Circle Sector Area Calculator

Enter radius, angle, diameter, chord, arc, or fraction. Compare sector measures with helpful geometry checks. Download clean results for reports, worksheets, and records quickly.

Advanced Sector Calculator

Example Data Table

Radius Angle Angle Unit Sector Area Arc Length
6 60 Degrees 18.8496 6.2832
10 1.2 Radians 60.0000 12.0000
7 90 Degrees 38.4845 10.9956
12 0.25 Turns 113.0973 18.8496

Formula Used

Sector area with radians: A = 0.5 × r² × θ

Sector area with degrees: A = (θ ÷ 360) × π × r²

Arc length: s = r × θ

Chord length: c = 2 × r × sin(θ ÷ 2)

Sector perimeter: P = 2r + s

Angle from arc length: θ = s ÷ r

Angle from chord: θ = 2 × asin(c ÷ 2r)

Here, r is radius and θ is the central angle in radians.

How To Use This Calculator

  1. Select the method that matches your known values.
  2. Enter radius, diameter, angle, arc, chord, or fraction data.
  3. Select the correct angle unit when an angle is used.
  4. Choose the complementary option for the larger remaining sector.
  5. Set decimal places for the final report.
  6. Press the calculate button to view results above the form.
  7. Use CSV or PDF buttons when you need a saved copy.

Circle Sector Area Guide

A circle sector is a slice of a circle. It is formed by two radii and one arc. The central angle decides the size of the slice. A larger angle creates a larger area. A smaller angle creates a narrow piece.

Why Sector Area Matters

Sector area appears in many math and design tasks. It helps with wheels, fans, gears, charts, sprinklers, and curved plates. Students use it to connect angles with area. Designers use it when a round object is not complete. Engineers use it when only part of a disk is active.

Key Measurements

The radius is the distance from the center to the edge. The diameter is twice the radius. The arc length is the curved outside edge. The chord is the straight line between arc endpoints. The sector perimeter is the arc length plus two radii. These values describe the same shape in different ways.

Using Different Inputs

This calculator accepts several input styles. You can enter radius and angle. You can enter diameter and angle. You can use arc length with radius. You can also use chord length with radius. A fraction of a full circle works for charts and rotation tasks. Each method is converted to a central angle first. Then the sector area is calculated.

Reading The Results

The main result is the sector area. The tool also reports arc length, chord length, angle, perimeter, triangle area, and segment area. The percent of full circle helps compare the sector with a complete disk. The full circle area is shown for context.

Good Input Habits

Use consistent units for all length fields. If the radius is in meters, the area is square meters. If the radius is in inches, the area is square inches. Check whether your angle is in degrees or radians. Use the major sector option when the larger slice is required. Export the results when you need a record.

Accuracy Tips

Round only the final answer when possible. Early rounding can change small sectors. Very large angles should be checked against one full turn. For chord based work, the chord cannot exceed the diameter. Negative values are not valid. Review exported rows before sharing them with others.

FAQs

What is a circle sector?

A circle sector is the region enclosed by two radii and the arc between them. It looks like a slice from a circular disk.

Which unit should I use for radius?

Use any length unit, such as meters, inches, feet, or centimeters. The area result will be in the square form of that unit.

Can I calculate area without an angle?

Yes. Use arc length with radius, chord length with radius, or fraction with radius. The calculator converts those inputs into an angle.

What is the difference between arc and chord?

The arc is the curved edge of the sector. The chord is the straight line connecting the two arc endpoints.

What does complementary sector mean?

The complementary sector is the remaining part of the circle. Use it when your entered data describes the smaller slice, but you need the larger slice.

Why are radians used in formulas?

Radians connect angle measure directly to radius and arc length. The main formula A = 0.5 × r² × θ requires θ in radians.

Can the chord be longer than the diameter?

No. The longest possible chord is the diameter. A chord greater than twice the radius is not valid for a circle.

What does sector perimeter include?

Sector perimeter includes the curved arc plus the two straight radius sides. It does not mean the full circle circumference.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.