Semicircle Area Calculator

Created by Hanna Pamuła, PhD candidate
Reviewed by Bogna Szyk and Jack Bowater
Last updated: Oct 26, 2022

With this semicircle area calculator, you can quickly find the area of half of a circle. What is more, the tool also doubles as a semicircle perimeter calculator, so inputting radius or diameter will help you find the basic features of the shape in the blink of an eye. In the article below, we provide the semicircle definition and explain how to find the perimeter and area of a semicircle. So what are you waiting for? Scroll down!

However, if you're searching for a moment of inertia of a semicircle, check out our comprehensive moment of inertia calculator.

What is a semicircle? Semicircle definition

A semicircle is simply half of a circle 🌗. You'll get a semicircle when you cut a circle along a diameter line - or, in other words, through the circle center. The prefix semi- comes from Latin, meaning half or partly (like in words such as semi-permanent, semi-formal, and semifinal). Now, when you know the etymology, you won't forget what a semicircle is: just remind yourself how the semifinals are connected with the finals, and you'll know how to link a semicircle to a circle.

How to find the area of a semicircle? Semicircle area formula

Knowing the semicircle definition – half of a circle – we can easily write the semicircle area formula using the well-known circle area, $\pi\cdot r^2$:

A_{\mathrm{semicircle}} = \frac{A_{\mathrm{circle}}{2} = \frac{\pi\cdot r^2}{2}

The area of a semicircle is just half of the area of a full circle. But can we use this rule for the circumference of a semicircle?

Perimeter of a semicircle formula (aka circumference of a semicircle)

If you want to calculate the outer boundary of a semicircle – the circumference or perimeter of a semicircle – you need to be careful not to fall into any traps. The circumference of a semicircle is not equal to half of the circle circumference - you need to add also the diameter of the semicircle, as another boundary was created:

$P_{\mathrm{semicircle}} = \frac{P_{\mathrm{circle}}}{2} + 2\cdot r$

Then:

$P_{\mathrm{semicircle}} = \pi\cdot r + 2\cdot r = r\cdot (\pi+2)$

Or:

$P_{\mathrm{semicircle}} = \pi\cdot r + d$

Where $d$ is the semicircle diameter

Find the area of a half circle with semicircle area calculator

Where do we find semicircular objects in everyday life? The shape of a half circle occurs in:

• Home furniture and decorations such as mirrors, tables with semicircular counters, sofas, benches, rugs, or even windows.
• Everyday objects like fans, protractors, circle skirts.
• All food that comes in round, cylindrical, or sphere shapes could also be sliced to approximate semicircles. For example, half a pizza, a slice of watermelon 🍉 or half a cookie 🍪

Let's figure out how to find an area of a semicircular object – a rug that would fit perfectly in front of your fireplace🔥:

1. Input the diameter or radius of the rug. Assume that our fireplace is $4\ \mathrm{ft}$ wide, so we'd like to have the same rug length. Enter $4\ \mathrm{ft}$ in the diameter box. Change the length units by clicking on the unit name and selecting the one you need from the drop-down list.
2. The semicircle area calculator displays the area of half-circle: for our rug, it's $6.28\ \mathrm{ft^2}$.
3. The tool works as semicircle perimeter calculator as well – e.g., if you want to braid the rug, you can calculate how much lace you'll need. In our case, the perimeter equals $10.28\ \mathrm{ft}$.

Now, as you know everything about semicircles, maybe you'd like to check our other circle-related calculators 🔴?

Hanna Pamuła, PhD candidate
in
Diameter (d)
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Semicircle Area and Perimeter
Area (A)
in²
Perimeter (L)
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