Area of a Circle Calculator

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.

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.

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.

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.

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.

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:

1. 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).

2. Enter your value into the proper field of the calculator.

3. 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 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 👗.

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.

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.

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

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

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.

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.