Semicircle Area Calculator
The area of a half circle from its radius, with the perimeter including the straight edge.
A semicircle is half a disc, so the area is ½πr².
How the semicircle area calculator works
A semicircle is half a disc, so the area is ½πr². The perimeter catches people out: it is the curved half-circumference πr plus the straight diameter 2r, because the flat edge is part of the boundary. If you only have the diameter, halve it first.
Formula: square a²; rectangle ab; triangle ½bh; circle πr²; parallelogram bh; trapezoid ½(a+b)h; ellipse πab
Worked examples
| Inputs | Area | Note |
|---|---|---|
| Radius 7 | 76.969 | 76.97 |
| Radius 10 | 157.0796 | 157.08 |
| An arched window 1.2 m wide | 0.5655 | 0.565 m² of glass in the arch |
FAQFrequently asked questions
What is the area of a semicircle?
Half of πr² — so ½πr².
What is its perimeter?
The curved edge πr plus the straight diameter 2r. Forgetting the flat edge is the usual error.
I only know the diameter — what now?
Halve it to get the radius, then apply the formula.
Where is this useful?
Arched windows and doorways, half-round mouldings, and the ends of a running track.
What about a quarter circle?
Use the sector page with an angle of 90°.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- Australian Curriculum (ACARA) — Mathematics — the terms and methods taught in Australian schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.