What this calculator does
A semicircle is exactly half a circle, cut straight through the centre, so the area of a semicircle formula is just half the area of a full circle: πr² ÷ 2. This calculator works from either a radius or a diameter and returns that area directly.
Alongside the area, it also gives the perimeter of the semicircle, which is easy to get wrong: it is not just the curved arc, but the arc plus the straight edge across the middle (the diameter), since that straight edge is also part of the shape’s boundary.
The formula
The area of a semicircle formula halves the area of a full circle with the same radius: area = πr² ÷ 2. If a diameter was entered instead of a radius, it is halved first (r = d/2). The arc length is half the full circle’s circumference, πr, and the perimeter adds the straight diameter edge to that arc: perimeter = πr + 2r.
| Term | Meaning |
|---|---|
| r | Radius: the distance from the centre of the original circle to its edge. |
| Arc length | The length of the curved edge of the semicircle: half the circumference of the full circle. |
| Perimeter | The total boundary of the semicircle: the curved arc plus the straight diameter edge. |
The inputs explained
| Field | What to enter |
|---|---|
| Value | The radius or diameter, whichever measurement you already have. |
| This value is the | Select which measurement the value above represents. |
When to use it
Costing a semicircular surface
Semicircular garden beds, rugs, windows and tabletops need their actual area for materials such as turf, glass or fabric, rather than being priced off the full-circle figure by mistake.
Working out material for the curved edge
Edging, trim or fencing around a semicircular shape needs the perimeter, which includes both the curved arc and the straight edge across the diameter, not the arc alone.
Comparing a semicircle to the full circle it came from
Showing the full-circle area alongside the semicircle area makes clear that halving a shape exactly halves its area, unlike some other proportional changes to a circle.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does the area of a semicircle change with radius?
The area, perimeter and arc length of a semicircle for a range of radius values.
| Radius | Area of semicircle | Perimeter (arc + straight edge) | Arc length |
|---|---|---|---|
| 1 | 1.571 | 5.142 | 3.142 |
| 2 | 6.283 | 10.283 | 6.283 |
| 5 | 39.270 | 25.708 | 15.708 |
| 10 | 157.080 | 51.416 | 31.416 |
| 20 | 628.319 | 102.832 | 62.832 |
| 50 | 3,926.99 | 257.080 | 157.080 |
Questions
What is the area of a semicircle formula?
Area = πr² ÷ 2, exactly half the area of a full circle with the same radius. If you only have the diameter, halve it first to get the radius before applying the formula.
How do you find the area of a semicircle from the diameter?
Halve the diameter to get the radius (r = d/2), then apply area = πr² ÷ 2. Equivalently, area = πd² ÷ 8.
Is the perimeter of a semicircle just the curved arc?
No. The full perimeter includes the curved arc plus the straight edge across the diameter, since that straight line is also part of the shape’s boundary. The arc length alone is only part of the total perimeter.
How much smaller is a semicircle than the full circle?
Exactly half. A semicircle’s area is always precisely πr² ÷ 2, which is half of the full circle’s πr² area at the same radius, regardless of how large or small the radius is.
For the full circle this shape is derived from, see the area of a circle calculator. For a wedge cut at an angle other than 180°, see the circle sector and arc calculator.