Sphere Volume Calculator: Formula, Surface Area and Step-by-Step Answer
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Enter the radius of the sphere.
A sphere with radius 6.0000 cm (diameter 12.0000 cm) has a volume of 904.7787 cm³ and a surface area of 452.3893 cm².
Show the steps
- r³ = 6.0000³ = 216.0000.
- Volume = (4/3) × π × r³ = 904.7787 cm³.
- Surface area = 4 π r² = 4 × π × 6.0000² = 452.3893 cm².
Sphere
V = (4/3) π r³
Surface area = 4 π r²
Circumference of a great circle = 2 π r
Estimates for planning and learning, not financial, tax, legal or medical advice. Check figures with your lender, tax preparer or doctor before you act.
About this calculator
A sphere is a perfectly round 3D shape, like a ball. Its volume is V = (4/3) π r³ and its surface area is 4 π r². Use this calculator for balls, bubbles, tanks and planets.
Enter the radius, or half the diameter, and get the volume, surface area, diameter and great-circle circumference.
How to use it
- Enter the radius of the sphere.
- Pick the unit.
- Read the volume, surface area and the steps.
Sphere formulas
- Volume: V = (4/3) π r³
- Surface area: 4 π r²
- Diameter: d = 2r
Example
A ball with radius 6 cm has V = (4/3) × π × 216 = 904.78 cm³ and surface area 4 × π × 36 = 452.39 cm².
Sources
Quick check: test yourself
A sphere has radius 2 cm. What is its volume to the nearest tenth?
Correct answer: 33.5 cm³. V = (4/3) π r³ with r = 2.
If the radius of a sphere doubles, the volume becomes
Correct answer: 8 times as large. Volume depends on r³: 2³ = 8.
Which formula gives the surface area of a sphere?
Correct answer: 4 π r². Surface area of a sphere is 4 π r².
Pick an answer for each question.
Common questions
How do I find the volume of a sphere?
Cube the radius, multiply by π, then multiply by 4/3.
What if I know the diameter?
Divide the diameter by 2 to get the radius.
Why is the volume proportional to r³?
Volume has three dimensions, so doubling the radius makes the sphere 2³ = 8 times as large.
What is the surface area of a sphere?
4 π r².
How is a sphere related to a cylinder?
A sphere that fits snugly inside a cylinder fills exactly two thirds of it.
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