Diameter of a Circle Calculator
Enter any one measurement of a circle - its radius, circumference, area, or diameter - and this calculator instantly finds all the others. Choose metric or imperial units, then read the step-by-step working that shows exactly how each value was derived.
Formula
Worked example
A circle with radius 5 cm has diameter 2 x 5 = 10 cm, circumference 3.14159 x 10 = 31.416 cm, and area 3.14159 x 25 = 78.540 cm squared.
What is the diameter of a circle?
The diameter of a circle is the longest straight line you can draw from one edge of the circle to the other, passing directly through the center. It is exactly twice the radius (d = 2r) and is the single most intuitive measurement of a circle's size. When a pipe, coin, wheel, or pizza is described by its size, that size is almost always the diameter. The circumference (the total distance around the outside) equals pi times the diameter, so C = pi x d, which is approximately 3.14159 times the diameter. The area enclosed by the circle is pi times the square of the radius, or A = pi x r squared.
How to calculate the diameter from any circle measurement
You only ever need one measurement to find all the others: - From the radius: d = 2 x r. If the radius is 7 cm, the diameter is 14 cm. - From the circumference: d = C / pi. If the circumference is 62.83 cm, divide by 3.14159 to get 20 cm. - From the area: d = 2 x square root of (A / pi). If the area is 314.16 cm squared, divide by pi to get 100, then take the square root (10), and double it to get 20 cm. Each of these formulas is reversible: plug in the diameter and you recover the original value. This calculator works all four directions, so select whichever measurement you already have.
Common real-world uses
Knowing the diameter of a circle is essential across many practical situations. A plumber needs the diameter of a pipe before selecting fittings. A baker measures the diameter of a cake tin. An engineer specifies circular cross-sections by diameter. A cyclist checks the diameter of a wheel to pick the right tire. In manufacturing, tolerances on circular holes are specified as a diameter with a plus or minus allowance. In astronomy, the angular diameter of a celestial object describes how wide it appears in the sky. Wherever circles appear, the diameter is the starting point for every other calculation.
Diameter vs. radius vs. circumference vs. area
These four quantities are all interlinked through the single constant pi (approximately 3.14159265). The radius is half the diameter; the circumference is pi times the diameter (roughly 3.14 times as long); and the area grows with the square of the radius, so doubling the diameter quadruples the area. That last point catches many people off guard: a pizza twice as wide has four times as much surface, not two times. When comparing circles of different sizes, area grows much faster than diameter.
Circle formulas at a glance
| Find | From radius | From diameter | From circumference | From area |
|---|---|---|---|---|
| Diameter (d) | 2r | d | C / π | 2√(A / π) |
| Radius (r) | r | d / 2 | C / (2π) | √(A / π) |
| Circumference (C) | 2πr | πd | C | 2√(πA) |
| Area (A) | πr² | πd² / 4 | C² / (4π) | A |
All four circle properties expressed in terms of each of the other three. d = diameter, r = radius, C = circumference, A = area.
Frequently asked questions
What is the formula for the diameter of a circle?
The basic formula is d = 2r, where r is the radius. If you know the circumference instead, use d = C / pi. If you know the area, use d = 2 x square root of (A / pi). All three formulas give the same diameter as long as the input is correct.
How do I find the diameter if I only know the circumference?
Divide the circumference by pi (approximately 3.14159). For example, a circle with circumference 25 cm has a diameter of 25 / 3.14159 = 7.958 cm. This is because the circumference formula is C = pi x d, so rearranging gives d = C / pi.
How do I find the diameter from the area?
Divide the area by pi, take the square root to get the radius, then double the radius to get the diameter. In one formula: d = 2 x square root of (A / pi). For example, an area of 50 cm squared gives d = 2 x square root of (50 / 3.14159) = 2 x square root of 15.915 = 2 x 3.989 = 7.979 cm.
What is the difference between diameter and radius?
The radius is the distance from the center of a circle to any point on its edge. The diameter is the distance from one edge to the opposite edge through the center. The diameter is always exactly twice the radius: d = 2r and r = d / 2.
Does doubling the diameter double the area?
No - it quadruples the area. Area is proportional to the square of the radius (A = pi x r squared), and since the radius is half the diameter, doubling the diameter doubles the radius, which squares to give four times the original area. This is why larger circles are so much more spacious than smaller ones.
What units does this calculator use?
You can switch between metric (centimetres) and imperial (inches) using the unit selector. The same formulas apply regardless of units; just make sure your input and output are in the same unit system. If you want the diameter in metres, enter the radius in metres.
Can I calculate the diameter of a circle in 3D (sphere)?
A circle is a flat, 2D shape. A sphere is the 3D equivalent. The diameter of a sphere is defined in the same way - the longest straight line through the center - and uses the same formula d = 2r. However, the surface area and volume of a sphere use different formulas: surface area = 4 x pi x r squared, and volume = (4/3) x pi x r cubed.