Perimeter of a Semicircle Formula
Geometry Formulas: Area, Volume, Perimeter
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.
Related Calculations
See Also
- Square Footage Calculator - Width × length in feet to square feet
- Square Feet to Square Meters (Sq Ft to Sq M) - Convert Square Feet to Square Meters
- Square Meters to Square Feet (Sq M to Sq Ft) - Convert Square Meters to Square Feet
- Gravel Calculator - Area to cubic yards, tons and coverage
- Topsoil Calculator - Cubic yards, weight and coverage for any area
- Multiplication Facts - Any two numbers from 1 to 9, with the working shown
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
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.
See Also
- Area of a Rectangle Formula
- Area of a Rhombus Formula
- Area of a Circular Sector Formula
- Area of a Square Formula
- Area of a Trapezoid Formula
- Area of a Triangle Formula
- Circumference of a Circle Formula
- Diameter of a Circle Formula
- Perimeter of a Regular Polygon Formula
- Perimeter of a Rectangle Formula
- Perimeter of a Square Formula
- Perimeter of a Triangle Formula
- Surface Area of a Cone Formula
- Surface Area of a Cube Formula
- Surface Area of a Cylinder Formula
- Surface Area of a Pyramid Formula
- Surface Area of a Rectangular Prism Formula
- Surface Area of a Sphere Formula
- Surface Area of a Triangular Prism Formula
- Volume of a Cone Formula
- Периметр полукруга
- Perímetro del semicírculo
- Perímetro do semicírculo