Circle Radius Calculator
Find the radius when you know a circle’s diameter, circumference, or area.
What is the radius of a circle?
The radius is the distance from the center of a circle to any point on its edge. It is one of the most useful measurements in geometry because once you know the radius, you can quickly calculate the diameter, circumference, and area.
In many real-world tasks—construction, engineering, design, manufacturing, and school math problems—you are often given a different value first. This calculator helps you convert that known value into radius instantly.
Radius formulas you should know
1) From diameter
If you know the diameter (d), radius is half of it:
r = d ÷ 2
2) From circumference
If you know the circumference (C):
r = C ÷ (2π)
3) From area
If you know the area (A):
r = √(A ÷ π)
How to use this radius of a circle calculator
- Select whether your known value is diameter, circumference, or area.
- Enter a positive number in the input field.
- Click Calculate Radius.
- Review the radius and additional circle values shown in the result box.
You can use any unit (cm, m, inches, feet, etc.) as long as you stay consistent.
Worked examples
Example A: Diameter is 18 cm
Use r = d ÷ 2:
r = 18 ÷ 2 = 9 cm
Example B: Circumference is 31.4 m
Use r = C ÷ (2π):
r = 31.4 ÷ (2 × 3.14159) ≈ 5 m
Example C: Area is 154 in²
Use r = √(A ÷ π):
r = √(154 ÷ 3.14159) ≈ √49 ≈ 7 in
Common mistakes to avoid
- Confusing radius and diameter. Diameter is always 2 × radius.
- Forgetting the 2 in the circumference formula (C = 2πr).
- Trying to use negative numbers for circle measurements.
- Mixing units (for example, inches and centimeters in the same calculation).
Quick reference
- Diameter: d = 2r
- Circumference: C = 2πr
- Area: A = πr²
- Radius from area: r = √(A/π)
FAQ
Can radius be a decimal?
Yes. In many practical measurements, radius is a decimal value.
What value does this calculator use for π?
It uses JavaScript’s built-in value of π for accurate results.
Can I use this for school homework?
Absolutely. It’s useful for checking your work and understanding formula relationships.