Circle Calculator

This professional-grade circle calculator instantly computes the missing dimensions of a circle—radius, diameter, circumference, and area—from any single input. It’s designed for students, educators, engineers, and anyone who needs quick, precise, and accessible geometry results.

Interactive Calculator

Choose the known value

Results

Radius (r)
—
Diameter (d)
—
Circumference (C)
—
Area (A)
—
Circle diagram with radius line A schematic circle with its radius drawn from center to the edge. Not to scale. r

Data Source and Methodology

Authoritative reference: Eric W. Weisstein, “Circle,” MathWorld—A Wolfram Web Resource (accessed 2025). https://mathworld.wolfram.com/Circle.html. All formulas align with standard Euclidean geometry.

Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.

The Formula Explained

Given a circle with radius r and diameter d:

LaTeX: \( d = 2r \)

LaTeX: \( C = 2\pi r = \pi d \)

LaTeX: \( A = \pi r^2 = \frac{\pi d^2}{4} = \frac{C^2}{4\pi} \)

Inverse relations:

LaTeX: \( r = \frac{d}{2} = \frac{C}{2\pi} = \sqrt{\frac{A}{\pi}} \)

Glossary of Variables

r — Radius: Distance from the center to the circle’s edge (length).
d — Diameter: Distance across the circle through the center; d = 2r (length).
C — Circumference: Perimeter length of the circle; C = 2πr (length).
A — Area: Surface enclosed by the circle; A = πr² (area units).
Unit handling: If input is an area, its unit is squared (e.g., cm²). Length-based outputs remain in the selected length unit.
Precision: Number of decimal places for rounding displayed numeric values.

How It Works: A Step-by-Step Example

Scenario: You measured a circumference of C = 31.4159 cm. Find d, r, and A with 4 decimal places.

  1. Select “Circumference (C)” as the known value and “centimeter (cm)” as the unit.
  2. Enter 31.4159 into the value field. Keep decimal places at 4.
  3. Apply formulas: \( d = \frac{C}{\pi} \), \( r = \frac{C}{2\pi} \), \( A = \pi r^2 \).
  4. Compute:
    • \( d = 31.4159/\pi \approx 10.0000 \) cm
    • \( r = 31.4159/(2\pi) \approx 5.0000 \) cm
    • \( A = \pi \cdot 5^2 = 25\pi \approx 78.5398 \) cm²

The calculator displays both exact forms (e.g., A = 25π cm²) and rounded values.

Frequently Asked Questions (FAQ)

What can I calculate with this tool?

Enter any one of radius, diameter, circumference, or area to instantly compute the remaining three, in your chosen unit.

How do units work for area vs. length?

Lengths use the unit directly (cm, in, etc.). Areas automatically use squared units (cm², in²). The tool handles this for you.

What value of π do you use?

Decimal results use double-precision Math.PI (≈ 3.141592653589793). Exact expressions are shown symbolically using π.

How many decimal places should I choose?

For most schoolwork, 3–4 decimals are sufficient. Engineering may require more. You can set 0–12 decimals.

Is the visualization to scale?

No. The SVG diagram is schematic to aid understanding. Numeric values are accurate, regardless of the drawing.

Can I copy results?

Yes. Use the copy buttons next to each value, or select and copy the text directly.

Tool developed by Ugo Candido. Content reviewed by CalcDomain Editorial Team.
Last reviewed for accuracy on: .