Circle Calculator

What this calculator does

The Circle Calculator converts between four measurements of a circle: radius, diameter, circumference, and area. You provide any one of them, and the calculator derives the other three. This is useful when a drawing, specification, or physical object gives you only one dimension.

Circles appear in wheels, pipes, tanks, gears, sports fields, and design work. A machinist may know a diameter and need the circumference. A painter may know the area of a round surface and need the radius. A student may be checking homework that gives only one property.

How to use this calculator

1. Choose which measurement you already know: radius, diameter, circumference, or area.
2. Enter its value.
3. Click Calculate.
4. Read the other three measurements in the result panel.

The default example uses an area of 100 square units. It produces a radius of about 5.6419, a diameter of about 11.2838, and a circumference of about 35.4491. If you instead enter a radius of 5, the calculator returns a diameter of 10, a circumference of about 31.4159, and an area of about 78.5398.

Circle formulas

Diameter:      d = 2r
Circumference: C = 2πr = πd
Area:          A = πr²
Radius from diameter:      r = d / 2
Radius from circumference: r = C / (2π)
Radius from area:          r = √(A / π)

Every formula is built from the radius, so the calculator first converts the known measurement to a radius and then computes the remaining values.

What the results mean

The highlighted result is the area. The supporting rows give the radius, diameter, and circumference. All four values describe the same circle, so they should remain consistent when you use them in another formula.

The value of π is not exact. JavaScript supplies a double-precision approximation, and the displayed numbers are rounded. For most practical measurements, the displayed precision is more than sufficient.

Assumptions and limitations

• The shape is a perfect circle. Ellipses and oval shapes are not supported.
• The known measurement must be greater than zero.
• All measurements use the same linear unit. Area is in that unit squared; the calculator does not convert units.
• Results are rounded for display and may differ slightly from hand calculations that use 3.14 for π.
• The calculator does not calculate arc length, chord length, sector area, or central angles.

Frequently asked questions

Why is the default based on area rather than radius?

The default is simply a convenient example that shows the conversion path from area back to radius. You can switch the known measurement to radius, diameter, or circumference at any time. The result always includes all four values.

What is the difference between radius and diameter?

The radius is the distance from the center to any point on the circle. The diameter is the distance across the circle through the center, so it is exactly twice the radius. Many physical specifications use diameter, while most formulas are written with radius.

Why does the area use square units?

Area measures a two-dimensional region, so the unit is multiplied by itself. A radius measured in centimeters produces an area in square centimeters. Converting the area to another unit requires converting the radius first or applying the appropriate squared conversion factor.

Source

Reference: Calculator.net — Circle Calculator.

This page is for general educational and estimation purposes. Confirm critical dimensions with a physical measurement before cutting or ordering materials.