Area of a Circle Calculator

Enter a radius, diameter, or circumference to get the area, circumference, diameter, and radius of a circle using A = π × r².

Quick Facts

Formula
A = π × r²
Area equals pi times the radius squared; π (pi) ≈ 3.14159.
Diameter form
A = π × d² ÷ 4
The same formula rewritten using diameter (d = 2r) instead of radius.

Your Results

Calculated
Area
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π × r² for this circle
Circumference
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Distance around the circle (2 × π × r)
Diameter
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Twice the radius (2 × r)
Radius
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Used in the area formula

Ready

Choose what you know (radius, diameter, or circumference), enter its value, and press Calculate.

Formula and method for the Area of a Circle

Area of a Circle:

A = π × r²

r = radius (distance from the center to the edge)

The area of a circle is the amount of two-dimensional space enclosed by its boundary. Multiply pi (π ≈ 3.14159) by the radius squared to get the area in square units. If you know the diameter instead, divide it by 2 to get the radius first, or use A = π × d² ÷ 4 directly. If you know the circumference, divide it by 2π to recover the radius before applying the area formula.

How the calculation works

This calculator accepts a radius, diameter, or circumference — whichever you have on hand — and converts it to a radius first: r = value for radius, r = value ÷ 2 for diameter, or r = value ÷ (2 × π) for circumference. From that radius it derives the area (π × r²), the circumference (2 × π × r), and the diameter (2 × r). Enter your measurement in one consistent unit; the calculator does not convert between unit systems, so keep every measurement in the unit you selected.

Common mistakes

  • Radius vs. diameter: the most frequent error is plugging a diameter into a field that expects a radius (or vice-versa). Since diameter = 2 × radius, using the wrong one changes the area by a factor of 4, not 2.
  • Units: area is always in square units — cm², m², in², ft² — never a plain linear unit. A circle with a 3 cm radius has an area of about 28.3 cm², not 28.3 cm.
  • Rounding pi too early: using 3.14 instead of a more precise value of π introduces small errors that grow with the radius; this calculator uses JavaScript's full-precision Math.PI.

Real-world applications

  • Estimating material for circular tabletops, rugs, or comparing pizza sizes by area rather than diameter
  • Sizing circular garden beds, pools, or irrigation coverage
  • Calculating the cross-sectional area of pipes, cylinders, and tubing
  • Fabric, sheet metal, or paper stock estimates for circular or disc-shaped pieces

Frequently Asked Questions

What is the formula for the area of a circle?
The area of a circle is A = pi times r squared (A = π × r²), where r is the radius and pi is approximately 3.14159. If you know the diameter d instead, use A = π × d² ÷ 4, since the diameter is twice the radius.
How do I find the area if I only know the diameter?
Divide the diameter by 2 to get the radius, then apply A = π × r². For example, a circle with a diameter of 10 cm has a radius of 5 cm, so its area is π × 5² ≈ 78.54 cm².
How do I find the area from the circumference?
First solve for the radius using r = C ÷ (2 × π), then apply A = π × r². For example, a circumference of 31.4 cm gives a radius of about 5 cm and an area of about 78.5 cm².
Why is area measured in square units?
Area measures two-dimensional space, so it is expressed in squared linear units, such as cm², m², in², or ft². A circle with a radius measured in centimeters always has an area in square centimeters, never plain centimeters.

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