How-to guides · 3 min read
How to Find the Area and Circumference of a Circle
From the radius
Square the radius, then multiply by π ≈ 3.14159.
Radius 5
- Radius 5
- Diameter 10
Step-by-step working 4 steps
- 1Radius given
r = 5
- 2Diameter
d = 2r = 10
- 3Circumference
C = 2πr = 2 × 3.141593 × 5 = 31.415927
- 4Area
A = πr² = 3.141593 × 5² = 78.539816
π is used at full calculator precision; the 6-decimal π shown is for display only.
From the diameter
Halve the diameter to get the radius first. A 12-unit diameter means r = 6.
Diameter 12
- Radius 6
- Diameter 12
Step-by-step working 4 steps
- 1Radius from diameter
r = d ÷ 2 = 12 ÷ 2 = 6
- 2Diameter
d = 2r = 12
- 3Circumference
C = 2πr = 2 × 3.141593 × 6 = 37.699112
- 4Area
A = πr² = 3.141593 × 6² = 113.097336
π is used at full calculator precision; the 6-decimal π shown is for display only.
Working backwards
From area: r = √(A/π). From circumference: r = C/(2π). The circle calculator does all four conversions.
Area 100
- Radius 5.6419
- Diameter 11.2838
Step-by-step working 4 steps
- 1Radius from area
r = √(A ÷ π) = √(100 ÷ 3.141593) = 5.641896
- 2Diameter
d = 2r = 11.283792
- 3Circumference
C = 2πr = 2 × 3.141593 × 5.641896 = 35.449077
- 4Area
A = πr² = 3.141593 × 5.641896² = 100
π is used at full calculator precision; the 6-decimal π shown is for display only.
Mistakes to avoid
- Using the diameter in πr².
- Rounding π to 3.14 too early.
- Forgetting that area is in square units.
More shapes in the geometry formulas cheat sheet.
Frequently asked questions
What is the area of a circle with diameter 10?
r = 5, so area 78.5398.
Why is it πr², not 2πr?
2πr is the circumference (a length). Area covers the inside, so it scales with the square of the radius.
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