Circular Segment Area
Take the sector area and subtract the triangle inside it. This shape is exactly the cross-section of a partly filled cylindrical tank.
Your numbers
Area
61.418cm²
Chord length
17.321cm
Height
5cm
Formula
Area = Radius² ÷ 2 × (θ − sin θ), θ = Angle (°) × π ÷ 180
At 180° it becomes a semicircle. Tank gauging for horizontal cylinders uses this formula directly.
What to enter
| Input | Default | Accepted range |
|---|---|---|
| Radius (cm)Centre to edge — half the diameter. | 10 | 0 and up |
| Angle (°) (°)An angle in degrees; a full turn is 360°. | 120 | 0 ~ 360 |
Step by step
Quick reference table
Results when only Radius (cm) changes and everything else stays put.
| Radius (cm) | Area (cm²) | Chord length (cm) | Height (cm) |
|---|---|---|---|
| 5 | 15.355 | 8.66 | 2.5 |
| 7.5 | 34.548 | 12.99 | 3.75 |
| 10 | 61.418 | 17.321 | 5 |
| 15 | 138.192 | 25.981 | 7.5 |
| 20 | 245.674 | 34.641 | 10 |
What each result means
| Result | At default values |
|---|---|
| Area (cm²)The space a shape covers — length squared. | 61.418 |
| Chord length (cm)The straight line between two points on a circle. | 17.321 |
| Height (cm)The perpendicular height from the base — not the slanted side. | 5 |
Common mistakes
At 180° it becomes a semicircle. Tank gauging for horizontal cylinders uses this formula directly.
Glossary
- Radius
- Centre to edge — half the diameter.
- Angle (°)
- An angle in degrees; a full turn is 360°.
- Area
- The space a shape covers — length squared.
- Chord length
- The straight line between two points on a circle.
- Height
- The perpendicular height from the base — not the slanted side.
Frequently asked questions
Q. How is Circular Segment Area calculated?
Area = Radius² ÷ 2 × (θ − sin θ), θ = Angle (°) × π ÷ 180 — Take the sector area and subtract the triangle inside it. This shape is exactly the cross-section of a partly filled cylindrical tank.
Q. Can you walk through an example?
With Radius 10cm, Angle (°) 120°, the answer is Area 61.418cm².
Q. What do I need to enter?
Enter Radius, Angle (°). The result recalculates as you type, and an empty box counts as zero.
Q. How much does the answer move if I change a number?
Changing only Radius (cm) moves the answer to Radius (cm) 5 → Area (cm²) 15.355 and Radius (cm) 20 → Area (cm²) 245.674. The table below lays out five steps.
Q. How are the numbers rounded?
Money is shown to the nearest whole unit, percentages to one decimal place and everything else to two. What you see is rounded; the calculation itself carries the unrounded value forward.
Q. Anything to watch out for?
At 180° it becomes a semicircle. Tank gauging for horizontal cylinders uses this formula directly.
Related calculators
Keep your length units consistent across inputs — mixing centimetres and metres throws results far off.