Last updated: Jul 01, 2024

Circle Formula Calculator

Q: What is the formula for the perimeter of a half-circle?

π (pi) times radius p half = πr. The formula for the perimeter of a half-circle is the same formula for the circle circumference, divided by two. That results in the product of π (pi) and the radius.

Q: What is the radius of a 3.65-inch diameter circle?

1.825 in . The formula for the diameter of a circle says the diameter is twice the radius. To find the radius, simply divide the diameter by two: r = 3.65 in / 2 = 1.825 in .

Created by Luis Hoyos

Luis Hoyos

Luis Hoyos is a fresh graduate Mechanical Engineer with thermodynamics and fluids mechanics expertise. He's interested in learning new things and applying them to real-life problems. Luis also likes to build tools that make repetitive and boring tasks a breeze, like calculators (surprise?). When he's not creating calculators, he's in the process of building the size of the tissue attached to his bones, aka bodybuilding. He also loves being with his little cat and seeing her do crazy things. See full profile

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Wojciech Sas

PhD, Institute of Physics in Zagreb

A physicist at the Institute of Nuclear Physics in Kraków. Currently looking for that one and only magnetic nanomaterial that will improve everyone's life. Interested in astronomy and likes playing board games. Also, fond of watching chess tournaments; he never refuses to play a game (or two) himself. See full profile

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Table of contents

Circle formulas How to use the area and circumference of a circle formula — An example Other helpful tools like the circle formula calculator FAQs

The circle formula calculator allows you to make circle calculations easily. Keep reading to learn things like:

The formula to calculate the diameter of a circle given its radius, or vice versa.
What is the formula for calculating the circumference of a circle?
What is the formula for the area of a circle?

Circle formulas

Although using the circle formula calculator is the fastest way to make circle calculations, it's crucial to know the formulas to understand the process better.

Formula to calculate the diameter of a circle given its radius, or vice versa

The formula of the diameter of a circle is the most straightforward of the equations and says that diameter (d) equals twice the radius (r):

d = 2r
r = d/2

The calculation of circumference and area of a circle formulas are more tricky. Look at the equations in the following sections.

Formula to calculate the circumference of a circle

The formula of the circle circumference (c) can be expressed in terms of radius, diameter, and area (A):

c = 2πr
c = πd
c = 2√(πA)

Formula to calculate the area of a circle

We can express the formula to calculate the area of a circle in terms of the radius, diameter, and circumference:

A = πr²
A = πd²/4
A = c²/(4π)

How to use the area and circumference of a circle formula — An example

Suppose you have a circle of radius 3 cm. If you want to calculate its area and circumference, you can do it by following these steps:

Input the radius in the circle area formula:

A = π × (3 cm)² = 28.2743 cm²
Also, input the radius in the circumference formula:

c = 2π × (3 cm) = 18.8496 cm
Check your results with the circle formula calculator. The results should also be 28.2743 cm² and 18.8496 cm for area and circumference.

Other helpful tools like the circle formula calculator

Now that you know how to calculate the formula of circumference and area of a circle, take a look 👀 at other calculators:

FAQs

What is the formula for the perimeter of a half-circle?

π (pi) times radius p_half = πr. The formula for the perimeter of a half-circle is the same formula for the circle circumference, divided by two. That results in the product of π (pi) and the radius.

What is the radius of a 3.65-inch diameter circle?

1.825 in. The formula for the diameter of a circle says the diameter is twice the radius. To find the radius, simply divide the diameter by two: r = 3.65 in / 2 = 1.825 in.