Circle Sphere Calculator
How to use it
Review the methodology below to make sure it aligns with your project's requirements, then:
- Choose US or metric units. Switching converts the value already entered.
- Choose what you know: the radius or diameter of a circle or sphere, the circumference, the area of a circle, the volume of a sphere, or the surface area of a sphere.
- Enter the value and choose its unit.
- Every other measurement appears in the results, in both units of the system, and updates as you type.
Methodology, equations and examples
The circle and sphere calculator finds the radius, diameter, circumference and area of a circle, and the volume and surface area of a sphere. Enter any one measurement and it gives all the others, with no manual calculation.
The mathematical constant π (pi), the ratio of a circle's circumference to its diameter, is approximately 3.14159. The radius is the distance between the center of a circle or sphere and any point on its circumference or surface. Knowing the radius or diameter gives the circumference and area, and the reverse. The calculator extends this to spheres: given the volume or surface area of a sphere, it finds the radius and diameter. This is particularly useful for engineers, mathematicians and students who work with three-dimensional shapes.
The equations:
- Diameter = 2 × R
- Area of a circle = π × D² / 4
- Circumference = π × D
- Volume of a sphere = 4/3 × π × R³
- Surface area of a sphere = 4 × π × R²
where D = diameter, R = radius, and π ≈ 3.14159.
Example 1: a soccer ball has a volume of 5,575 cm³. Calculate its radius.
Volume = 4/3 × π × R³. Rearranging to solve for R: R = (3 × V / 4 / π)1/3
Substituting the volume: R = (3 × 5,575 cm³ / 4 / π)1/3 = 10.9998 cm
Example 2: find the surface area of the soccer ball from Example 1.
Surface area of a sphere = 4 × π × R². Substituting the radius from Example 1 (10.9998 cm):
A = 4 × π × (10.9998 cm)² = 1,520.48 cm²
