Circle Measurements Calculator
This calculator works out every key measurement of a circle, radius, diameter, circumference and area, from just one value you already know, which is useful whenever you are working from a plan, a pipe spec, a garden design or a maths problem that only gives you a single figure to start with. You choose which measurement you are starting from, enter its value in whatever unit you are using, cm, m, mm, inches or feet, and pick a unit label purely for display. The calculator instantly returns all four measurements together: radius, diameter, circumference and area, each shown in your chosen unit, with area given in square units. It uses the exact value of pi (3.14159265358979) rather than a rounded approximation, so results stay accurate to four decimal places. A worked example below the results spells out the actual arithmetic behind your answer, so you can see how each figure was derived rather than just trusting the output. This makes it handy for checking maths homework, sizing a circular garden bed, pool or tabletop, working out how much edging, fencing or trim you need around a round feature, or converting between measurements on a building plan. Because all four measurements are linked through pi, you only ever need to know one of them; the calculator handles the rest of the geometry for you instantly as you type.
1. Enter a Known Value
2. Circle Formulas Used
d = 2r
C = 2πr
A = πr²
r = C / (2π)
r = d / 2
r = √(A / π)
Worked Example
How to Use This Calculator
Select which measurement you know (radius, diameter, circumference, or area), enter its value, and the calculator will immediately display all other circle measurements. The unit label you choose affects display only; the maths works in whatever unit you input.
The Four Key Circle Measurements
| Measurement | Symbol | Formula from radius | Formula to find radius |
|---|---|---|---|
| Radius | r | r (known) | r = r |
| Diameter | d | d = 2r | r = d / 2 |
| Circumference | C | C = 2πr | r = C / (2π) |
| Area | A | A = πr² | r = √(A / π) |
Understanding the Formulas
All four measurements of a circle are linked through the mathematical constant pi (π), which equals approximately 3.14159. Because of this relationship, knowing any one measurement lets you derive all others:
- Radius and diameter are directly proportional: the diameter is always exactly twice the radius.
- Circumference grows linearly with radius. Doubling the radius doubles the circumference.
- Area grows with the square of the radius. Doubling the radius quadruples the area.
This quadratic relationship between radius and area is why a circle with twice the radius looks much larger: it has four times the surface area, not twice.
Worked Example: Starting from Radius = 5 cm
With radius r = 5 cm:
- Diameter: d = 2 x 5 = 10.00 cm
- Circumference: C = 2 x π x 5 = 2 x 3.14159 x 5 = 31.42 cm
- Area: A = π x 5² = 3.14159 x 25 = 78.54 cm²
These are the exact values the calculator shows when you enter 5 as the radius with units set to cm.
Worked Example: Starting from Circumference = 31.42 cm
If you only know the circumference is 31.42 cm:
- Radius: r = 31.42 / (2 x π) = 31.42 / 6.28318 = 5.00 cm
- Diameter: d = 2 x 5.00 = 10.00 cm
- Area: A = π x 5.00² = 78.54 cm²
Worked Example: Starting from Area = 78.54 cm²
If you know the area is 78.54 cm²:
- Radius: r = √(78.54 / π) = √(25.00) = 5.00 cm
- Diameter: d = 10.00 cm
- Circumference: C = 31.42 cm
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Method: All calculations use the standard Euclidean geometry formulas for a perfect circle. The value of pi used is JavaScript's Math.PI (3.141592653589793). Results are rounded to four decimal places for display.