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Quickly calculate the area of a sector based on the radius and central angle (degrees or radians), with support for custom units and adjustable precision.
Overview
Understand what the tool solves, how it works, and the boundaries of its data.
A circular sector is the wedge bounded by two radii and the arc between them. Enter the circle radius r and central angle θ in degrees. The calculator returns sector area and curved arc length; it does not calculate the straight chord or the full sector perimeter.
The central angle tells what fraction of the full 360° circle is included. Area and circumference scale by that same fraction:
Sector area: A = (θ / 360) × πr²
Arc length: L = (θ / 360) × 2πr
For example, with a 5-inch radius and a 60° angle, the sector covers one-sixth of the circle. Its area is about 13.09 square inches and its arc is about 5.24 inches. The result is rounded to four decimal places.
The angle field is interpreted as degrees; there is no radians selector. If your source gives radians, convert first using degrees = radians × 180 / π. Radius must be greater than zero and angle must be greater than zero for a result to appear. The input has no explicit upper bound, so values above 360° are mathematically treated as multiple turns by the same proportion; use 0° through 360° for a single circle sector.
No unit is selected automatically. If the radius number is in inches, interpret area as square inches and arc length as inches; for a radius in feet, read the outputs in square feet and feet. Do not mix measurement units within one calculation.
Area measures the two-dimensional wedge. Arc length measures only its curved boundary. A chord is the straight line between the arc’s endpoints, and a circular segment is the region between that chord and arc. These are separate quantities; this calculator provides only the first two. The angle formulas follow from taking θ/360 of the circle’s area and circumference.
Guide
Follow the workflow and verify inputs and outputs with practical examples.
Use a positive radius measured from the circle’s center to its edge. Keep the unit in mind because outputs inherit it.
For a semicircle use 180; for a quarter circle use 90. Convert radians before entering them.
The main result is area in squared units. The additional result is arc length in the original length unit. For r = 5 and θ = 60°, expect approximately 13.09 square units and 5.24 units of arc.
Compare the angle with a full 360° turn and check that area is a fraction of πr². A smaller central angle at the same radius should produce proportionally smaller area and arc length.
Use cases
See how the tool fits into real work and everyday tasks.
Enter the measured radius and degree angle, then compare both sector area and arc length with work shown from the formulas.
Use one consistent unit for a pie-shaped region or curved boundary, then carry squared units for area and linear units for the arc.
Q&A
Find concise answers to common questions and confusing cases.
Convert it to degrees first: multiply the radian value by 180/π. This input is degree-only.
Enter a radius in a known unit and attach that same unit to the arc length; the area uses its square. The calculator does not include a unit picker or convert units.
No. It gives the sector area and curved arc length only. The chord is straight across the wedge, and the perimeter would also include two radii.
Notes
Review scope, result limitations, and important precautions before use.
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