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Geometry & Measurement

Circle Calculator

Choose what you know — radius, diameter, circumference or area — enter the value, and the calculator works out the other three, starting by finding the radius.

Updated October 3, 2026Written and reviewed by Mateuss M.Method: how we calculate

A positive number
Try an example:
AnswerArea 78.5398 · Circumference 31.4159
  • Radius 5
  • Diameter 10
Step-by-step working 4 steps
  1. 1
    Radius given
    r = 5
  2. 2
    Diameter
    d = 2r = 10
  3. 3
    Circumference
    C = 2πr = 2 × 3.141593 × 5 = 31.415927
  4. 4
    Area
    A = πr² = 3.141593 × 5² = 78.539816

    π is used at full calculator precision; the 6-decimal π shown is for display only.

How to use the circle calculator

  1. Pick which measurement you know.
  2. Enter its value.
  3. Read all four measurements in the answer.
  4. Open the steps to see how the radius was found first.

Circle formulas

d = 2r
C = 2πr = πd
A = πr²
r = C / 2π = √(A / π)

Area is in square units; circumference is a length.

Worked examples

Each example below is generated by the same calculator you used above, so the working always matches the answer.

Radius 5
AnswerArea 78.5398 · Circumference 31.4159
  • Radius 5
  • Diameter 10
Step-by-step working 4 steps
  1. 1
    Radius given
    r = 5
  2. 2
    Diameter
    d = 2r = 10
  3. 3
    Circumference
    C = 2πr = 2 × 3.141593 × 5 = 31.415927
  4. 4
    Area
    A = πr² = 3.141593 × 5² = 78.539816

    π is used at full calculator precision; the 6-decimal π shown is for display only.

Diameter 12
AnswerArea 113.0973 · Circumference 37.6991
  • Radius 6
  • Diameter 12
Step-by-step working 4 steps
  1. 1
    Radius from diameter
    r = d ÷ 2 = 12 ÷ 2 = 6
  2. 2
    Diameter
    d = 2r = 12
  3. 3
    Circumference
    C = 2πr = 2 × 3.141593 × 6 = 37.699112
  4. 4
    Area
    A = πr² = 3.141593 × 6² = 113.097336

    π is used at full calculator precision; the 6-decimal π shown is for display only.

Circumference 31.4
AnswerArea 78.4602 · Circumference 31.4
  • Radius 4.9975
  • Diameter 9.9949
Step-by-step working 4 steps
  1. 1
    Radius from circumference
    r = C ÷ 2π = 31.4 ÷ 6.283185 = 4.997465
  2. 2
    Diameter
    d = 2r = 9.99493
  3. 3
    Circumference
    C = 2πr = 2 × 3.141593 × 4.997465 = 31.4
  4. 4
    Area
    A = πr² = 3.141593 × 4.997465² = 78.460204

    π is used at full calculator precision; the 6-decimal π shown is for display only.

Area 100
AnswerArea 100 · Circumference 35.4491
  • Radius 5.6419
  • Diameter 11.2838
Step-by-step working 4 steps
  1. 1
    Radius from area
    r = √(A ÷ π) = √(100 ÷ 3.141593) = 5.641896
  2. 2
    Diameter
    d = 2r = 11.283792
  3. 3
    Circumference
    C = 2πr = 2 × 3.141593 × 5.641896 = 35.449077
  4. 4
    Area
    A = πr² = 3.141593 × 5.641896² = 100

    π is used at full calculator precision; the 6-decimal π shown is for display only.

Common mistakes to avoid

Mixing up radius and diameter

A = πr² uses the radius. If you were given the diameter, halve it first.

Using the circumference formula for area

Circumference is a length (units); area is units squared. They are not interchangeable.

Rounding pi too early

Using 3.14 gives a small error that grows with large circles. Keep full precision until the end.

Frequently asked questions

Why is the radius found first?

Every other measurement can be written in terms of the radius, so converting once keeps the working short.

Does it work for half or quarter circles?

It gives full-circle values. Divide the area by 2 or 4 for a semicircle or quadrant; arc lengths need the angle too.