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Circle from Area Calculator

Find a circle's dimensions from its area.

How it is calculated

The area of a circle is A = π r², so the tool reverses it: r = √(A ÷ π). From the radius it gets the diameter d = 2r and the circumference C = 2πr. The area must be above zero. Radius and diameter are shown with four decimals and circumference with two. The tool does not know your unit: the results are labelled "units" and are in the length unit whose square matches your area. If the area is in square metres the lengths are metres, if it is in square inches the lengths are inches. Squaring changes scale quickly, so quadrupling the area only doubles the radius.

Worked example

A circle with an area of 100. Divide by π: 100 ÷ 3.14159 = 31.8310. Square root: 5.6419 units is the radius. Diameter: 2 × 5.6419 = 11.2838 units. Circumference: 2 × π × 5.6419 = 35.45 units.

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Common mistakes

  • Forgetting the square root and dividing the area by π only. That gives r², not r.
  • Mixing units. A round table top of 0.5 square metres has a radius in metres; entering 5000 cm² and expecting metres gives a result in centimetres.
  • Treating the area as the diameter or radius of something else. The input is the whole area of the disc, not a side length.
  • Expecting doubling the area to double the radius. Radius grows with the square root, so you need four times the area to double it.
  • Rounding π to 3.14 early in a hand calculation, which shifts the fourth decimal of the radius.

About this calculator

This calculator works Circle Area = π·r² backward: given the area, it solves for radius as r = √(A/π), then derives diameter (2r) and circumference (2πr or π·d) from that radius — the reverse direction of the more commonly known area calculation.

Students checking geometry homework where area is given but radius is asked for, engineers and designers sizing a circular part or opening to hit a target area (like a vent, gasket, or pipe cross-section), and land or landscaping planners converting a plot's area into a circular boundary radius use this.

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  • Editorial team

    A handy use is sizing a round opening to a target area, such as a vent or port. A 100 cm² opening needs a diameter of about 11.28 cm. Keep in mind that this is the clear area, so for a pipe use the inside diameter, not the outside, and for a ring or tube subtract the wall yourself. Keep area and length in matching units. What are you sizing, and in which unit is your area given?

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