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Area of a Semicircle

Phoebe Belza-Barrientos

Updated on February 11, 2026

Various everyday objects, such as protractor shapes and railway tunnels, resemble a semicircle in a two-dimensional plane. In today’s Brighterly article, we will learn how to find area of a semicircle, the semicircle area formula, and explore some examples of semicircle. 

What is a semicircle?

A semicircle is a shape formed by dividing a circle into two equal halves. It consists of the points forming half of a circle. A semicircle has an arc of 180 degrees, which equals π radians. As a semicircle exhibits only reflection symmetry, it only has one line of symmetry.

What is the area of a semicircle?

A semicircle’s area is the amount of space enclosed within its boundary. See the following figure, which shows that the colored area within the semicircle’s boundary is its occupied area. 

A semicircle’s area is measured in square units, such as

cm², in², ft², m², etc.

How to find the area of a semicircle?

You can find the area of a semicircle using either the radius or the diameter with the appropriate formula.

• Step 1. Take note of the radius or diameter of the semicircle, whichever is given. Use the value of π as 22/7 or 3,14
• Step 2. To find the area of a semicircle, apply the appropriate semi circle area formula. When the radius is given, we use the formula of area of semi circle = (π × r²) / 2, (r —  radius). When the diameter is known, we use the formula, Area of Semicircle = (π × d²) / 8, (d — diameter).
• Step 3. In square units, solve the equation and mention the area.

Area of semicircle formula

A semicircle is half of a full circle, and the same concerns its area. The formula using the radius (r) is:

Area = πr²/2

To find the semi circle area, square the radius, multiply by pi (approximately 3.14 or 22/7), and divide the result by two.

Area of a semicircle using diameter

When the diameter (d) is known, the area of a semicircle is calculated using:

Area = πd²/8

Alternatively, divide the diameter by two to find the radius, then apply the standard radius area of half circle formula. Since d^2 = 4r^2, dividing by 8 accounts for both the radius conversion and the semicircular shape. It is an original half circle area formula.

Derivation of area of a semicircle formula

Below is an image that explains how to derive the area of a semicircle.

Since the area of a circle is A = πr², the area of a semicircle is A = (πr²)/2. That’s because a semicircle is half of the area of a circle (just like its name suggests).

Examples on the area of semicircle

Example 1: How to calculate the area of a football ball if its radius is 7?

Solution: Area of semicircle = πr² / 2 = 3,14×7×7 / 2 = 3,14 x 49/2 = 76.93 cm²

Example 2:  How to find the area of a semicircle with a diameter of 20 m?

Solution: Area of semicircle = πd² / 8  = 3,14×20×20/ 8 = 3,14 x 400/8 = 3,14 x 50 = 157,14 m²

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Practice questions on the area of semicircle

Problem 1: How to calculate a pizza’s size if the diameter of one semicircular slice is 14 cm?

Problem 2: If a garden bed is shaped like a semicircle with a diameter of 6 cm, how do you find its perimeter?

Problem 3: Find the circumference of a semicircular plate whose diameter is 12 cm.

Problem 4: An apple slice is semicircular with a radius of 10 cm. What is its perimeter?

Problem 5: Calculate the area of a glass’s half-circular top if the radius of the semicircle is 7 cm.

Conclusion

As we discovered in this article, a semicircle is half of a circle, and now we know how to find area of a semicircle with diameter. 

As a matter of fact, the area of a semicircle is the area of a half circle. In terms of radius ‘r’, the area of a circle is πr². When we talk about a semicircle, the area is calculated with the formula πr²/2. 

Frequently asked questions on area of a semicircle

What is the difference between a semicircle and a circle?

A circle is a complete round figure, while a semicircle is half of a circle formed by cutting it along the diameter.

How to find the area of a semi circle?

To find the area of a semicircle, we use the formula Area = πr² ÷ 2. Also, we can do it by knowing the diameter, Area = πd2/8

Can a semicircle be called a half-circle?

Yes, a semicircle can be called a half-circle. It is because, in reality, a semicircle is half of a circle.

How do you find the circumference of a semicircle?

To find the circumference, we usually add half the circle’s circumference (πr) to the diameter (2r).

Phoebe Belza-Barrientos

23 articles

Phoebe Belza-Barrientos is a Brighterly math tutor with 13 years of teaching background. Math is far more than just another basic subject for Phoebe; it’s a passion she now channels into every lesson. She builds study materials in a way that her students begin to feel the same discovery and enjoyment as she did in her school years.