Volume Calculator

The Volume Calculator helps you determine the amount of space occupied by a 3D object. It's useful for students learning geometry, engineers designing structures, and anyone needing to calculate capacities for practical applications.

S. Siddiqui

Edited by

S. SiddiquiFounder & Editor-in-Chief
Sources:WikipediaWolfram AlphaUpdated May 2026

Shape

Shape Diagram

3 × 4

Volume

27

Cubic Meters

27 m³

Liters

27,000 L

Cubic Centimeters

27,000,000 cm³

What Is the Volume Calculator?

Volume is the measure of three-dimensional space enclosed within an object, expressed in cubic units. Whether you are working out how much water a tank can hold, figuring out how much concrete is needed for a foundation, or carrying out a physics or chemistry problem, being able to calculate volume accurately is a core practical skill.

This calculator covers four common three-dimensional shapes: cubes, cylinders, spheres, and cones. Each has its own formula, and the tool shows the working alongside the result so you can build on the calculation if needed. MathIsFun's geometry section is a solid visual reference for understanding how these shapes relate to each other, and Khan Academy's unit on geometric solids covers the derivations of each volume formula in detail.

How to Use the Volume Calculator

  1. Select the shape from the dropdown: cube, cylinder, sphere, or cone.
  2. Enter the required dimensions. The input fields update to show exactly which measurements are needed for the selected shape.
  3. Choose your unit of measurement. The output will be in the corresponding cubic unit.
  4. The result appears instantly along with the formula used and a step-by-step breakdown of the calculation.
  5. For the surface area of any of these shapes, note that the calculator also shows this alongside the volume, which is useful when you need to figure out how much material is needed to cover the outside of an object.

Formulas and Methodology

Each shape uses a distinct formula that captures its geometry. The table below sets out the key formulas, with all four shapes covered by this calculator.

Shape Volume Formula Variables
Cube V = s³ s = side length
Rectangular prism V = l x w x h l = length, w = width, h = height
Cylinder V = πr²h r = radius, h = height
Sphere V = (4/3)πr³ r = radius
Cone V = (1/3)πr²h r = base radius, h = height

Worked example (cylinder): A cylindrical water tank has a radius of 0.5 m and a height of 2 m. Its volume is π x 0.25 x 2 = π x 0.5 = approximately 1.571 cubic metres, which is 1,571 litres (since 1 cubic metre equals 1,000 litres).

Worked example (sphere): A football has a radius of approximately 11 cm. Its volume is (4/3) x π x 11³ = (4/3) x π x 1,331 = approximately 5,575 cubic centimetres.

Worked example (cone): An ice cream cone with a base radius of 3 cm and a height of 10 cm has a volume of (1/3) x π x 9 x 10 = 30π = approximately 94.25 cubic centimetres.

Real-World Applications

Volume calculations are used across a wide range of industries and everyday situations:

  • Construction and civil engineering: Calculating how much concrete is needed for a cylindrical column, a rectangular foundation slab, or a conical pile of aggregate requires accurate volume figures. Ordering too little or too much material has real cost implications.
  • Plumbing and tank sizing: Water tanks, boilers, and storage vessels are typically cylindrical or spherical. Knowing the volume tells you how much water or liquid they can hold, which informs pump selection, pipe sizing, and supply calculations.
  • Packaging and logistics: The volume of a box or container determines how many products can be packed inside, which affects shipping costs and storage planning. On top of that, knowing the volume of a product helps manufacturers design packaging that minimises wasted space.
  • Chemistry and physics: Volume is a fundamental quantity in both disciplines. Reaction rates, density calculations, and fluid dynamics all require accurate volume measurements. Converting between cubic centimetres and millilitres (they are numerically equal) is a routine task in laboratory work.
  • Cooking: Baking and cooking often involve volumes of liquids and dry ingredients. Understanding that a cylindrical pot has a volume of pi r squared times height helps you figure out whether a recipe will fit in a given vessel.

Key Considerations

A few practical points help ensure your volume calculations are accurate and useful:

  • Units must be consistent: If the radius is in centimetres and the height is in metres, the result will be numerically wrong. Convert all dimensions to the same unit before calculating. Given that volumes are in cubic units, a small difference in the input unit has a large effect on the output: 1 metre cubed equals 1,000,000 cubic centimetres.
  • Radius versus diameter: The volume formulas for cylinders, spheres, and cones all use the radius, not the diameter. If you have measured the diameter (the full width across the centre), divide by two before entering the value.
  • Real objects are rarely perfect shapes: A sphere is rarely a mathematically perfect sphere in practice. For engineering and construction purposes, volume calculations give a close approximation that is accurate enough for ordering materials, but adding a 5 to 10 percent margin is prudent.
  • Volume and capacity conversions: 1 cubic metre = 1,000 litres. 1 cubic centimetre = 1 millilitre. These conversions come up constantly when working with liquid volumes, and having them to hand saves a step when interpreting results.

Conclusion

The Volume Calculator takes the arithmetic out of one of the most practically important geometry tasks, covering the four most common three-dimensional shapes with clear formulas and step-by-step working. Whether you are ordering materials, sizing a tank, completing a school problem, or working through an engineering calculation, having accurate volume figures quickly makes a real difference. For related tools, the Area Calculator handles the two-dimensional faces of these shapes, and the Circle Calculator is useful for working out the circular cross-sections of cylinders and cones.

Last reviewed: May 31, 2026
Founder's Real-World Experience
S. Siddiqui

S. Siddiqui

Founder & Editor-in-Chief, YourToolsBase

How I ordered exactly the right amount of soil for raised garden beds

In spring 2026 I built two raised garden beds from scaffold boards: one rectangular at 2.4 m by 1.2 m by 0.3 m deep, and one round water butt I converted into a planter with an internal diameter of 0.6 m and a depth of 0.5 m. I needed to work out how much topsoil to order and soil is sold by the cubic metre. Getting this wrong in either direction is expensive: too little means a second delivery charge, too much means a pile of soil I have nowhere to put.

I used the rectangular volume formula for the first bed: 2.4 times 1.2 times 0.3 gives 0.864 m3. For the converted water butt I used the cylinder formula, as covered in the Maths Is Fun geometry reference: pi times 0.3 squared times 0.5 gives 0.141 m3. Combined that came to 1.005 m3. I added 5% for settling and ordered 1.06 m3, which the supplier rounded up to 1.1 m3 as their minimum bag size.

The soil filled both beds to within about 20 mm of the intended level after settling. That is a far better result than the previous year when I estimated by eye and ended up 40 kg short on the first delivery.

Rectangular bed: 0.864 m3Cylinder planter: 0.141 m3Total ordered: 1.1 m3
Also used alongside: Area Calculator

Frequently Asked Questions

How do I calculate the volume of a cylinder?
Multiply pi (approximately 3.14159) by the square of the radius, then multiply by the height. The formula is V = pi x r squared x h. For a cylinder with radius 4 cm and height 10 cm: V = 3.14159 x 16 x 10 = approximately 502.65 cubic centimetres. Remember that the radius is half the diameter if you have measured across the full width.
What is the difference between volume and surface area?
Volume measures the three-dimensional space enclosed inside a shape, expressed in cubic units such as cubic metres or cubic centimetres. Surface area measures the total area of all the outer faces or surfaces of the shape, expressed in square units. When calculating how much paint to coat a tank you need surface area; when calculating how much liquid it holds you need volume.
How do I convert cubic metres to litres?
Multiply the volume in cubic metres by 1,000 to get litres. One cubic metre is exactly 1,000 litres. For smaller volumes, 1 cubic centimetre equals 1 millilitre. These conversions are particularly useful when the calculator gives you a result in cubic metres and you want to express it as a capacity in litres.
Why is the cone formula one third of the cylinder formula?
A cone fits exactly one third of the volume of a cylinder with the same base radius and height. This can be demonstrated by filling a cone with water and pouring it into a matching cylinder: it takes exactly three cones to fill the cylinder. The mathematical proof uses calculus to integrate the cross-sectional areas from the tip to the base, but the one-third relationship is the key result.
How do I calculate the volume of an irregular object?
For irregular solid objects, the most practical method is the water displacement technique: submerge the object in a known volume of water in a graduated container and measure how much the water level rises. The rise in volume equals the volume of the object. This approach is used in laboratories and is how Archimedes famously worked out the volume of the king's crown.
What units should I use for volume calculations?
Use whichever unit is most convenient for the scale of your problem: millimetres and cubic millimetres for small engineering components, centimetres and cubic centimetres for everyday objects, metres and cubic metres for large structures. The important thing is to keep all input dimensions in the same unit throughout the calculation, since mixing units is the most common source of errors.
How do I find the volume of a half-sphere (hemisphere)?
Calculate the full sphere volume using (4/3) x pi x r cubed, then divide by 2. The result is (2/3) x pi x r cubed. For a hemisphere with radius 5 cm: (2/3) x 3.14159 x 125 = approximately 261.8 cubic centimetres. The same principle applies to any fraction of a sphere.

Formula

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💡 Pro Tip

Unit conversion tip: 1 m³ = 1,000 liters = 1,000,000 cm³. When in doubt, convert all dimensions to meters first.

About the Author

S. Siddiqui

S. Siddiqui

Founder & Editor-in-Chief

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S. Siddiqui is the founder and editor-in-chief of YourToolsBase, overseeing all content, tool accuracy, and editorial standards.

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Authoritative Sources

Formulas and data in this tool are based on guidelines from the above sources.