Semicircle Area Calculator

Calculate area, perimeter, and arc length of any semicircle from radius, diameter, or area.

What is a Semicircle?

A semicircle is exactly half of a circle, formed by cutting a complete circle along its diameter. The boundary of a semicircle consists of two parts: the curved arc (which is exactly half the circumference of the full circle) and the straight diameter (the flat edge created by the cut). Together, these form the complete perimeter of the semicircle.

The semicircle is one of the most commonly encountered geometric shapes in the real world. Arched windows and doorways, tunnel cross-sections, the D-shaped area in football and basketball courts, protractors, and half-round mouldings are all semicircular. Understanding how to calculate the area and perimeter of a semicircle is essential knowledge in architecture, civil engineering, product design, and everyday practical geometry.

The area of a semicircle is always exactly half the area of the full circle with the same radius. Since a full circle has area pi times r squared, the semicircle area is pi times r squared divided by 2. The arc length (curved portion) is exactly half the circumference of the full circle, giving pi times r. The total perimeter includes both the arc and the straight diameter, totalling r times (pi + 2), which is approximately 5.14159 times the radius.

What makes the semicircle particularly useful to work with is that you only need one measurement to calculate everything else. If you know the radius, diameter, or even just the area, this calculator derives all other properties instantly. The relationships between radius, diameter, arc, area, and perimeter are all direct consequences of the circle formulas divided by two, making them elegant and straightforward to remember.

In engineering applications, the centroid (centre of mass) of a semicircular area is located at a distance of 4r/(3pi) from the flat diameter, approximately 0.4244 times the radius. This is important for structural calculations involving semicircular cross-sections in beams, plates, and arches.

Formula and Derivation

All semicircle formulas are derived from the corresponding full circle formulas, divided by 2 where applicable.

Given radius r:

Area = πr² / 2

r = Radius of the semicircle

π = Pi ≈ 3.14159265

Arc length = πr

This is exactly half the circumference of the full circle (2πr / 2 = πr)

Perimeter = πr + 2r = r(π + 2)

Includes curved arc (πr) plus straight diameter (2r)

Given diameter d: r = d / 2, then apply the radius formulas above.

Given area A:

r = √(2A / π)

Rearrange A = πr²/2 to solve for r

How to Use This Calculator

Select your input type - click the tab for “Radius”, “Diameter”, or “Area” depending on which measurement you know. All three modes compute the same complete set of results.
Enter your value - type any positive number. For radius and diameter, use a length unit (cm, m, inches, feet). For area, use square units.
Click Calculate - the calculator immediately shows the radius, diameter, area, arc length, and perimeter.
Check the formula note - the grey box below the results shows the exact calculations performed, making it easy to verify results or understand the method.
Share or print - use the action buttons to copy results to the clipboard, print the page, get a shareable link, or send results via WhatsApp.

Example Calculations

Example 1 - Radius of 7 units

A semicircular window has a radius of 7 cm. Find its area and frame length (perimeter).

r = 7 cm. Diameter = 2 × 7 = 14 cm

Area = π × 7² / 2 = 3.14159 × 49 / 2 = 76.969 cm²

Arc = π × 7 = 21.991 cm

Perimeter = 7 × (π + 2) = 7 × 5.14159 = 35.991 cm

Area = 76.969 cm² | Arc = 21.991 cm | Perimeter = 35.991 cm

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Example 2 - Diameter of 10 units

A semicircular tunnel has a diameter of 10 m. Find the cross-sectional area and curved tunnel lining length.

d = 10 m, so r = 10 / 2 = 5 m

Area = π × 5² / 2 = 3.14159 × 25 / 2 = 39.270 m²

Arc = π × 5 = 15.708 m (length of curved lining)

Perimeter = 5 × (π + 2) = 5 × 5.14159 = 25.708 m

Radius = 5 m | Area = 39.270 m² | Arc = 15.708 m

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Example 3 - Area of 25 square units

A garden bed has a semicircular area of 25 sq m. Find the radius and the length of edging needed.

A = 25 sq m. r = √(2 × 25 / π) = √(50 / 3.14159) = √(15.915) = 3.989 m

Arc = π × 3.989 = 12.530 m

Perimeter (total edging) = 3.989 × (π + 2) = 3.989 × 5.14159 = 20.510 m

Diameter = 2 × 3.989 = 7.978 m

Radius ≈ 3.989 m | Arc ≈ 12.530 m | Perimeter ≈ 20.510 m

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Example 4 - Radius of 3 units

A small semicircular gasket has a radius of 3 mm. Find all dimensions for the manufacturing specification.

r = 3 mm. Diameter = 6 mm

Area = π × 9 / 2 = 14.137 mm²

Arc length = π × 3 = 9.425 mm

Perimeter = 3 × (3.14159 + 2) = 3 × 5.14159 = 15.425 mm

Area = 14.137 mm² | Arc = 9.425 mm | Perimeter = 15.425 mm

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Frequently Asked Questions

What is the area of a semicircle?+

The area of a semicircle is A = pi times r squared divided by 2, where r is the radius. It is exactly half the area of a full circle. For a semicircle with radius 7 cm, Area = 3.14159 times 49 / 2 = 76.969 sq cm. If you know the diameter d, the radius is r = d / 2.

What is the perimeter of a semicircle?+

The perimeter (total boundary length) of a semicircle = arc length + diameter = pi times r + 2r = r(pi + 2). For radius 7, perimeter = 7 times (3.14159 + 2) = 7 times 5.14159 = 35.991 cm. The perimeter includes both the curved arc and the straight flat edge.

What is the arc length of a semicircle?+

The arc length (curved edge only) of a semicircle = pi times r, which is half the circumference of the full circle. For radius 5 cm, arc = 3.14159 times 5 = 15.708 cm. Note that the arc length does not include the straight diameter edge.

How do I find the radius from the area of a semicircle?+

Rearrange A = pi r squared / 2 to get r = sqrt(2A / pi). For example, if area = 25 sq cm, r = sqrt(2 times 25 / 3.14159) = sqrt(50 / 3.14159) = sqrt(15.915) = 3.989 cm approximately 4 cm.

What is the formula for the diameter of a semicircle?+

The diameter is simply twice the radius: d = 2r. The diameter forms the straight flat edge of the semicircle. If you know the area A, then d = 2 times sqrt(2A / pi).

What is the difference between a semicircle and a half circle?+

A semicircle and a half circle are the same thing - a semicircle is literally half of a circle, formed by cutting a full circle along its diameter. The semicircle shape includes both the curved arc (half circumference) and the straight diameter edge.

How is the semicircle perimeter different from the arc length?+

The arc length is only the curved part of the semicircle boundary: arc = pi times r. The full perimeter includes both the arc and the straight diameter: perimeter = pi times r + 2r = r(pi + 2). For radius 5, arc = 15.708, perimeter = 25.708.

What are practical uses of semicircle area calculations?+

Semicircle area calculations appear in architecture (arched windows and doorways), civil engineering (tunnel cross-sections), sports (semicircular playing areas like the D in football), and manufacturing (half-round gaskets and seals). Any curved structure that is half a circle requires these formulas.

How does the semicircle area relate to the full circle area?+

The area of a semicircle is always exactly half the area of the full circle with the same radius. Full circle area = pi r squared. Semicircle area = pi r squared / 2. Similarly, the arc of a semicircle is half the circumference of the full circle.

What is a semicircle with radius 3?+

For radius r = 3: Area = pi times 9 / 2 = 14.137 sq units. Arc length = pi times 3 = 9.425 units. Perimeter = 3 times (pi + 2) = 3 times 5.14159 = 15.425 units. Diameter = 6 units.

Semicircle Area Calculator

What is a Semicircle?

Formula and Derivation

How to Use This Calculator

Example Calculations

Example 1 - Radius of 7 units

Example 2 - Diameter of 10 units

Example 3 - Area of 25 square units

Example 4 - Radius of 3 units

Frequently Asked Questions

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