Enter either a radius or a circumference and calculate instantly. Leave the other value blank, then choose the matching button.
Circumference: C = 2πr
Radius: r = C / (2π)
What this radius and circumference calculator does
This calculator helps you quickly move between two of the most common circle measurements: radius and circumference. If you know one value, you can find the other in a single click. That makes it useful for schoolwork, engineering estimates, home projects, crafts, and everyday geometry tasks.
Because it uses the mathematical constant π (pi) through JavaScript’s built-in precision, it gives accurate results without requiring you to do manual arithmetic.
Quick circle definitions
Radius
The radius is the distance from the center of a circle to its edge. It is usually written as r.
Circumference
The circumference is the total distance around a circle. It is similar to perimeter, but specifically for circular shapes. It is usually written as C.
Core formulas you should know
These two formulas power the calculator:
- C = 2πr (find circumference from radius)
- r = C / (2π) (find radius from circumference)
If you remember these equations, you can solve most basic circle problems.
How to use the calculator
To find circumference
- Enter a positive number in the Radius field.
- (Optional) add a unit like cm or in.
- Click Calculate from Radius.
To find radius
- Enter a positive number in the Circumference field.
- (Optional) add a unit.
- Click Calculate from Circumference.
Example calculations
Example 1: radius to circumference
Suppose the radius is 10 cm. Using C = 2πr:
C = 2 × π × 10 = 62.8319 cm (approximately)
Example 2: circumference to radius
Suppose the circumference is 31.416 m. Using r = C / (2π):
r = 31.416 / (2π) = 5 m (approximately)
Common mistakes to avoid
- Using diameter when the formula needs radius.
- Forgetting that radius must be positive.
- Mixing units (for example, entering inches but reading the result as centimeters).
- Rounding too early during multi-step calculations.
Practical uses in real life
Radius and circumference calculations show up more often than many people expect:
- Measuring circular tables, lids, and pipes
- Designing wheels, gears, and rotating parts
- Planning circular gardens, patios, or fountains
- Estimating distance around tracks or curved boundaries
- Crafting sewing, pottery, or woodworking templates
FAQ
Is circumference the same as perimeter?
Circumference is a type of perimeter specifically for circles.
Can I use any unit?
Yes. Just keep units consistent. If radius is in inches, circumference will be in inches too.
What if I know diameter instead of radius?
Convert first: radius = diameter / 2. Then use the calculator from radius.
Final takeaway
If you know either radius or circumference, finding the other is straightforward with the right formula. Use this calculator to save time, reduce arithmetic mistakes, and get reliable circle measurements quickly.