Segment Area Calculator
Find the area of a circular segment (the part cut off by a chord) from the central angle and the radius or diameter.
Change the values and press Calculate to work out your own figures.
Enter the central angle and either the radius or the diameter.
| Amount | Unit |
|---|---|
| 0.0009058607371 | m² |
| 9.058607371 | cm² |
| 0.009750603824 | ft² |
| 1.404086951 | in² |
| 0.001083400425 | yd² |
| 2.23843063e-7 | acres |
Show the working
- θ = 60°
- Segment area = ½ r² (θ − sin θ), θ in radians
- Segment area = 9.058607371 cm²
How to use it
Enter the central angle and either the radius or the diameter.
Enter the measurements (decimals, fractions such as 3/4, or mixed numbers such as 1 1/2) and, if you like, their unit; the answer is then also given in other units. Show the working gives the formula.
Key facts
A = ½ r² (θ − sin θ), θ in radians
Segment or sector?
A sector is bounded by two radii and an arc; a segment by a chord and an arc. The segment is the sector minus the triangle.
Questions
What is the segment area for 60° and radius 10?
≈ 9.058607371.
And for 180°?
Half the circle.
Formulas
A = ½ r² (θ − sin θ), θ in radians
Sources
Limitations
- All measurements in one calculation use the same unit; the answer is also given in other units.
- Measurements up to 10¹⁵.