Circle Area Calculator: A = pi r^2

The area of a circle, or the radius for an area.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose which quantity you want to find.

Enter the other values in the units shown.

The calculator gives the answer with the formula, the substituted numbers, and the answer in other units.

Formulas used

  • A = \pi r^2
  • r = \sqrt{\frac{A}{\pi}}

Worked example

With the default numbers in the calculator above:

  1. The formula, arranged to find the area: area = pi x radius^2
  2. Put the values in (every value in its SI unit): area = pi x 0.5^2
  3. The answer: area: 0.785398 m2
  4. The same answer in other units: 7853.98 cm2; 785398 mm2; 1217.37 in2; 8.45396 ft2

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: What do you want to find? Radius; Area (leave it as it is if this is what you are finding) 0.785398163 m2.

  1. The formula, arranged to find the radius: radius = square root of ((area) / (pi))
  2. Put the values in (every value in its SI unit): radius = square root of ((0.785398) / (pi))
  3. The answer: radius: 0.5 m
  4. The same answer in other units: 50 cm; 500 mm; 19.685 inches

Common questions

What is the formula for the area of a circle?

Pi times the radius squared. A radius of 0.5 m gives an area of 0.785 m2.

How do I find the radius from the area?

Divide the area by pi and take the square root.

How do I find the area from the diameter?

Pi times the diameter squared, divided by 4.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any school mathematics text (area of a circle).

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