Free · Circles
Circle Area, Radius and Diameter
Find a circle area from its radius or diameter, or recover its nonnegative dimensions from area, with selectable length and area units.
- Formula & worked example
- Private in your browser
- No signup
Calculator inputs
Loading calculator…
How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
A radius of 2 cm gives a diameter of 4 cm and an area of 4π cm², about 12.5664 cm².
A=πr²; d=2r; r=√(A/π).
Worked example
Enter these known values and leave the other values blank.
- Radius (r)
- 2 cm
- Diameter (d)
- 4 cm
- Area (A)
- 12.566 cm²
Assumptions and limitations
- The shape is a circle in a flat plane. Radius, diameter and area are nonnegative; zero is the degenerate limit.
- All captured length and area units remain selectable. The squared-radius step follows the area selector, so the equation displays consistent squared units.
- Clear an unknown to solve an inverse. The nonnegative square-root branch supplies radius; the static diagram is illustrative.
- Values smaller than fixed-decimal display resolution use scientific notation while retaining the computed finite precision; this avoids silently displaying nonzero values as zero.
- Area choices preserve the captured source conventions: acre uses the rounded factor 4046.856 m² (the exact international acre is 4046.8564224 m²), and soccer field uses a 7140 m² reference area rather than a universal field size.
Common questions
Can I calculate area from diameter?
Yes. Radius is half the diameter, so area is πd²/4.
Why does changing a length unit not change the circle?
Unit selection changes the displayed measure while retaining the same physical size. Area uses the square of a length conversion factor.
References
- OpenStax: properties of circles
- NIST: exact international-foot area conversions
- Calculation definition and unit reference
Keep exact nonnegative circle dimensions, including the degenerate zero limit, while preserving the captured radius/diameter/area inverses and the hidden squared-radius explanation in the selected area unit. Preserve finite nonzero results in scientific notation only when the existing 1000-decimal rounding search cannot meet its own relative precision; ordinary formatting is unchanged.