Perimeter of a Semicircle Formula

Geometry Formulas: Area, Volume, Perimeter
Formula:

What is the formula for the perimeter of a semicircle?

Answer

Perimeter of a semicircle
P = π · r + 2 · r

Here r is the radius. The result comes out in units.

Where the formula comes from

P = π · r + 2 · r

The outline of a half-disc is two different things joined: the curved half of the circumference, πr, plus the straight edge across it, which is the diameter 2r. Leave the diameter out and you have measured an arc, not a shape.

Worked examples

Let r = 5. Then the perimeter of a semicircle ≈ 25.71 units.

Let r = 3.2. Then the perimeter of a semicircle ≈ 16.45 units.

The common mistake

Halving the full circumference and stopping there. That gives πr and forgets the straight side — the perimeter comes out about 39 % short.

See Also

Geometry Formulas: Area, Volume, Perimeter

These are the formulas for the area, perimeter, circumference, volume and surface area of the standard shapes — 31 of them. Each page shows not only the formula but where it comes from, what every letter stands for, two worked examples and the mistake that this particular shape invites. For example, it can help you find out what is the formula for the perimeter of a semicircle? (The answer is: P = π · r + 2 · r). Pick the pair — "Area of a circle", for instance — and hit the "Find out" button.
Geometry Formulas: Area, Volume, Perimeter
Formula:

Values from the Formula

If r =Perimeter
1≈ 5.14 units
2≈ 10.28 units
3≈ 15.42 units
4≈ 20.57 units
5≈ 25.71 units
10≈ 51.42 units

FAQ

What is the formula for the perimeter of a semicircle?

Perimeter of a semicircle P = π · r + 2 · r

Where does this formula come from?

The outline of a half-disc is two different things joined: the curved half of the circumference, πr, plus the straight edge across it, which is the diameter 2r. Leave the diameter out and you have measured an arc, not a shape.

What is the most common mistake here?

Halving the full circumference and stopping there. That gives πr and forgets the straight side — the perimeter comes out about 39 % short.

How do I use this formula?

Put your own numbers in place of the letters. With r = 3.2, for instance, the formula P = π · r + 2 · r gives ≈ 16.45 units.