Circle Area Calculator
Calculate the area of a circle from its radius using A = πr². The foundational geometry formula for circles, used in everything from pizza sizing to engineering.
Last updated: May 2026
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About this calculator
The area of a circle is the amount of space enclosed by its boundary, and it is found with the formula A = π × r², where r is the radius (the distance from the center to the edge) and π (pi) is the mathematical constant approximately equal to 3.14159. The radius is squared and then multiplied by π. The squaring is the key feature: area grows with the square of the radius, so doubling the radius quadruples the area, and tripling it increases the area ninefold. This non-linear relationship surprises many people and explains why a 16-inch pizza has far more than twice the food of an 8-inch one. If you know the diameter (the full width across) instead of the radius, halve it first, since r = d ÷ 2. If you know the circumference C, the radius is C ÷ (2π). Edge cases: a radius of 0 gives an area of 0, and the formula assumes a perfect circle — for ellipses you use π × a × b with the two semi-axes. The constant π is irrational, so any numerical answer is an approximation, though using the built-in value of pi keeps it accurate to many decimal places. Area is always expressed in square units: if the radius is in centimeters, the area is in square centimeters.
How to use
Example 1 — a circle with radius 5. Enter Radius = 5. Area = π × 5² = π × 25 ≈ 78.54 square units. Verify: 25 × 3.14159 = 78.54, confirming the calculation. Example 2 — a circle with radius 10. Enter Radius = 10. Area = π × 10² = π × 100 ≈ 314.16 square units. Verify: doubling the radius from 5 to 10 increased the area from 78.54 to 314.16 — exactly four times larger, demonstrating the squared relationship.
Frequently asked questions
What is the difference between radius and diameter?
The radius is the distance from the center of the circle to any point on its edge, while the diameter is the full distance across the circle through the center — so the diameter is always exactly twice the radius. This formula requires the radius, so if you measured the diameter, divide it by two first. Mixing up the two is the single most common mistake and leads to an answer four times too large or too small, because the radius is squared. When measuring a real object, it is often easier to measure the diameter across the widest point and then halve it. Always confirm which measurement you have before calculating.
Why does doubling the radius quadruple the area?
Because the radius is squared in the formula, any change to it has a magnified effect on the area. When you double the radius, you square the doubling: 2² = 4, so the area becomes four times larger. Tripling the radius multiplies the area by 3² = 9, and so on. This squared relationship is fundamental to all area calculations and explains many real-world observations, such as why a slightly larger pizza or pipe has dramatically more area than its size difference suggests. It is also why area is measured in square units. Keeping this in mind helps you estimate how scaling a circle affects the space it covers.
How do I find the area if I only know the circumference?
If you know the circumference C but not the radius, first find the radius using r = C ÷ (2π), then apply the area formula. Alternatively, you can combine the steps into a single formula: A = C² ÷ (4π). For example, a circle with a circumference of 31.42 has a radius of about 5 and an area of about 78.54. This is useful when measuring round objects where the circumference is easier to measure with a tape than the radius. Just be sure to use a consistent value of π throughout. The two-step method is less error-prone if you are doing it by hand.
What value of pi should I use?
Pi (π) is an irrational number whose digits never end or repeat, beginning 3.14159265…. For most everyday calculations, using 3.14 or 3.1416 is sufficient, but this calculator uses the full precision built into the computer, which is accurate to many more decimal places. The level of precision you need depends on the application: a craft project is fine with 3.14, while engineering or scientific work benefits from more digits. Because π is irrational, every numerical area of a circle is technically an approximation. Using more digits of π simply makes that approximation more accurate.
When should I NOT use this formula?
This formula applies only to a perfect circle, so do not use it for ellipses, ovals, or any irregular rounded shape — an ellipse uses A = π × a × b with its two semi-axes, and irregular shapes need other methods or numerical estimation. It also gives a flat, two-dimensional area, not the surface area or volume of a three-dimensional object like a sphere or cylinder, which have their own formulas. Make sure your radius is a single consistent unit, and remember the answer is in square units. If you are measuring a real object that is not truly circular, the result will only be an approximation. For partial circles like sectors, scale the area by the fraction of the full angle.