Sphere Volume Calculator
Volume, surface area, and diameter of a sphere from radius, metric or imperial.
What it does
A sphere packs the most volume for a given surface of any shape, which is why balls, tanks, and fruit all favor it. Feed the tool a radius and it returns volume with surface area and diameter beside them, in metric or imperial units.
The metric default uses radius 10 cm. Cubing gives 4/3 x pi x 1000 = 4188.79 cm3, which is 4.19 L, while the surface is 4 x pi x 100 = 1256.6 cm2 and the diameter is 20 cm. Switch to imperial and radius 4 in converts to the same math in gallons.
Two formulas carry the whole page. Volume scales with the cube of the radius, so small radius changes move capacity fast: a 5 cm ball holds 0.52 L while a 10 cm one holds 4.19 L, eight times more. Surface scales with the square, which decides paint, coating, and heat loss.
Watch the units inside each system. Metric volumes print in liters and surfaces in cm2; imperial prints gallons and in2. Diameter simply doubles the radius, so measure across the full width and halve it when only that is known.
How to use
- Pick metric (cm) or imperial (inches).
- Type the radius from center to surface.
- Read volume first: liters or gallons.
- Read surface beside it for coating or material estimates.
- Use diameter to check the ball fits its space.
Formula
- r
- Radius from center to surface, in cm or inches.
- V
- Volume, printed in liters or gallons.
- S, d
- Surface area and diameter in matching square and length units.
Pi uses full machine precision here, so answers sit a hair above textbook examples rounded with 3.14. Volume per radius cubed stays constant either way.
Worked example
Example: radius 10 cm
Metric defaults: radius 10 cm.
- Cube: 10 x 10 x 10 = 1000.
- Volume: 4/3 x pi x 1000 = 4188.79 cm3 = 4.19 L.
- Surface: 4 x pi x 100 = 1256.6 cm2.
- Diameter: 2 x 10 = 20 cm.
- Tool shows 4.19 L, 1256.6 cm2, 20 cm.
Reference table
| Radius | Volume | Surface |
|---|---|---|
| 5 cm | 0.52 L | 314.2 cm2 |
| 10 cm | 4.19 L | 1256.6 cm2 |
| 4 in | 1.16 gal | 201.1 in2 |
| 6 in | 3.92 gal | 452.4 in2 |
Limits
- Perfect spheres only; dents and seams add or remove a little.
- Radius range caps at 2540 cm to keep floats exact.
- Wall thickness ignored, so hollow balls hold slightly less.
- Liters and gallons are US liquid gallons here.
Common mistakes
- Typing diameter where radius belongs, which octuples volume.
- Mixing cm radius with the gallon output.
- Using 3.14 for pi then wondering why cents differ.
- Forgetting volume cubes while surface only squares.
- Reading in2 surface as a volume.
Try it yourself
Quick checks. Answers sit tucked under each question.
Radius 5 cm?
4/3 x pi x 125 = 523.6 cm3 = 0.52 L, surface 314.2 cm2.
Radius 6 in?
904.78 in3 = 3.92 gal, surface 452.4 in2.
Radius 7 cm?
1436.76 cm3 = 1.44 L, surface 615.8 cm2.
Questions
What is the volume of a 10 cm sphere?
4.19 L with 1256.6 cm2 of surface.
Why does doubling radius octuple volume?
Volume cubes the radius: 2 cubed is 8.
How do I get radius from diameter?
Halve it. A 20 cm ball has radius 10 cm.
Liters or gallons here?
Metric prints liters; imperial prints US gallons.
What about a hemisphere?
Halve the volume result; surface needs its own treatment.
Why 4.19 L instead of 4.18?
Full pi versus 3.14 rounding in handbooks.