Circle Area Calculator
Type the radius or the diameter of a circle and read its area at once, with the formula π r² shown and the working written out. Sides in millimetres, centimetres, metres, inches or feet, and the answer listed in six more units underneath, from square inches to acres.
Circle · π r²7,853.98 mm² · 0.00785398 m² · 12.1737 in²
From the radius, or switch to the diameter: the radius is half of it.
The formula is on the stage, and the working is the first row. Every answer here is one textbook formula with your numbers put in, printed so you can check it: a circle is π r², a three-sided triangle is Heron's formula, a regular polygon is n s² / (4 tan(π/n)). The solids give surface area for a closed shape, both ends of a cylinder and the base of a cone included. Conversions use exact definitions, so a square foot is 0.09290304 m² and 43,560 of them make an acre.
Common questions
- Should I use the radius or the diameter?
- Whichever you measured. The radius is the distance from the centre to the edge; the diameter is the full width across, and it is what a tape measure gives you. The switch beside the field takes either, halves a diameter before it goes into the formula, and says so on the formula line: π r², r = d/2. A radius of 5 and a diameter of 10 both give 78.5398.
- What is the formula for the area of a circle?
- Area = π r², where r is the radius. With a diameter, r = d / 2, so the same formula reads π (d / 2)². The working row shows the numbers in place, for example π × 5² = 78.5398163397, so you can check the arithmetic yourself.
- Can I get the area in square feet if I measured in centimetres?
- Yes. Choose the unit you measured in, and the rows under the answer give the same area in six more units. Measured in centimetres, that list includes square metres, square inches, square feet and square yards, and the conversions use exact definitions: an inch is exactly 2.54 cm, so a square inch is exactly 6.4516 square centimetres.
- What about part of a circle, or a ring?
- For a slice from the centre, switch the shape to Sector and give the angle in degrees: 90 degrees is a quarter of the circle, 360 is all of it. For a ring, work out the outer circle and the inner circle and subtract; the page does not do the subtraction for you.
- How precise is the answer?
- As precise as the number you typed. π is the standard double-precision constant, correct to about 16 significant figures, and the answer is shown to six figures on the stage and twelve in the rows below. A circle measured with a tape carries the tape's error, which the page cannot know.
Every area is computed from the formula shown, exact to the precision of the numbers you type, and conversions use exact unit definitions. Measurements from the real world carry their own error.