How to Use the Circle Area Calculator
Use one known circle measurement to calculate the other three.
- Choose Radius, Diameter, Area, or Circumference.
- Enter the value and select its unit. For Area, use the squared version of that unit.
- Click Calculate.
- Review the four measurements and the displayed steps under Formula & steps.
- Use Copy result or Download result (.txt) to save the plain-text output.
Changing the known-measurement option hides the current result and updates the input field for the new measurement.
If clipboard access fails, the tool shows “Could not copy - select and copy manually.”
What the Result Shows
The result includes Radius, Diameter, Circumference, and Area. Length results use the selected unit, while area uses its squared version. Formula & steps lists the displayed calculation steps. Values are rounded and formatted for display, so they are not guaranteed to represent every intermediate value exactly.
Formulas Used
The calculator first derives the radius when you enter another measurement:
- Diameter:
r = d / 2 - Area:
r = sqrt(A / pi) - Circumference:
r = C / (2 * pi)
It then calculates the remaining values with d = 2 * r, C = 2 * pi * r, and A = pi * r^2. The calculation uses JavaScript's built-in double-precision value of pi.
Inputs and Supported Units
- Choose Radius, Diameter, Area, or Circumference as the known measurement.
- Enter a positive plain decimal made from digits, with an optional decimal point and at least one digit after the point. Signs, commas, and scientific notation are not accepted.
- Supported units are millimeters (
mm), centimeters (cm), meters (m), kilometers (km), inches (in), feet (ft), yards (yd), and miles (mi). - For Area, the entered value is treated as the squared version of the selected unit. The calculator converts internally to meters or square meters, then displays results in your selected unit.
Validation and Limitations
The calculator rejects blank or non-matching input, zero, negative values, and values greater than 1e12. It shows an error instead of a result when validation fails or when it cannot derive a valid radius.
It assumes a perfect two-dimensional circle. It does not calculate ellipses, sectors, segments, arbitrary arc lengths, spheres, or cylinders, and it does not account for measurement error, material, tolerances, or certified professional calculations.
Privacy and Calculation Scope
The calculation and the measurement you enter are processed locally in your browser. No account is required for this workflow. This describes the calculator calculation only; it does not mean that no other page activity or form submission can reach a server.
Frequently Asked Questions
What is the formula for the area of a circle?
The area of a circle is A = pi * r^2, where r is the radius. If you know the diameter instead, r = d / 2, so A = pi * (d / 2)^2.
How do I find the radius from the area?
Rearranging A = pi * r^2 gives r = sqrt(A / pi). The calculator does this automatically when you enter the area.
What is the formula for circumference?
Circumference is C = 2 * pi * r, equivalently C = pi * d. If you enter the circumference, the calculator finds r = C / (2 * pi) and works out the rest.
What units does this calculator support?
Millimeters, centimeters, meters, kilometers, inches, feet, yards, and miles. Area is shown in the squared version of the unit you choose, e.g. square meters or square feet.
What value of pi does the calculator use?
It uses JavaScript's built-in double-precision value of pi (about 3.14159265358979), which is accurate to about 15 significant digits - far more precise than any real-world measurement.