Diameter of a Circle Calculator

Enter a circle's radius, area, or circumference to get its diameter, along with the matching radius, circumference, and area, using d = 2r = C/π = 2√(A/π).

Quick Facts

Formula
d = 2r = C / π = 2√(A / π)
Diameter is always twice the radius, and it scales the circumference and area of every circle.
Constant used
π ≈ 3.14159265358979
Calculations use the JavaScript double-precision value of π (Math.PI).

Your Results

Calculated
Diameter
-
d = 2r = C/π
Radius
-
r = d/2
Circumference
-
C = πd
Area
-
A = πr²

Ready

Choose what you know about the circle, enter its value and unit, then press Calculate.

Formula and method for the Diameter of a Circle

A circle's diameter, radius, circumference, and area are all locked together by fixed ratios. This calculator lets you enter whichever one you already know — radius, circumference, or area — and solves for the diameter plus the other two, so you never need to look up or rearrange the formula by hand.

How the calculation works

Every formula here follows from the definition of π (pi), the ratio of a circle's circumference to its diameter (π ≈ 3.14159265358979):

  • From radius: diameter is always twice the radius — d = 2r.
  • From circumference: since circumference C = πd, dividing both sides by π gives d = C / π.
  • From area: since area A = πr², solving for radius gives r = √(A / π), and doubling that radius gives d = 2√(A / π).

Once the diameter is known, the calculator derives the radius (r = d / 2), circumference (C = πd), and area (A = πr²) so all four values are shown together. Enter the value in whichever length unit matches your measurement — the diameter, radius, and circumference are reported in that same unit, while the area is reported in that unit squared.

Common mistakes

  • Radius vs. diameter: the radius is half the diameter, not the same value. Plugging a diameter into a formula that expects a radius (or vice versa) doubles or halves the error.
  • Units: the diameter, radius, and circumference share one length unit (e.g., cm), but area is in that unit squared (e.g., cm²) — a diameter of 10 cm gives an area of about 78.54 cm², not 78.54 cm.
  • Mixing unit systems: enter your known value in a single consistent unit; converting between metric and imperial mid-calculation produces incorrect results.

Real-world applications

  • Ordering round tabletops, pipes, or wheels, where suppliers list diameter but you measured radius or circumference with a tape
  • Sizing circular gardens, pools, or rugs from a known area or a fence-length (circumference) measurement
  • Woodworking, welding, and machining, where circular stock is specified by diameter
  • Checking a manufacturer's spec sheet by cross-verifying diameter, circumference, and area against each other

Frequently Asked Questions

What is the formula for the diameter of a circle?
Diameter is twice the radius: d = 2r. If you know the circumference instead, divide by π: d = C / π. If you know the area, take d = 2√(A / π).
How is diameter related to circumference?
Circumference equals π times diameter: C = πd. Rearranged, diameter equals circumference divided by π: d = C / π, where π is approximately 3.14159.
How do I find the diameter from the area?
Area equals π times radius squared: A = πr². Solve for radius first, r = √(A / π), then double it to get the diameter: d = 2r.
What units does the calculator use?
The diameter, radius, and circumference are all reported in whatever length unit you select (inches, feet, cm, etc.). The area is reported in that same unit squared, since area is a two-dimensional measurement.

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