter.	10	0 and up
Angle (°) (°)An angle in degrees; a full turn is 360°.	60	0 ~ 360

Step by step

FormulaArea = π × Radius² × Angle (°) ÷ 360

With the default numbersArea = π × 10² × 60 ÷ 360

AnswerArea = 52.36 cm²

Quick reference table

Results when only Radius (cm) changes and everything else stays put.

Radius (cm)	Area (cm²)	Arc length (cm)	Perimeter (cm)
5	13.09	5.24	15.24
7.5	29.45	7.85	22.85
10	52.36	10.47	30.47
15	117.81	15.71	45.71
20	209.44	20.94	60.94

What each result means

Result	At default values
Area (cm²)The space a shape covers — length squared.	52.36
Arc length (cm)The length of the curved piece cut from a circle’s edge.	10.47
Perimeter (cm)The total length around the outside of a shape.	30.47

Common mistakes

Enter 360° and you get the whole circle. This is exactly how you size a slice of pizza.

Glossary

Radius: Centre to edge — half the diameter.
Angle (°): An angle in degrees; a full turn is 360°.
Area: The space a shape covers — length squared.
Arc length: The length of the curved piece cut from a circle’s edge.
Perimeter: The total length around the outside of a shape.

Frequently asked questions

QHow is Circular Sector Area calculated?

Area = π × Radius² × Angle (°) ÷ 360 — A sector is a fraction of the circle, so multiply the full area by the angle over 360. The perimeter is the arc plus two radii.

QCan you walk through an example?

With Radius 10cm, Angle (°) 60°, the answer is Area 52.36cm².

QWhat do I need to enter?

Enter Radius, Angle (°). The result recalculates as you type, and an empty box counts as zero.

QHow much does the answer move if I change a number?

Changing only Radius (cm) moves the answer to Radius (cm) 5 → Area (cm²) 13.09 and Radius (cm) 20 → Area (cm²) 209.44. The table below lays out five steps.

QHow are the numbers rounded?

Money is shown to the nearest whole unit, percentages to one decimal place and everything else to two. What you see is rounded; the calculation itself carries the unrounded value forward.

QAnything to watch out for?

Enter 360° and you get the whole circle. This is exactly how you size a slice of pizza.

Related calculators

Circle Area CalculatorGet the area and circumference of a circle from its radius.Radius from CircumferenceMeasure around an object and work back to radius and area.Triangle Area CalculatorFind a triangle’s area from its base and height.Heron's Formula CalculatorFind a triangle’s area from three side lengths, without knowing the height.

Keep your length units consistent across inputs — mixing centimetres and metres throws results far off.