How to get the area of a circle

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Table of Contents Show

How to Calculate the Area
Example: What is the area of a circle with radius of 3 m ?
How to Remember?
Comparing a Circle to a Square
Example: Compare a square to a circle of width 3 m
A "Real World" Example
Example: Max is building a house. The first step is to drill holes and fill them with concrete.
How to calculate the area of a circle? Area of a circle formula
How to use the area of a circle calculator? Diameter to area and radius to area.
Why do we need the surface area of a circle calculators?
Why is area of a circle π r 2?

images/circle-dia-circ.js

How to Calculate the Area

The area of a circle is:

π (Pi) times the Radius squared:A = π r2

or, when you know the Diameter:A = (π/4) × D2

or, when you know the Circumference:A = C2 / 4π

Example: What is the area of a circle with radius of 3 m ?

Radius = r = 3

Area= π r2

= π × 32

= 3.14159... × (3 × 3)

= 28.27 m2 (to 2 decimal places)

How to Remember?

To help you remember think "Pie Are Squared"
(even though pies are usually round)

Comparing a Circle to a Square

It is interesting to compare the area of a circle to a square:

A circle has about 80% of the area of a similar-width square.
The actual value is (π/4) = 0.785398... = 78.5398...%

Why? Because the Square's Area is w2
and the Circle's Area is (π/4) × w2

Example: Compare a square to a circle of width 3 m

Square's Area = w2 = 32 = 9 m2

Estimate of Circle's Area = 80% of Square's Area = 80% of 9 = 7.2 m2

Circle's True Area = (π/4) × D2 = (π/4) × 32 = 7.07 m2 (to 2 decimals)

The estimate of 7.2 m2 is not far off 7.07 m2

A "Real World" Example

Example: Max is building a house. The first step is to drill holes and fill them with concrete.

The holes are 0.4 m wide and 1 m deep, how much concrete should Max order for each hole?

The holes are circular (in cross section) because they are drilled out using an auger.

The diameter is 0.4m, so the Area is:

A = (π/4) × D2

A = (3.14159.../4) × 0.42

A = 0.7854... × 0.16

A = 0.126 m2 (to 3 decimals)

And the holes are 1 m deep, so:

Volume = 0.126 m2 × 1 m = 0.126 m3

So Max should order 0.126 cubic meters of concrete to fill each hole.

Note: Max could have estimated the area by:

1. Calculating a square hole: 0.4 × 0.4 = 0.16 m2
2. Taking 80% of that (estimates a circle): 80% × 0.16 m2 = 0.128 m2
3. And the volume of a 1 m deep hole is: 0.128 m3

And something interesting for you:

See Circle Area by Lines

Created by Łucja Zaborowska, MD, PhD candidate

Reviewed by Dominik Czernia, PhD and Jack Bowater

Last updated: Aug 26, 2022

The area of a circle calculator helps you compute the surface of a circle given a diameter or radius. Our tool works both ways - no matter if you're looking for an area to radius calculator or a radius to the area one, you've found the right place ◔

We'll give you a tour of the most essential pieces of information regarding the area of a circle, its diameter, and its radius. We'll learn how to find the area of a circle, talk about the area of a circle formula, and discuss the other branches of mathematics that use the very same equation.

How to calculate the area of a circle? Area of a circle formula

So, let's see how to find the area of a circle. There are several ways to achieve it. Here, we can calculate the area of a circle using a diameter or using a radius.

💡 The diameter is the line that crosses the center of the figure and touches both of its margins. The radius begins at the center of the figure and ends at the figure's margin.

You can find the diameter of a circle by multiplying the radius of a circle by two:

Diameter = 2 * Radius

Area of a circle radius. The radius of a circle calculator uses the following area of a circle formula:

Area of a circle = π * r2

Area of a circle diameter. The diameter of a circle calculator uses the following equation:

Area of a circle = π * (d/2)2

Where:

π is approximately equal to 3.14. It doesn't matter whether you want to find the area of a circle using diameter or radius - you'll need to use this constant in almost every case.

🔎 Another relevant aspect of circles is their circumference. You can learn more about it and its relationship with area in our circle formula calculator

Now that you know how to calculate the area of a circle, we encourage you to try our other circle calculators:

All-in-one circle tool;
Circle circumference and perimeter;
Sector of a circle;
Pie chart;
Area of largest circle in a square.

A sector of a circle is section of a circle between two radii. You can think of it as a giant slice of pizza.

Segment of a circle;

It's a "cut-off" part of a circle, limited by a chord or a secant.

Circle angle;

It's an angle with the vertex in the center, whose arms extend to the circumference.

Semicircle area; and
If you want to know how to draw a circle?, the equation for the coordinates and the center of a circle in the coordinate system might come in handy.

How to use the area of a circle calculator? Diameter to area and radius to area.

You can easily calculate everything, the area of a circle, its diameter, and its radius, using our area of a circle calculator in a blink of an eye:

Determine whether your given value is a diameter or a radius using the picture on the right and definitions available in the section above (you can calculate the area of a circle using its diameter as well as radius).
Enter your value into the proper field of the calculator.
It didn't take long - your results are here! We decided to include the step-by-step solution and all the most important data right below the calculator.

That is how to calculate the area of a circle in no time 😉.

🔎 The area is not the only property related to the diameter, as the circumference is too. Learn more about it in our circumference to diameter calculator.

Why do we need the surface area of a circle calculators?

The circle's area found with both the radius and diameter calculators serves as a base for many other equations - not only in mathematics but also in everyday life! Here are a few examples where knowing how to find the area of a circle might be useful:

We need to know the surface area of a circle in order to calculate a cone's volume and its surface area 🎉
Your pizza party wouldn't be complete without our pizza tool based on the diameter to area calculator 🍕
We use calculations similar to this one when obtaining information about a sphere, such as sphere volume.🌐
Do you fancy nice dresses? Maybe you love to sew? Discover our circle skirt calculator! Efficient sewing has never been easier. 👗

Łucja Zaborowska, MD, PhD candidate

Arc lengthCircle calc: find c, d, a, rCircumference… 5 more

Why is area of a circle π r 2?

The usual definition of pi is the ratio of the circumference of a circle to its diameter, so that the circumference of a circle is pi times the diameter, or 2 pitimes the radius. ... This give a geometric justification that the area of a circle really is "pi r squared".

area circle