Sphere Volume Calculator
Calculate the volume of a sphere using radius, diameter or circumference with sphere volume calculator. Get results with the sphere volume formula and steps.
What Is a Sphere?
A sphere is a perfectly round three-dimensional geometric object in 3D space. Every point on the surface of a sphere is at an equal distance from its center point. Common real-world examples of spheres include basketballs, planets, marbles, and teardrops.
Unlike two-dimensional circles that only possess surface area, spheres enclose a definite three-dimensional space called volume.
Volume of a Sphere Formula
Formula Variables Explained:
The distance from the center of the sphere to any point on its outer boundary.
The straight-line distance across the sphere passing through its center (d = 2r).
Mathematical constant approximately equal to 3.14159265.
The formula for calculating the volume of a sphere was first derived by the ancient Greek mathematician Archimedes. He proved that the volume of a sphere is equal to two-thirds of the volume of its circumscribed cylinder.
The standard volume formula is V = (4/3) × π × r³, where r represents the radius. If you only know the diameter (d), you can divide the diameter by 2 to get the radius (r = d/2), or use the direct diameter formula: V = (1/6) × π × d³.
How to find the volume of a Sphere?
- 1Identify the radius (r) or diameter (d) of the sphere.
- 2If given the diameter, divide by 2 to obtain the radius: r = d / 2.
- 3Cube the radius value: r³ = r × r × r.
- 4Multiply the result by Pi (π ≈ 3.14159).
- 5Multiply by 4/3 (or multiply by 4 and divide by 3).
- 6Attach the cubic units (e.g., cm³, m³, in³, ft³) to express your final answer.
Example: Calculate the Volume of a Sphere
Example 1: Find the volume of a sphere with a radius of 6 cm
Problem: Given a sphere with radius r = 6 cm, calculate its total three-dimensional volume.
- Formula: V = (4/3) × π × r³
- Substitute r = 6 cm: V = (4/3) × π × (6³)
- Calculate 6³ = 216
- V = (4/3) × π × 216
- V = 288 × π ≈ 288 × 3.14159265
- V ≈ 904.78 cm³
Example 2: Calculate the volume of a sphere given a diameter of 10 inches
Problem: Determine the enclosed volume of a beach ball with a diameter of 10 inches.
- Find radius: r = d / 2 = 10 / 2 = 5 inches
- Formula: V = (4/3) × π × r³
- V = (4/3) × π × (5³)
- Calculate 5³ = 125
- V = (500 / 3) × π ≈ 166.67 × 3.14159
- V ≈ 523.60 in³
Frequently Asked Questions (FAQ)
Q: How do you calculate sphere volume if you only know the circumference?
First, calculate the radius using the formula r = C / (2π). Then plug that radius value into the volume formula V = (4/3)πr³.
Q: What happens to the sphere volume if the radius doubles?
Since the radius is cubed in the formula (r³), doubling the radius increases the volume by a factor of 2³ = 8 times.
Q: What is the ratio between a sphere and a cylinder of equal radius and height?
A cylinder with radius r and height h = 2r has volume V = 2πr³. The sphere inside it has volume V = (4/3)πr³. Therefore, the sphere is exactly 2/3 of the cylinder volume.