HesapHanem

Circle Sector Calculator

Find the area and arc length of a circle sector.

How it is calculated

A sector is the slice of a circle between two radii. The tool first finds the fraction of the full circle that the slice covers: f = angle / 360, with the angle in degrees (not radians). Then it scales the whole circle: area = f × π × r2 and arc = f × 2 × π × r, where r is the radius. The area comes out in square units of the radius you entered and the arc length in the same linear unit. Both results are rounded to two decimals. The radius and the angle must be greater than zero, otherwise no result is shown. The angle can be at most 360, the whole circle; a larger angle gives no result.

Worked example

Take a radius of 10 and a central angle of 60 degrees. The fraction is 60 / 360 = 1/6. The full circle area is π × 102 ≈ 314.16, and one sixth of that is 52.36 square units. The full circumference is 2 × π × 10 ≈ 62.83, and one sixth of that gives an arc length of 10.47 units. Note that the arc (10.47) is slightly longer than the radius, because 60 degrees is about 1.047 radians.

Try this example →

Common mistakes

  • Typing the angle in radians (for example 1.047) while the tool expects degrees, which yields a tiny sector.
  • Entering the diameter instead of the radius, which makes the area four times too large and the arc twice as long.
  • Confusing arc length with the straight chord between the two ends; the arc is always longer.
  • Forgetting that the area is in square units and the arc in plain units, then adding the two together.
  • Entering the angle of the remaining part of the circle (for example 300 instead of 60).

About this calculator

This calculator finds the area and arc length of a circular sector — the pie-slice-shaped region bounded by two radii and the arc between them — from the circle's radius and the sector's central angle, scaling the full circle's area and circumference by what fraction of 360° the angle represents.

It is used by students solving circle-geometry problems, and in practical contexts like designing a pie chart segment, calculating material for a fan-shaped or wedge-cut piece in construction or fabrication, or figuring out the coverage area of a rotating sprinkler that only sweeps part of a full circle.

Was this helpful?

You can pick up to 3 reactions.

Comments (1)

  • Editorial team

    Enter the angle in degrees, not radians; multiply a radian value by 180 and divide by pi first. A good check is a pizza of radius 15 cm cut into 8 slices, so each slice is 45 degrees: the area is about 88.36 square cm and the crust (arc) about 11.78 cm. Angles run up to 360, the full circle; anything larger gets no result, so check for a typo. What are you cutting?

Popular calculators

Loan Calculator

Monthly payment, total interest and full amortization schedule.

Percentage Calculator

Percent change, percent of, and ratio calculations.

Discount Calculator

Calculate final price, savings, and discount amount.

BMI Calculator

Body mass index from height and weight (metric or imperial).

Age Calculator

Compute your exact age in years, months and days from a birth date.

Compound Interest Calculator

Calculate the final amount and interest earned with compounding.

All Calculators