yCalculator

Volume Calculator

Last updated: April 2026

Choose a 3D shape

Select a solid to show the matching volume formula and dimensions.

Dimensions

Cylinderradius r, height h

Volume

785.3982 cm³

V = pi x r^2 x h

Surface area

471.2389 cm²

SA = 2pi r(r+h)

Practical conversions

cm³

785.3982

litres

0.7854

millilitres

785.3982

m³

0.0008

Step-by-step working

Formula: V = pi x r^2 x h

Substitution: V = pi x 5^2 x 10

  1. r^2 = 5^2 = 25
  2. pi x 25 = 78.5398
  3. 78.5398 x 10 = 785.3982 cm^3
  4. In litres: 785.3982 cm^3 converted from cm^3 = 0.7854 L

Also need surface area?

Surface Area Calculator

Volume vs capacity

Volume measures the space inside a 3D shape. Capacity is the amount a container can hold, often shown in litres or millilitres.

Common volume formulas

Prisms multiply base area by height. Pyramids and cones use one third of the matching prism or cylinder. Spheres and curved solids use radius-based formulas with pi.

Real-world volume examples

Volume calculations help size tanks, pools, boxes, concrete pours, storage containers, packaging, and any project where space or capacity matters.

About this calculator

The Volume Calculator finds the space inside common 3D shapes, including boxes, cubes, cylinders, spheres, cones, pyramids, prisms, capsules, and tanks. It is useful for geometry, packaging, storage, construction, shipping, aquariums, landscaping, concrete, liquid capacity, and any task where cubic units or litres matter.

Shape volume formulas

Each 3D shape uses its standard volume formula. The calculator keeps dimensions in consistent units, calculates cubic units, and shows practical conversions where useful. For liquids, 1 litre equals 1,000 cubic centimetres and 1 cubic metre equals 1,000 litres.

  • box volume = length x width x height
  • cube volume = side^3
  • cylinder volume = pi x radius^2 x height
  • sphere volume = 4 / 3 x pi x radius^3
  • cone volume = 1 / 3 x pi x radius^2 x height

How to use the volume calculator

  1. Choose the 3D shape that best matches the object.
  2. Enter all measurements in the same unit where possible.
  3. Use radius rather than diameter if the formula asks for radius.
  4. Review cubic-unit and litre outputs.
  5. Convert centimetres to metres before using results for building or delivery estimates.
  6. Add waste or freeboard separately where the real-world use needs it.

Worked examples

Box volume

Input: 40 cm x 30 cm x 25 cm

Calculation: 40 x 30 x 25 = 30,000 cm3

Result: The volume is 30,000 cm3, or about 30 litres.

Cylinder volume

Input: Radius 0.5 m, height 1.2 m

Calculation: pi x 0.5^2 x 1.2

Result: The volume is about 0.942 m3, or 942 litres.

Choosing the right formula

A volume query often hides a shape-specific problem. A box, cylinder, cone, and sphere all use different formulas. Pick the closest shape before entering dimensions, otherwise the result can be far away from the real capacity.

Shape formula guide

ShapeFormulaCommon use
Box or cuboidlength x width x heightParcels, rooms, crates
Cylinderpi x radius^2 x heightPipes, tanks, cans
Sphere4 / 3 x pi x radius^3Balls and round vessels
Cone1 / 3 x pi x radius^2 x heightConical piles and funnels

Units and litre conversion

Volume is cubic. If you convert length units, all three dimensions change. That is why 1 m3 equals 1,000 litres, while 1 cm3 equals only 0.001 litres. Check units before using a result for buying materials or estimating shipping capacity.

Common mistakes and edge cases

  • Do not use diameter where radius is required.
  • Do not mix centimetres and metres in the same calculation.
  • Usable capacity may be lower than geometric volume.
  • Material estimates often need waste or compaction allowances.
  • Irregular shapes may need approximation or subdivision into simpler shapes.

Limitations and cautions

This calculator follows standard geometry formulas. Real containers, materials, and sites can have wall thickness, unusable space, uneven surfaces, compaction, or waste.

  • Use internal dimensions for capacity.
  • Use external dimensions for shipping size.
  • Add material allowances separately where needed.

Frequently asked questions

How do I calculate volume?

Choose the shape and use the matching formula, such as length x width x height for a box.

How many litres are in a cubic metre?

There are 1,000 litres in one cubic metre.

Is radius the same as diameter?

No. Radius is half the diameter.

Can I use this for water tanks?

Yes for geometric capacity, but leave allowance for safe fill level and internal fittings.

Can I use this for concrete or soil?

Use it for base volume, then add waste, compaction, or site allowances as needed.

Related calculators

  • area-calculator
  • surface-area-calculator
  • circle-calculator
  • pool-volume-calculator

What does this mean?

This calculator is designed to help you understand the likely number before you make a decision or start an application.

Your result should be checked against official UK guidance, especially if your circumstances include dependants, exemptions, prior leave, or a complex immigration history.

Treat the figure as a planning tool rather than legal advice. Where the answer affects an application deadline or major payment, speak to an authorised adviser.

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