Circle Calculator

About this tool

The Circle Calculator computes radius, diameter, area, and circumference from any one of those measurements. It also calculates arc length and sector area when you provide a radius and a central angle in degrees. Results use JavaScript's Math.PI and are rounded to six decimal places for display. The calculator is unit-neutral: enter values in a consistent length unit and the linear results use that unit while area uses its squared form. It accepts positive values only; it does not calculate chord length, circle segments, or three-dimensional solids.

Why use it

• Enter any one value and all other circle properties are derived automatically.

• Includes arc length and sector area calculation.

• High-precision results using JavaScript's Math.PI constant.

• Unit-neutral: works in mm, cm, inches, feet or any other consistent unit.

• Single source of truth for any circle property — eliminates the need to manually rearrange π formulas.

• Privacy-first: all geometry inputs stay in your browser, no values logged or transmitted.

How to use

1. Choose the known value from the dropdown: Radius, Diameter, Area, or Circumference.
2. Enter its value — radius, diameter, area and circumference are all calculated instantly.
3. For arc length and sector area, enter the central angle in degrees (default 90°) in the Arc / Sector box.
4. Check the diagram below, which shades the sector for the angle you entered.
5. Keep every input in one length unit; linear results come back in that unit and area in its square.
6. For multi-circle layouts, note the radius value and reuse it for each subsequent circle to maintain consistency.

When it helps

• Geometry homework involving circles, sectors, or arcs.
• Engineering or construction calculations for circular components.
• Converting between circle measurements (area to radius, circumference to diameter).
• Calculating fabric, fencing, or material needed for circular shapes.
• Designing round tables, garden layouts, or other circular components and needing exact dimensions.
• Working geometry homework where quick conversion between radius, diameter, area, and circumference is needed.

Examples

Tips

• Always confirm whether the input is the radius or diameter — the most common error is entering diameter when the formula expects radius.
• The angle field expects degrees — convert a radian angle by multiplying it by 180/π (about 57.2958) first.
• For practical applications (cutting fabric, fence layout), add a 5-10% material buffer to the calculated circumference for waste and overlaps.
• When the problem gives only chord length and arc height, use the formula r = (h² + (chord/2)²) / (2h) to find the radius first.
• Approximate π as 22/7 only for back-of-envelope estimates — the calculator uses Math.PI for full 15-digit precision.
• Sector area scales linearly with central angle — half a sector (angle/2) has half the area, useful for proportional planning.

Frequently Asked Questions

Glossary

Radius (r)

Distance from the center of a circle to any point on its edge. Half the diameter.

Diameter (d)

Distance across a circle through the center; d = 2r. The longest chord of a circle.

Circumference (C)

The total perimeter (boundary length) of a circle. C = 2πr = πd.

Area (A)

The two-dimensional space inside a circle. A = πr².

Arc length (s)

Length along the curved edge between two points. s = rθ (θ in radians) or s = (θ/360) × 2πr (degrees).

Sector

A pie-slice region bounded by two radii and an arc. Sector area = ½r²θ (radians) or (θ/360) × πr² (degrees).

Chord

A straight line segment whose endpoints both lie on the circle. Length = 2r·sin(θ/2) where θ is the central angle.