How to calculate the area of a circle
Area is the flat surface enclosed by a circle. With radius r, use A = π × r². The radius runs from the centre to the edge. The diameter d goes across the centre and equals twice the radius, so A = π × d² ÷ 4.
If you measured around the edge, choose circumference C. The radius is C ÷ (2π), and the area is C² ÷ (4π). Circumference is a length; area is measured in square units. The calculator also shows radius, diameter, circumference and the equivalent area in square metres.
The calculation uses π at JavaScript number precision, rather than 3.14 or 22/7. Results display up to six decimal places, with six significant figures for very small nonzero values. A precise-looking result cannot improve the accuracy of your original measurement.
Worked example: a circular tabletop
A tabletop with a diameter of 100 cm has a radius of 50 cm. Its area is π × 50², approximately 7,853.981634 cm², or 0.785398 m². Its circumference is approximately 314.159265 cm. Choose Diameter, select centimetres and enter 100 to reproduce the example.
Changing centimetres to metres converts the diameter to 1 m. Changing Diameter to Radius then shows 0.5 m. Calculate again after each change: both entries describe the same tabletop and return the same physical area.
For another area unit such as hectares or acres, use the unit converter after calculating the area here.
Units, limits and common mistakes
Metric prefixes and international inches, feet, yards and miles are supported. One inch is exactly 0.0254 metres; one foot is 0.3048 metres. Area factors must be squared, so one square foot is exactly 0.09290304 square metres. Historical US survey feet and survey miles are not supported.
Use a positive measurement and a decimal point, for example 2.5. A properly grouped number such as 1,000 is accepted; 2,5 is rejected. Zero and negative lengths do not define a supported circle. The largest supported radius is 1,000,000,000,000 metres. Extremely small values that underflow the numeric representation are rejected.
Selecting a different measurement type converts a valid entry instead of reinterpreting it. If you want a new diameter rather than the equivalent radius, select Diameter and then type your new number. An invalid or blank entry is retained for correction; it cannot be converted until it is valid.
This tool calculates a complete, flat Euclidean circle. It does not calculate an ellipse, a ring, a sector, the surface area of a sphere, or the volume of a cylinder. It does not include material waste, overlaps, thickness or purchasing quantities. Knowing an area and solving backwards is outside this page's area-finding task.
To work out a chosen percentage of the completed circle's area, use the percentage calculator with the area result. Any allowance you choose is your own assumption.
Use and save your result
The example starting values are a 10 cm radius. Reset inputs restores those values and their result. Editing an input hides the previous result and asks you to calculate again, so an old answer is never shown with new units. Copy result copies the result with its units and assumptions; Print opens your browser's print controls.
Inputs for the circle area calculator
Measurement you know
Choose Radius for centre to edge, Diameter for a straight line across the centre, or Circumference for the full distance around the edge. Only one measurement is needed.
Measurement unit
Choose mm, cm, m, km, international in, ft, yd or mi. Switching units converts the current valid length in place. The area uses the square of the selected unit.
Measurement
Enter a positive number in the selected unit. Keep all the precision you measured; the calculator rounds only when presenting the result.
CALCULATOR QUESTIONS
Area calculator for a circle questions
Can I calculate circle area from diameter?
Yes. Choose Diameter and enter the full width through the centre. The calculator divides it by two before applying the area formula.
What if I only know the circumference?
Choose Circumference and enter the complete distance around the edge. The radius is that length divided by 2π, then the area is π times radius squared.
Does changing units change the circle?
No. A valid entry is converted to preserve the same length. Calculate again to show the result in the new unit. The numeric area changes because square units have different sizes.
Why is my textbook answer slightly different?
Textbooks sometimes use a rounded value of π such as 3.14 or 22/7, or round the measurements first. This calculator uses π at numeric precision and rounds only the displayed result.
Is the formula different in another country?
No. This geometric formula is universal. The supported customary units use international definitions, so historical survey measurements need a separate conversion.