Diameter of a Circle Calculator

This calculator works out the diameter of a circle from whichever measurement you already have to hand: the radius, the area, or the circumference. Select which one you know from the dropdown, type in that value, and choose how many decimal places you want in the answer. The calculator instantly returns the diameter alongside the matching radius, circumference and area, so you get every dimension of the circle in one go rather than working through several formulas by hand. Behind the scenes it applies the standard geometry relationships: doubling the radius, dividing the circumference by pi, or rearranging the area formula and taking a square root before doubling the result. The results panel also shows the exact formula and working used for your chosen input, so you can see how the answer was reached and check it against your own figures if needed. This is useful for maths homework, checking measurements on an engineering or construction drawing, sizing pipes and ducts, or working out how much material you need to cut a circular shape from. Pi is calculated to eight decimal places for accuracy, and no unit conversion is applied, so the diameter, radius, circumference and area are all returned in the same unit you entered, whether that is millimetres, centimetres, metres or any other consistent unit.

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Method verified  Standard Euclidean geometry formulas for a circle.

1. What Do You Know?

units

2. About the Formula

From radiusd = 2r
From aread = 2 x sqrt(A / pi)
From circumferenced = C / pi
Value of pi used3.14159265

Your Circle's Dimensions

Diameter
10.00
d = 2r
Radius
5.00
r = d / 2
Circumference
31.42
C = pi x d
Area
78.54
A = pi r²

Calculation Steps

You entered5.00 (radius)
Formula usedd = 2r = 2 x 5.00 = 10.00
Diameter10.00 units

All Circle Measurements

Radius5.00 units
Diameter10.00 units
Circumference31.42 units
Area78.54 sq units

How to Find the Diameter of a Circle

The diameter of a circle is the straight-line distance across the circle, passing through its centre. It is the longest chord you can draw inside a circle. Depending on what you already know about the circle, there are three common ways to work out its diameter.

From the Radius

This is the simplest method. The radius is the distance from the centre of the circle to any point on its edge, and the diameter is always exactly twice the radius:

d = 2r

For example, if the radius is 5 cm, the diameter is 2 x 5 = 10 cm.

From the Area

The area of a circle is given by A = pi r^2. To find the diameter from the area, first rearrange this formula to solve for the radius, then double the result:

r = sqrt(A / pi) and then d = 2r

For example, if the area is 78.54 square cm, dividing by pi (3.14159) gives 25, and the square root of 25 is 5. Doubling gives a diameter of 10 cm.

From the Circumference

The circumference is the total distance around the outside of the circle, given by C = pi x d. Since the diameter and circumference are directly proportional, you can find the diameter by dividing the circumference by pi:

d = C / pi

For example, if the circumference is 31.42 cm, dividing by pi gives a diameter of 10 cm.

Diameter Formulas at a Glance

You knowFormula for diameterExample
Radius (r)d = 2rr = 5 → d = 10
Area (A)d = 2 x sqrt(A / pi)A = 78.54 → d = 10
Circumference (C)d = C / piC = 31.42 → d = 10

Once you have the diameter, you can easily find the other measurements: the radius is half the diameter, the circumference is pi multiplied by the diameter, and the area is pi multiplied by the radius squared.

Where This Is Used

Finding the diameter of a circle is a common task in maths homework, engineering drawings, construction (such as pipe or duct sizing), and DIY projects (such as cutting a circular piece of material). Knowing the diameter lets you quickly work out how much material fits inside a circular space, or check that a round object will fit through a gap.

Related Calculators

Sources: Standard Euclidean geometry formulas for circles (National Institute of Standards and Technology, NIST Digital Library of Mathematical Functions, dlmf.nist.gov).

This calculator uses pi to 8 decimal places (3.14159265) for accuracy. Results are rounded to the number of decimal places you select. Units are not converted, so the diameter is returned in the same units as the value you enter.

Frequently asked questions

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

The diameter is always twice the radius: d = 2r. The radius is the distance from the centre of the circle to its edge, and the diameter is the full distance across the circle through the centre. For example, a circle with a radius of 5 cm has a diameter of 10 cm.

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

Rearrange the area formula A = pi r^2 to solve for the radius, then double it. First divide the area by pi and take the square root to get the radius: r = sqrt(A / pi). Then multiply by 2 to get the diameter: d = 2 x sqrt(A / pi). For example, a circle with an area of 78.54 square cm has a diameter of about 10 cm.

How do you find the diameter of a circle from the circumference?

Divide the circumference by pi: d = C / pi. Circumference and diameter are directly proportional, and pi (approximately 3.14159) is the constant ratio between them. For example, a circle with a circumference of 31.42 cm has a diameter of 10 cm.

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