How do you find the radius of a circle from the area?

Reverse the area formula A equals pi times r squared. Divide the area by pi, then take the square root: r equals the square root of (A divided by pi). An area of 50 gives a radius of about 3.99.

Pi is the ratio of any circle's circumference to its diameter, about 3.14159, the same for every circle. It is irrational, so its decimals never end, which is why circle answers are usually rounded.

Circle Calculator

Q: How do you find the radius from the circumference?

Divide the circumference by 2 pi. Since C equals 2 pi r, rearranging gives r equals C divided by (2 pi).

Q: How do you find the area of a circle from its diameter?

Halve the diameter to get the radius, then use A equals pi r squared. In one step that is A equals pi times (d divided by 2) squared, the same as pi d squared divided by 4.

Q: How do you find the diameter from the circumference?

Divide the circumference by pi. Because C equals pi d, it follows that d equals C divided by pi.

Enter any one of radius, diameter, circumference or area, and the other three appear instantly — drawn to scale. You can also click a value on the drawing to change it.

Known value

from radius

Enter any one value — the rest update automatically.

Radius (r)

Diameter (d)

Circumference (C)

Area (A)

Units Decimals

Click an amber value to edit it · not to printed scale

Results

Circle formulas

A circle is set by a single measurement, so any one of the four values gives the rest. The radius is the link between them all.

Area · A = π r²

Circumference · C = 2 π r = π d

Diameter · d = 2 r

Working backwards

From the circumference, the radius is C ÷ (2π); from the area, it's the square root of A ÷ π. Once the radius is known, everything else follows directly.

Tips

Pick your units in the Display row — areas are shown in square units automatically. Increase the decimals if you need more precision for engineering or drafting work.

Working with circles

A circle is the simplest shape to calculate, because it's defined by a single measurement. Give the calculator any one of the four values — radius, diameter, circumference or area — and it works out the other three. The radius is the hub that connects them all: once you know it, everything else is one short step away.

How the four values connect

Diameter is just twice the radius: d = 2r. It's the distance straight across the circle through the centre.
Circumference is the distance around the edge: C = 2πr, which is the same as πd.
Area is the space inside: A = πr². Because the radius is squared, area grows much faster than the radius does.
π (pi) is the constant link between a circle's width and its perimeter — about 3.14159 — and it appears in every circle formula.

Worked example: starting from the area

Say you know a circle's area is 50 square units and you need its radius, diameter and circumference. Going "backwards" from the area just means undoing the A = πr² formula.

Step 1 — radius, by reversing the area formula

Divide by π, then take the square root:

r = √(A ÷ π) = √(50 ÷ 3.14159) = √15.915 = 3.9894

Step 2 — diameter

d = 2r = 2 × 3.9894 = 7.9788

Step 3 — circumference

C = 2πr = 2 × 3.14159 × 3.9894 = 25.0663

Result

A circle of area 50 has radius 3.9894, diameter 7.9788 and circumference 25.0663. Type 50 into the area field above and you'll see exactly these values, with the circle drawn and dimensioned.

Formulas this calculator uses

Area · A = π r²

Circumference · C = 2 π r = π d

Diameter · d = 2 r

Radius from area · r = √(A ÷ π)

Radius from circumference · r = C ÷ (2 π)

Frequently asked questions

How do you find the radius from the area?

Reverse the area formula A = πr². Divide the area by π, then take the square root: r = √(A ÷ π). For example, an area of 50 gives a radius of about 3.99.

How do you find the radius from the circumference?

Divide the circumference by 2π. Since C = 2πr, rearranging gives r = C ÷ (2π). A circumference of about 25.07 gives a radius of roughly 3.99.

How do you find the area of a circle from its diameter?

Halve the diameter to get the radius, then use A = πr². Combined into one step that's A = π(d ÷ 2)², which is the same as πd² ÷ 4.

What's the difference between diameter and circumference?

The diameter is the straight distance across the circle through its centre. The circumference is the distance all the way around the edge. They're linked by π: the circumference is always π times the diameter.

What is π (pi)?

Pi is the ratio of any circle's circumference to its diameter — the same value, roughly 3.14159, for every circle. It's an irrational number, so its decimals never end or repeat, which is why circle answers are usually rounded.

How do you find the diameter from the circumference?

Divide the circumference by π. Because C = πd, it follows that d = C ÷ π. No need to find the radius first.