Library / Foundations: Maths / FMA-08
Foundations: Maths
Circle: circumference and area
Area of a circle from its radius.
- Ref
- FMA-08
- Rev
- v1
- Field
- Foundations: Maths
- Result
- A [cm²]
r is the radius (half the diameter). C is the circumference.
The area of a circle grows with the square of its radius, so doubling the radius gives four times the area.
Calculator
cm²
cm
- Circumference 2πr37.7 cm
- Diameter12 cm
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
Area (cm²) current value 113.1 cm²
rRadiusKey driver
0.7857,850
- Area scales with r²; circumference scales with r.
- Pipe flow area depends on the diameter squared, so small diameter changes matter a lot.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (cm²) | Local step | Change in result |
|---|---|---|---|---|---|---|
| r Radius | 0.5 to 50 cm | 0.7854 | 7,854 | 7,853 | +10% | +21 % |
Sweep of Radius
| Radius (cm) | Area (cm²) |
|---|---|
| 0.5 | 0.7854 |
| 0.8891 | 2.484 |
| 1.581 | 7.854 |
| 2.812 | 24.84 |
| 5 | 78.54 |
| 8.891 | 248.4 |
| 15.81 | 785.4 |
| 28.12 | 2,484 |
| 50 | 7,854 |
Sweep one variable
Area (cm²)Hover, touch, or use the arrow keys on the chart
Variables and how each one contributes
A
Area
What the equation gives you. Everything else feeds it.
r
Radius
Distance from the centre to the edge. Squared: +10% radius gives +21% area.
Worked example with the values above
- Square the radius: 6² = 36.
- Multiply by π ≈ 3.14159.
- A = 113.1 cm².
Assumptions and limits
- A perfect circle.
- Radius measured from the centre.
Common mistakes
- Using the diameter in place of the radius.
- Confusing πr² with 2πr.
Statistics and uncertainty
Because r is squared, a relative error in the radius is doubled in the area: δA/A = 2δr/r.
Where it is used
- Flow area of pipes and ducts.
- Cross-sections of shafts and cables.
Maths you need
- Squares: r²
- Pi: ratio of circumference to diameter