Area of a Circle Calculator

Q: What is the radius of a circle of area 10?

The radius is approximately equal to 1.784 . The precise answer is √(10 / π) . To get this result, recall the formula area = π × r 2 . We transform it to the form r 2 = area / π , and so we see that the radius is equal to the square root of area / π . Plugging in area = 10 , we obtain: radius = √(10 / π) ≈ √(10 / 3.14) ≈ √3.185 ≈ 1.785 .

Q: How do I find the circumference of a circle given area?

To determine the circumference of a circle from its area , follow these steps: Multiply the area by π. Take the square root of the result from Step 1. Multiply by 2. You found the circle's circumference from its area! Well done!

Q: Can the area and circumference of a circle be equal?

Yes , the area and circumference of a circle have the same value 4π if the radius of the circle has length 2 . Remember, however, that the units are different! The circumference has length units , and the area has, well, area units .

Q: Can the area and radius of a circle be equal?

Yes , take a circle with radius r = 1/π . Then its area is equal to πr 2 = π(1/π) 2 = 1/π , so it has the same value as the radius. Remember, however, that the units differ ! The radius and area have, respectively, length and area units; for instance, in and in sq.

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Łucja Zaborowska, MD, PhD candidate

Łucja Zaborowska

MD, PhD candidate

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Łucja is a physician and researcher specializing in obstetrics and gynecology. She is currently pursuing a Ph.D. in Medical Sciences at the Jagiellonian University in Cracow, Poland. Her engagement in the subject is extensive, including academics, research, and clinical practice. In addition to her main duties, she also lectures at the university and oversees student research groups. On a personal note, her love for dogs has inspired her to start fostering, giving them a safe place to stay until they find their forever homes. See full profile

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Dominik Czernia, PhD

Dominik Czernia

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Dominik Czernia, PhD, is a physicist at the Institute of Nuclear Physics in Kraków, specializing in condensed matter physics with a focus on molecular magnetism. He has led several national research projects, pioneering innovative approaches to novel materials for high technology. Passionate about making science accessible, Dominik has created various calculators, mostly in physics and math categories. In his free time, he enjoys family walks, city explorations, mountain hiking, and traveling everywhere by bike. See full profile

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and Jack Bowater

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

The formula to calculate the area of a circle using radius is as follows:

Area of a circle = π × r²

And, to calculate the area of a circle using diameter use 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 discover similar topics:

Circle circumference and perimeter.
Pie chart.
Area of the incircle of a square, that is, of the largest circle that fits inside the square.
Sector of a circle — this is a section of a circle between two radii. You can think of it as a giant slice of pizza.

Sector of a circle and the formula for calculating the area of a such a sector.

Also, why don't you try our other circle calculators:

Segment area of a circle calculator:

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

Central angle calculator:

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

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

Special lines of the circle - diameter, radius, chord, and circumference.

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 estimating the pizza's size based on the diameter to area calculator 🍕.
We use calculations similar to this one when obtaining information about a sphere, such as a sphere volume 🌐.
Do you fancy nice dresses? Maybe you love to sew? Efficient sewing of circle skirts has never been easier 👗.

FAQs

How do I calculate the diameter of a circle given area?

The formulas linking the diameter and area of a circle reads area = π × (diam/2)² and diam = 2 × √(area / π). For instance, the diameter of a circle with unit area is approximately equal to 1.128 because diam = 2 × √(1 / π) ≈ 1.128.

What is the radius of a circle of area 10?

The radius is approximately equal to 1.784. The precise answer is √(10 / π). To get this result, recall the formula area = π × r². We transform it to the form r² = area / π, and so we see that the radius is equal to the square root of area / π. Plugging in area = 10, we obtain:

radius = √(10 / π) ≈ √(10 / 3.14) ≈ √3.185 ≈ 1.785.

How do I find the circumference of a circle given area?

To determine the circumference of a circle from its area, follow these steps:

Multiply the area by π.
Take the square root of the result from Step 1.
Multiply by 2.
You found the circle's circumference from its area! Well done!

Can the area and circumference of a circle be equal?

Yes, the area and circumference of a circle have the same value 4π if the radius of the circle has length 2. Remember, however, that the units are different! The circumference has length units, and the area has, well, area units.

Can the area and radius of a circle be equal?

Yes, take a circle with radius r = 1/π. Then its area is equal to πr² = π(1/π)² = 1/π, so it has the same value as the radius. Remember, however, that the units differ! The radius and area have, respectively, length and area units; for instance, in and in sq.