Volume Calculator Formulas for Common Shapes
Use this formula reference for cubes, boxes, cylinders, spheres, cones, prisms, pyramids, and tanks.
Written by Calzivo Editorial Team
Published: June 3, 2026
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Quick answer
In short
- Reference: Most volume formulas multiply a base area by height or length, with special factors for cones, spheres, and pyramids.
- Check: Use matching units before substituting values.check with the calculator
Formula check: Use the Volume Calculator to test the formulas below with your own dimensions.
Quick formula table
| Shape | Inputs | Formula |
|---|---|---|
| Cube | Side s | V = s^3 |
| Rectangular prism / box | Length l, width w, height h | V = l x w x h |
| Cylinder | Radius r, height h | V = pi x r^2 x h |
| Sphere | Radius r | V = 4/3 x pi x r^3 |
| Cone | Radius r, height h | V = 1/3 x pi x r^2 x h |
| Pyramid | Base area A, height h | V = 1/3 x A x h |
| General prism | Base area A, length h | V = A x h |
Box and cube formulas
Box: V = length x width x height Cube: V = side^3
These formulas work for storage bins, rectangular tanks, packages, and cube-shaped objects.
Cylinder formula
V = pi x radius^2 x height
If you have diameter, divide it by 2 first. Round tanks, cans, barrels, and pipes often use this formula.
Sphere and cone formulas
Sphere: V = 4/3 x pi x radius^3 Cone: V = 1/3 x pi x radius^2 x height
Prism and pyramid formulas
Prism: V = base area x length Pyramid: V = 1/3 x base area x height
Use the Area Calculator if you need to find a base area first.
Unit rules
If dimensions are in feet, the result is cubic feet. If dimensions are in centimeters, the result is cubic centimeters. Convert mixed measurements with the Unit Converter.
Formula mistakes to avoid
- Using diameter instead of radius.
- Forgetting the 1/3 factor for cones and pyramids.
- Using square units as the final volume unit.
- Rounding pi too early.
What is the most common volume formula?
For boxes, length x width x height is the most common formula.
What is the cylinder formula?
V = pi x r^2 x h, where r is radius and h is height.
Why are volume units cubic?
Volume uses three dimensions, so the result is a cubic unit.
The right formula depends on the shape, but every formula needs matching units and a final cubic unit.
Use the tool instead
Use the matching calculator when you want to plug in your own numbers and get a result faster.
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