Perimeter of Semicircle Calculator
Enter the radius of a semicircle, or its diameter or area, to find its perimeter.
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Perimeter of Semicircle Calculator
Our Perimeter of Semicircle Calculator adds the curved arc of a half circle, πr, to its straight edge, 2r, to give the full distance around it. Know the diameter or the area instead? Switch the input and it works the perimeter out from that, with the arc length, area and other units.
Quick answer
The perimeter of a semicircle is P = πr + 2r = (π + 2)r: (π + 2) × 7 = 7π + 14 ≈ 35.99 cm.
- From the diameter: P = (π + 2)d ÷ 2, so a 10 m diameter gives ≈ 25.71 m
- From the area: r = √(2A ÷ π), so 77 cm² gives r ≈ 7.0014 cm and P ≈ 36 cm
- Radius from the perimeter: r = P ÷ (π + 2), so 36 m gives r ≈ 7.0017 m
- Arc only: the curved edge alone is πr, half the circumference of the circle
What Is the Perimeter of a Semicircle?
A semicircle is half a circle, cut along a diameter. Its perimeter is the total length of its edge: the curved arc plus the straight diameter that closes it. It is measured in ordinary length units such as cm, m or ft.
Perimeter of a Semicircle Formula
P = (π + 2)r ≈ 5.1416 × r
P = (π + 2)d ÷ 2
- Find the radius. It runs from the centre of the straight edge to the arc.
- Find the arc. π × 7 cm ≈ 21.99 cm (half the circumference).
- Find the straight edge. 2 × 7 cm = 14 cm (the diameter).
- Add them. 21.99 + 14 ≈ 35.99 cm.
Leave the answer as 7π + 14 cm for an exact value. For a whole circle, use the Perimeter of Circle Calculator.
Semicircle Perimeter Examples
| Radius | Arc (πr) | Perimeter |
|---|---|---|
| 1 cm | ≈ 3.14 cm | ≈ 5.14 cm |
| 3 m | ≈ 9.42 m | ≈ 15.42 m |
| 5 m | ≈ 15.71 m | ≈ 25.71 m |
| 7 cm | ≈ 21.99 cm | ≈ 35.99 cm |
| 6 in | ≈ 18.85 in | ≈ 30.85 in |
| 10 ft | ≈ 31.42 ft | ≈ 51.42 ft |
The perimeter grows in step with the radius: double the radius and the perimeter doubles too, so a 10 ft semicircle has twice the edge of a 5 ft one.
Perimeter From the Diameter
The diameter is the straight edge, so the arc is half of πd. Add the two:
P = 15.71 + 10 ≈ 25.71 m
This is the easiest measurement to take on an arched window or a half-round patio: measure straight across the flat side.
Perimeter From the Area
The area of a semicircle is πr² ÷ 2. Undo it to find the radius, then use (π + 2)r:
√(154 ÷ π) ≈ 7.0014 cm
P = (π + 2)r ≈ 36 cm
For the area itself, use the Area of Semicircle Calculator.
Radius From the Perimeter
Unroll the edge and it is one line about 5.14 radii long, so divide by π + 2:
36 ÷ 5.14159 ≈ 7.0017 m
Common Mistakes
- Leaving out the straight edge. πr is only the arc; the perimeter is πr + 2r.
- Halving the circle. Half of 2πr is πr, which misses the diameter.
- Using the diameter as the radius. The answer comes out twice too big.
- Square units. A perimeter is a length: 35.99 cm, not cm².
Key Terms
- Semicircle
- Half a circle, cut along a diameter.
- Radius
- Centre to arc, r.
- Diameter
- The straight edge, 2r.
- Arc length
- The curved edge, πr.
- Perimeter
- Arc plus diameter, (π + 2)r.
How to Use the Perimeter of Semicircle Calculator
- Choose what you know. Pick Radius, Diameter or Area. Radius is the usual choice; Diameter is the straight edge, and Area is the space inside.
- Enter the value. Type it, such as 7, and pick a unit if you want one (mm, cm, m, km, in, ft, yd or mi). Decimals and fractions such as 3/4 work.
- Read and copy the result. The perimeter appears as you type, with a drawing, the working, the exact value in terms of π, the arc length, straight edge, area and the perimeter in other units. Press Copy to copy it, or Clear or Esc to start again.
Example: an arched window is 1.2 m wide along its base. Choose Diameter, enter 1.2 and pick m. The perimeter is about 3.084956 m, of which the arc is about 1.884956 m.
Who Can Use This Calculator?
Frequently Asked Questions (FAQs)
How do you find the perimeter of a semicircle?
Add the curved arc, πr, to the straight diameter, 2r. A semicircle with a 7 cm radius has a perimeter of 7π + 14 ≈ 35.99 cm.
What is the formula for the perimeter of a semicircle?
P = πr + 2r = (π + 2)r, where r is the radius and π ≈ 3.14159. With the diameter d it is P = (π + 2)d ÷ 2.
Is the perimeter of a semicircle half the circumference of a circle?
No. Half the circumference, πr, is only the curved arc. The perimeter also includes the straight diameter, so it is πr + 2r.
How do you find the perimeter of a semicircle from the diameter?
Halve the diameter to get the radius, then use (π + 2)r. A 10 m diameter gives r = 5 m and a perimeter of about 25.71 m.
How do you find the radius of a semicircle from its perimeter?
Divide the perimeter by π + 2, about 5.14159. A perimeter of 36 m gives r ≈ 7.0017 m.
What is the arc length of a semicircle?
The curved edge alone is πr, half the circumference of the full circle. For a 7 cm radius it is about 21.99 cm.
Is the Perimeter of Semicircle Calculator free?
Yes. It is completely free, needs no sign-up, and can be used as many times as you like.
Try our Perimeter of Semicircle Calculator to find the distance around any half circle from its radius, diameter or area, in any units.