Explanation
Circle measurements
Use a circle’s radius to find the enclosed area, the distance around its circumference, or its diameter. Radius is the distance from centre to edge; all supplied lengths are metres.
A = πr²
| r | Radius (m) |
|---|
Area of a circle with radius 1 m
| Radius | 1 |
|---|---|
| Result | 3.14 m² |
A = πr² = π × (1 m)² = 3.1415926536 m²
C = 2πr
| r | Radius (m) |
|---|
Circumference of a circle with radius 1 m
| Radius | 1 |
|---|---|
| Result | 6.28 m |
C = 2πr = 2π × 1 m = 6.2831853072 m
d = 2r
| r | Radius (m) |
|---|
Diameter of a circle with radius 1 m
| Radius | 1 |
|---|---|
| Result | 2 m |
d = 2r = 2 × 1 m = 2 m
Diagram of this result
The circle shows the radius from the centre. The shaded disc, the heavy rim or the line through the centre marks the area, circumference or diameter.
The circle shows the radius from the centre. The shaded disc, the heavy rim or the line through the centre marks the area, circumference or diameter.
Common mistakes
A diameter is twice the radius. Entering a diameter into the radius field makes the computed area four times too large. Circumference measures a length in m; area measures a region in m².
Assumptions and limits
The shape is an exact Euclidean circle. Radius must be positive. Diameter is 2r; area πr² and circumference 2πr are approximate because π has a finite internal representation. Canonical inputs are limited to 30 significant digits, 256 characters and adjusted exponent magnitude 100. Computation uses 50 significant digits without intermediate presentation rounding; output overflow fails explicitly. Approximate fixtures use absolute tolerance 1e-12 plus relative tolerance 1e-12.
How do the three measurements relate?
For radius 1 m, area is π m², circumference is 2π m and diameter is 2 m. Doubling radius multiplies area by four and circumference by two.
Sources
Standard Euclidean measurement formulas: OpenStax Prealgebra 2e, measurement and geometry topics, https://openstax.org/details/books/prealgebra-2e. Worked examples use independent geometric identities.