Geometry

Circle Calculator

What this does

Enter a radius to get a circle’s area, circumference and diameter instantly, all from π-based formulas.

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Runs in your browser

Calculator inputs

How to use it

Using the circle calculator

  1. 01

    Measure or enter the radius

    Halfway across the circle through its center.

  2. 02

    Read all three results

    Area, circumference and diameter appear together; no separate runs needed.

  3. 03

    Keep units consistent

    A radius in centimeters gives square-centimeter area and centimeter circumference.

Good to know

Why area and circumference scale differently

Circumference is one-dimensional: twice the radius, twice the rim. Area is two-dimensional: the r² term means modest radius increases produce dramatic coverage gains; the reason pizza pricing per square inch rewards larger pies.

Radius versus diameter inputs

Formulas exist in both forms (A = πr² = πd²/4). If you can only measure across the circle, halve the diameter first; measuring across the widest point is usually easier than finding the true center.

  • Area scales with r².
  • Circumference scales with r.
  • Diameter is always exactly twice the radius.

How it's calculated

The math behind this calculator

A = πr² C = 2πr d = 2r

Every circle measurement flows from the radius. Area grows with r², so doubling the radius quadruples the area, while circumference and diameter scale linearly with r.

Results use full-precision π and are rounded for display only; downstream calculations should reuse the raw values rather than the rounded strings.

Assumptions & limitations

  • Radius is given in your chosen unit; outputs share that unit.
  • π is evaluated numerically at double precision.
  • Negative radii are rejected.

Worked example

A circle of radius 3 has an area of 28.27 square units and a circumference of 18.85 units; with diameter 6.

FAQ

Frequently asked questions

Can I enter the diameter instead?
Yes; divide it by two and enter the result as the radius, or work backward from the diameter row.
What precision are the results?
Computed at full floating-point precision and displayed to two decimals; exact values like r = 3 giving C = 6π round accordingly.
Does this handle partial circles (arcs, sectors)?
Not directly; multiply circumference by the fraction for arc length, or area by degrees/360 for sectors.
Why is my measured circumference slightly off?
Real objects deform and centers are hard to locate; expect small deviations from idealized math on physical measurements.

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