Circumference and Area of a Circle Calculator

Created by Luis Hoyos
Reviewed by Wojciech Sas, PhD candidate
Last updated: Sep 25, 2022

Are you interested in calculating the area and circumference of a circle and the formula behind it? This is the perfect tool.

Circles are present in many places. Coins, pizzas, and vinyl disks are examples of circular objects, and the area is an essential aspect of them.

Read on if you're interested in:

  • How to find the area and circumference of a circle.
  • How the circumference and area of a circle relate to each other.
  • How to find the area of a quarter circle.

💡 Did you know
The diameter and, therefore, the area of a pizza are critical in determining the optimum pizza size for your budget and taste. In fact, we have a pizza size calculator for your delight.

Formula to calculate the circumference and area of a circle

These are the formulas to calculate the circumference and area of a circle:

c = 2πr
A = πr² = πd²/4

, where:

  • c stands for circumference;
  • r for radius; and
  • d for the diameter of the circle.

π is a constant approximately equal to 3.14159265359 and, among other things, represents the circumference-to-diameter ratio of any circle.

How to find the circumference and area of a circle?

Suppose you want to know how to find the circumference and area of a circle with an 8 cm radius. In that case, these would be the steps to follow:

  1. Use the formulas to calculate the circumference and area: c = 2πr and A = πr².
  2. The circumference should equal c = 2π × 8 cm = 50.265 cm.
  3. The area should equal A = π × (8 cm)² = 201.06 cm².
  4. To check your results, input the 8 cm diameter in the calculator. The results should also be 50.265 cm and 201.06 cm².

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How are the circumference and area of a circle related?

They relate to each other by the following formula: c = 2√(πA). The equation says circumference is proportional to the square root of the area, so the bigger the circle size, the greater the circumference.

What is the area of a 9-inch circle?

63.617 in². To find the area of any circle, given its diameter:

  1. Multiply π (pi) by the diameter square: π × (9 in)² = 254.47 in².
  2. Divide that result by four:
    254.47 in²/4 = 63.617 in².
  3. Now you know what the area of a 9-inch circle is ✔️

How do I find the area of a quarter-circle?

To get the area of a quarter-circle:

  1. Take the formula of the area of an ordinary circle: A = πr².
  2. Divide that formula by four.
  3. After following these steps, we can note that the area of a quarter circle is A = πr²/4.
Luis Hoyos
Image of a circle with radius, diameter, circumference and area marked.
Radius (r)
Diameter (d)
Circumference (c)
Area (A)
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