A half-circle’s area and perimeter, both computed directly from the radius.
How it works
Halving the full circle area formula (π times radius squared) gives the semicircle area; adding the curved arc length to the straight diameter edge gives the perimeter.
What this does not include
This does not include a full circle’s area — for that, use this site’s general area calculator or area-of-a-circle page instead.
How to use this calculator
- Enter the radius.
A worked example
A semicircle with radius 4: area = (πr²)/2 = 25.132741, perimeter = πr + 2r = 20.566371.
Radius 10: area = 157.079633.
What the variables mean
| Variable | Meaning |
|---|---|
| Radius | Distance from the center of the flat edge to the curved edge |
Edge cases worth knowing
Perimeter includes both the curved arc and the straight diameter edge — a common point of confusion, since “perimeter” for a full circle only refers to the curved circumference.
Area is exactly half a full circle’s area at the same radius, while perimeter is not exactly half the circumference — it also has to include the straight diameter line, which is why the perimeter formula adds 2r on top of πr.
Frequently asked questions
Why does the perimeter include the straight edge?
Because a semicircle’s actual boundary is the curved arc plus the flat diameter line closing it off — leaving out the straight edge would understate the true perimeter.
Is a semicircle’s area always exactly half a full circle’s area?
Yes — a semicircle is defined as exactly half a circle, so its area formula is simply the full-circle formula divided by 2.
What’s a practical use for this?
Architectural features like an arched window or a semicircular patio, where material or paint coverage needs to be estimated.
