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 .

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Luis Hoyos

Luis is a mechanical engineer who works at Omni Calculator as a content creator and researcher specializing in math and physics calculators with a focus on thermodynamics and classical mechanics. With a strong foundation in mechanical engineering, Luis is passionate about creating tools that simplify complex concepts and improve everyday life. Outside of work, Luis likes weightlifting and applying his engineering knowledge to optimize the thermal conditions of his home, all while caring for four beloved cats. See full profile

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Wojciech Sas, PhD

Wojciech Sas

PhD, Institute of Physics in Zagreb

Wojciech, PhD, is a physicist at the Institute of Physics in Zagreb, investigating materials under extreme conditions such as low temperatures and high pressures. He specializes in experimental work, including participation in Large-scale User Facilities such as synchrotrons. Wojciech uses his experience and knowledge to create calculators in physics, math, and statistics categories. In his free time, he likes swimming, playing board games, and looking for meteors while stargazing. See full profile

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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.