Circle Area Calculator
Enter a radius, diameter, or circumference. Get the area first, then check the circle’s related measurements.
Fractions are supported. Changing the unit changes the label only; it does not convert the value.
Private by design: Your entered value and result stay in this browser tab. They are not added to the URL, stored, or included in analytics fields.
Circle area
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Calculate area from radius, diameter, or circumference
Choose the measurement you already know, enter a positive decimal or fraction, and select its unit label. Area stays the primary answer. Radius, diameter, and circumference appear underneath so you can verify the same circle.
Circle formulas used
For a known radius, the core formulas are A = πr², d = 2r, and C = 2πr.
For a known diameter, use A = πd²/4, r = d/2, and C = πd. For a known circumference, use r = C/(2π), d = C/π, and A = C²/(4π). These diameter and circumference forms are algebraic rearrangements of the radius formulas documented by OpenStax.
Exact π form versus decimal approximation
The exact result preserves the original finite decimal or fraction before applying the formula. For example, radius 5 gives exactly 25π. The decimal answer uses π’s numeric value and is marked as an approximation.
Why area uses square units
A length such as 5 cm is one-dimensional. Area multiplies two lengths, so the corresponding result is measured in square units such as cm². If you choose Unitless, the page labels the area as square units.
Frequently asked questions
How do I find a circle's area from its diameter?
Divide the diameter by 2 to get the radius, then use A = πr². Equivalently, use A = πd²/4. The calculator keeps the exact π form and also shows a decimal approximation.
How do I find area from circumference?
Use r = C/(2π), then substitute that radius into A = πr². This simplifies to A = C²/(4π).
Is the decimal result exact?
No. A positive rational radius, diameter, or circumference produces an area involving π, so the decimal is an approximation. The exact π expression is shown separately.
How do units apply to circle area?
Radius, diameter, and circumference use the selected length label. Area uses the corresponding square unit, such as cm² or ft². The selector labels one shared basis and does not convert the entered number.