A circle sector is the slice of a circle bounded by two radii and the arc between them. If you know the radius and the central angle, the sector area is easy to calculate with a standard formula.

This calculator does that work for you. It is useful in geometry, design, construction, and any situation where a circular slice needs an area, such as fan blades, pie-shaped layouts, curved signs, or sectors in technical drawings. For a broader geometry reference, see the circle calculator or the area calculator.

What a circle sector area calculator does

A sector is not the same as a full circle and not the same as a triangle. It is the “slice” of the circle between two radii.

This calculation answers a simple question: how much surface area does that slice cover?

You usually need it when:

  • you know the radius of a circle and the angle at the center,
  • you need a piece of a circular design measured in square units,
  • you want to compare part of a circle to the whole circle,
  • you are solving geometry problems involving arcs, sectors, or circular segments.

A sector can be drawn in two common ways:

  • as a minor sector, with angle less than a full turn,
  • as a major sector, with a larger angle that covers most of the circle.

The calculator works for either one, as long as the angle is understood correctly.

The sector area formula

The area of a circular sector depends on the radius and the central angle.

If the angle is measured in degrees, use:

Area = (θ / 360) × πr²

Where:

  • r is the radius,
  • θ is the central angle in degrees,
  • πr² is the area of the whole circle.

If the angle is measured in radians, use:

Area = (1/2) r²θ

Where θ is the angle in radians.

These two formulas are equivalent. The degree formula is often easier to read because it shows the sector as a fraction of the full circle. The radian formula is often used in higher-level math and physics.

If you are working from a sector angle and need the rest of the circle relationships, a circle calculator can help connect radius, circumference, and area. If you only need an area in general, the area calculator may be more direct.

How to calculate a sector area by hand

The method is straightforward.

  1. Identify the radius.
  2. Identify the central angle.
  3. Make sure the angle is in the correct unit for the formula you are using.
  4. Square the radius.
  5. Multiply by π.
  6. Multiply by the angle fraction, or use the radian formula directly.

For degrees, think of the sector as a fraction of the full circle:

  • a 90° sector is one quarter of the circle,
  • a 180° sector is one half,
  • a 45° sector is one eighth.

That makes the result easy to check mentally before you trust the exact value.

Worked example 1: angle in degrees

Suppose a circle has radius 10 and a central angle of 60°.

Use the degree formula:

Area = (60 / 360) × π × 10²

That gives:

Area = 52.36

So the sector area is 52.36 square units.

This is a good example of a small wedge. Since 60° is one sixth of a full turn, the area should also be one sixth of the full circle’s area.

Worked example 2: a quarter-circle sector

Suppose the radius is 8 and the central angle is 90°.

Use the formula:

Area = (90 / 360) × π × 8²

That becomes:

Area = 50.27

So the sector area is 50.27 square units.

This result should make sense because a 90° sector is one quarter of the circle. If you already know the full circle area, the sector should be exactly one quarter of that value.

Worked example 3: angle in radians

Suppose the radius is 5 and the angle is 1.2 radians.

Use the radian formula:

Area = (1/2) × 5² × 1.2

That gives:

Area = 15

So the sector area is 15.00 square units.

This formula is useful when the angle is already given in radians, because you do not need to convert it first. If your problem uses degrees, convert only if needed and keep the units consistent.

How to read the result

The result is an area, so it should always be written in square units.

That means:

  • square centimeters if the radius is in centimeters,
  • square meters if the radius is in meters,
  • square inches if the radius is in inches.

The number tells you how much flat surface lies inside the sector boundaries. It does not tell you:

  • the arc length,
  • the perimeter of the sector,
  • the height of the curved edge,
  • the volume of any shape.

If you need more than area, you may need a different formula. For example, a sector’s curved boundary is part of the circumference, while the straight sides are radii. Those parts are not included in the area result.

Common mistakes to avoid

A few errors come up often in sector problems:

  • Using the wrong angle unit. The degree formula and radian formula are not interchangeable unless you convert properly.
  • Forgetting to square the radius. The formula uses \(r^2\), not \(r\).
  • Using diameter instead of radius. The radius is half the diameter.
  • Mixing up sector area with arc length. Arc length is a different calculation.
  • Assuming the angle is the exterior angle. You need the central angle at the circle’s center.
  • Missing the fraction of the circle. A sector is a portion of the whole circle, not a separate shape with its own independent area formula.

If you are unsure about the basic circle terms, the circle calculator can help reinforce the difference between radius, diameter, circumference, and area.

When the formula has limits

The standard sector area formula works for a flat circle in ordinary geometry.

It does not handle:

  • shapes that are only approximately circular,
  • ellipses,
  • sectors in curved surfaces,
  • circular segments unless you are intentionally treating the shape as a sector,
  • cases where the given angle is measured from a different reference point.

If your problem asks for a segment of a circle, that is not the same as a sector. A segment is the region cut off by a chord and an arc, so it needs a different method. If the geometry is unclear, identify whether the boundary includes two radii or a chord before calculating.

For unit conversion problems, an area converter may also be useful after you find the sector area, especially if you need the result in a different square unit.

Practical way to check your answer

Before you rely on the result, ask three quick questions:

  1. Is the angle a central angle?
  2. Is the angle in degrees or radians?
  3. Does the size of the answer seem reasonable compared with the full circle?

A quick reasonableness check helps catch unit mistakes. For example, a sector with a very small angle should give a small area, and a sector close to a full turn should give an area close to the whole circle’s area.

If you want to explore the related formulas that sit behind many calculators, the general idea is similar to how a calculator performs a fixed method from your inputs: you enter known values, and the rule determines the result.

Frequently asked questions

What is a circle sector?
A circle sector is the slice of a circle formed by two radii and the arc between them. It looks like a pizza slice or wedge. Its area depends on the radius and the central angle.
How do I calculate the area of a sector?
Use Area = (θ / 360) × πr² when the angle is in degrees. If the angle is in radians, use Area = (1/2)r²θ. Both formulas give the same result when used with the correct unit.
Do I need the diameter or the radius?
The formula uses the radius. If you only know the diameter, divide it by 2 first. Using the diameter directly will give the wrong answer.
What unit will the result use?
The result is always in square units. If the radius is in centimeters, the area is in square centimeters; if the radius is in meters, the area is in square meters.
What is the difference between sector area and arc length?
Sector area measures the flat region inside the wedge. Arc length measures the curved edge only. They are related, but they are different calculations.
Can the angle be more than 360 degrees?
In standard circle geometry, a full circle is 360 degrees. If a problem gives a larger angle, it usually needs interpretation or conversion, because the usual sector area formula assumes a standard central angle.
What if my problem uses radians instead of degrees?
Use the radian formula directly: Area = (1/2)r²θ. That avoids converting units and is often simpler in algebra and calculus problems.

About this article

Written by Yahav Atia, WSO – the digital agency (wso.co.il) that owns and founded this site, with the help of AI, and passed automated quality checks before publication. Numbers in the worked examples were computed in code, not estimated.