Enter sector values
Choose a calculation mode. The calculator displays only the required inputs.
Calculation history
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| Date | Mode | Primary result | Radius | Angle | Action |
|---|---|---|---|---|---|
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Formula explanation
A circular sector is part of a circle. Two radii and one arc create its boundary. The central angle controls the sector size.
For radians, sector area equals one-half times radius squared times angle. Arc length equals radius multiplied by angle. Sector perimeter adds both radii to that arc.
| Measurement | Degrees formula | Radians formula |
|---|---|---|
| Sector area | A = (θ ÷ 360)πr² | A = ½r²θ |
| Arc length | s = (θ ÷ 360)2πr | s = rθ |
| Perimeter | P = 2r + s | P = 2r + rθ |
| Chord | c = 2r sin(θ ÷ 2) | |
| Segment area | Asegment = ½r²(θ − sin θ), using radians | |
How to use
- Select the required calculation mode.
- Enter the visible radius, angle, area, or arc values.
- Choose matching input and output units.
- Select direct, minor, or major sector interpretation.
- Set the desired decimal precision.
- Press Calculate sector to display complete results.
Use positive values for every required measurement. Angles cannot exceed one complete circle. Invalid combinations produce a clear correction message.
Example data
| Radius | Angle | Sector area | Arc length | Perimeter |
|---|---|---|---|---|
| 10 m | 60° | 52.3599 m² | 10.4720 m | 30.4720 m |
| 5 cm | 90° | 19.6350 cm² | 7.8540 cm | 17.8540 cm |
| 12 ft | 120° | 150.7964 ft² | 25.1327 ft | 49.1327 ft |
| 8 in | 270° | 150.7964 in² | 37.6991 in | 53.6991 in |
Common applications
Sector calculations support engineering layouts, rotating equipment, road curves, and architectural plans. They also help with pizza slices and circular gardens. Accurate units prevent costly measurement errors.
Chord and segment results help analyse curved boundaries. Minor and major sectors describe complementary circle regions. The diagram makes each relationship easier to verify.
Frequently asked questions
What is a circular sector?
A circular sector is a region enclosed by two radii and their connecting arc. It resembles a slice cut from a circle.
How is sector area calculated?
Use A = ½r²θ when the angle is measured in radians. For degrees, use A = (θ ÷ 360)πr².
How is arc length calculated?
Use s = rθ for radians. For degrees, multiply the circle circumference by θ divided by 360.
What is sector perimeter?
Sector perimeter includes the curved arc and both straight radii. Therefore, P = s + 2r.
What is the difference between a sector and segment?
A sector uses two radii and an arc. A segment uses a chord and the corresponding arc.
Can the calculator handle reflex angles?
Yes. Enter an angle above 180 degrees and up to 360 degrees. The diagram displays the reflex sector.
How do minor and major sector options work?
The minor option uses the smaller central angle. The major option uses its full-circle complement.
Why are radians used internally?
Radians make sector formulas direct and consistent. The calculator converts degrees and gradians before applying those formulas.
Can results be exported?
Yes. You can copy the complete calculation, download CSV data, create a PDF, or print the result.