# Circle Calculator

- **URL:** https://codeasystem.com/calculators/geometry/circle-calculator/
- **Category:** geometry
- **Description:** Enter a radius to get a circle’s area, circumference and diameter instantly, all from π-based formulas.
- **Primary output:** Area: 28.27

## Inputs
- Radius (r) (name: `radius`, type: number, example: 3)

## Outputs
- Area: 28.27
- Circumference: 18.85
- Diameter: 6

## Formula / methodology
```
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.

## How to use
1. **Measure or enter the radius**; Halfway across the circle through its center.
2. **Read all three results**; Area, circumference and diameter appear together; no separate runs needed.
3. **Keep units consistent**; A radius in centimeters gives square-centimeter area and centimeter circumference.

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

Result for these inputs:

```
Area: 28.27
```

## About this calculator
### 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.

## FAQs
### 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.

## Related calculators
- [Sphere Volume & Surface Area Calculator](https://codeasystem.com/calculators/geometry/sphere-volume-surface-calculator/)
- [Cylinder Volume Calculator](https://codeasystem.com/calculators/geometry/cylinder-volume-calculator/)
- [Cone Volume Calculator](https://codeasystem.com/calculators/geometry/cone-volume-calculator/)

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Last updated: 2026-08-23 · Version: 1.0.0 · [HTML version](https://codeasystem.com/calculators/geometry/circle-calculator/)