Sphere Volume Calculator
Volume and surface area of a sphere from a single radius — the 3D counterpart to the circle calculator, for anything from a scoop of ice cream to a storage tank's capacity.
Inputs
Result
523.5988
Surface area 314.1593
How the sphere volume calculator works
Volume = (4/3)πr³.
Surface area = 4πr².
Worked example: radius 5
- Volume = (4/3) × π × 5³ = (4/3) × π × 125 ≈ 523.6.
- Surface area = 4 × π × 5² = 4 × π × 25 ≈ 314.16.
Common mistakes to avoid
Entering the diameter instead of the radius
Volume scales with the cube of whatever length is entered, so mistaking diameter for radius here overstates the volume by a factor of 8, not just 2.
Mixing up volume and surface area units
Volume is in cubic units (like cm³) while surface area is in square units (cm²) — a result reported with the wrong unit label is a common but easily caught error.
Frequently asked questions
Why does volume use r³ while surface area uses r²?
Volume measures 3D space (length × width × height, conceptually), while surface area measures a 2D covering — this is why volume grows much faster than surface area as a sphere gets bigger.
What's a practical way to double-check a sphere volume result?
For a sphere with the same radius as a cylinder's radius and height equal to its diameter, the sphere's volume is exactly two-thirds of that cylinder's volume — a useful sanity check.
How would I find the radius if I only know the volume?
Rearrange to r = ((3V) ÷ (4π))^(1/3) — divide the volume appropriately and take the cube root.
Does this work for a hemisphere (half a sphere)?
Not directly — halve the full-sphere volume for a hemisphere's volume, but note the surface area calculation needs adjusting differently since a hemisphere also has a flat circular face.
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