How to Work Out the Radius of a Circle
Learn how to work out the radius of a circle from diameter, circumference, or area with formulas, examples, mistakes, troubleshooting, and FAQs.
Quick Answer
To work out the radius of a circle, divide the diameter by 2, divide the circumference by 2π, or take the square root of area divided by π.
Formulas
- Diameter if known
- Circumference if known
- Area if known
- Calculator
- Value of pi, about 3.1416
Safety Precautions
- Use the same units throughout the calculation.
- Label the answer with units.
- Do not confuse radius with diameter.
- Round only at the end for more accurate answers.
- Check which measurement the problem gives you.
Step-by-Step Instructions
- Step 1
Identify known value
See whether you have diameter, circumference, or area.
- Step 2
Use diameter formula
If diameter is known, radius = diameter / 2.
- Step 3
Use circumference formula
If circumference is known, radius = circumference / (2π).
- Step 4
Use area formula
If area is known, radius = square root of (area / π).
- Step 5
Calculate carefully
Enter the formula in a calculator if needed.
- Step 6
Keep units
Radius uses length units, such as cm, m, or ft.
- Step 7
Check reasonableness
Radius should be half of diameter and smaller than diameter.
Practical Example
Example: If the diameter is 14 cm, the radius is 14 / 2 = 7 cm.
Common Mistakes
- Forgetting to divide diameter by 2
- Using π incorrectly
- Rounding too early
- Giving square units for radius
- Confusing circumference and area formulas
- Missing parentheses in calculator entry
Troubleshooting
Answer is larger than diameter
You likely used the wrong formula; radius should be half the diameter.
Area formula feels confusing
Divide area by π first, then take the square root.
Units look wrong
Radius should be a length unit, not square units.
Calculator result differs
Check parentheses around 2π or area divided by π.
Helpful Internal Links
FAQs
What is the radius?
Radius is the distance from the center of a circle to its edge.
How do I find radius from diameter?
Divide the diameter by 2.
How do I find radius from circumference?
Divide circumference by 2π.
How do I find radius from area?
Take the square root of area divided by π.
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