Circle Sector Area & Arc Length Calculator
Circle Sector Area & Arc Length Calculator
A circle sector is the pie-slice-shaped region bounded by two radii and the arc between them. Enter the radius and the angle of the slice, and this calculator finds the sector's area and the length of its curved edge (the arc), along with a diagram and the full step-by-step working.
Both the sector area and arc length formulas work by taking the full circle's area or circumference and scaling it down by the fraction of the circle the sector's angle represents — a 90° sector is exactly a quarter of the full circle (90/360), so both its area and arc length come out to precisely one quarter of the full circle's corresponding values. This same underlying logic — angle divided by 360, applied as a scaling fraction — is the pattern behind pie charts, clock-face geometry, and any problem involving a wedge-shaped piece of a circle.
- Sector Area = (angle/360) × πr², so a 90° sector (a quarter circle) of a radius-5 circle has an area of ¼ × π × 5² ≈ 19.63.
- Arc Length = (angle/360) × 2πr, for the same sector that's ¼ × 2 × π × 5 ≈ 7.85 - notice both formulas simply scale the full circle's area/circumference by the fraction of the circle the angle covers.
- A 360° "sector" is the whole circle - the calculator caps the angle at 360° so results stay meaningful.
How do I find the area of a sector?
Use Sector Area = (angle/360) × πr². For radius 5 and angle 90°: (90/360) × π × 5² ≈ 19.63.
How is arc length different from sector area?
Arc length is a distance (the curved edge of the sector, measured in the same unit as the radius), while sector area is a 2D measurement (measured in that unit squared) - they use similar formulas but describe different things.
Circle Sector Area & Arc Length Calculator
A circle sector is the pie-slice-shaped region bounded by two radii and the arc between them. Enter the radius and the angle of the slice, and this calculator finds the sector's area and the length of its curved edge (the arc), along with a diagram and the full step-by-step working.
Both the sector area and arc length formulas work by taking the full circle's area or circumference and scaling it down by the fraction of the circle the sector's angle represents — a 90° sector is exactly a quarter of the full circle (90/360), so both its area and arc length come out to precisely one quarter of the full circle's corresponding values. This same underlying logic — angle divided by 360, applied as a scaling fraction — is the pattern behind pie charts, clock-face geometry, and any problem involving a wedge-shaped piece of a circle.
- Sector Area = (angle/360) × πr², so a 90° sector (a quarter circle) of a radius-5 circle has an area of ¼ × π × 5² ≈ 19.63.
- Arc Length = (angle/360) × 2πr, for the same sector that's ¼ × 2 × π × 5 ≈ 7.85 - notice both formulas simply scale the full circle's area/circumference by the fraction of the circle the angle covers.
- A 360° "sector" is the whole circle - the calculator caps the angle at 360° so results stay meaningful.
How do I find the area of a sector?
Use Sector Area = (angle/360) × πr². For radius 5 and angle 90°: (90/360) × π × 5² ≈ 19.63.
How is arc length different from sector area?
Arc length is a distance (the curved edge of the sector, measured in the same unit as the radius), while sector area is a 2D measurement (measured in that unit squared) - they use similar formulas but describe different things.