How do I convert m³ to litres or gallons?

1 cubic metre is exactly 1,000 litres. To convert to US gallons, multiply litres by 0.2642 (so 1 m³ ≈ 264.17 US gal). For UK/imperial gallons, multiply by 0.2200 (so 1 m³ ≈ 219.97 imp gal). The most common error is mixing centimetres and metres in the same calculation — 1 m³ is 1,000,000 cm³, not 100.

Why does the cone formula have ⅓ in it?

Because a cone is exactly one-third of the cylinder that would enclose it. The full derivation uses integration — slicing the cone into thin disks and summing — but the intuition is that three identical cones with the same base and height fill the matching cylinder exactly. The same one-third factor applies to pyramids for the same reason.

How do I find the volume of an irregular shape?

Archimedes' displacement method: submerge the object in a container of water, measure the volume of water displaced, and that equals the object's volume. Works for anything that does not absorb water and is denser than water. For porous or floating objects, weigh the object dry, weigh it submerged on a string, and divide the difference (in grams) by the water's density (1 g/cm³).

What is the difference between volume and capacity?

Volume is the space an object occupies; capacity is the space a container can hold. For a solid object they are the same. For a container, the capacity is the internal volume — calculated from internal dimensions, which differ from external dimensions by the wall thickness. A 1-litre bottle has more than 1 litre of external volume because the glass takes up space.

How much concrete do I order for a slab?

Calculate the volume in cubic metres or cubic yards (length × width × thickness, all in the same unit), then add 5–10% for waste. A 4×3×0.15 m slab is 1.8 m³; order 2.0 m³. Concrete is sold in cubic-yard increments in the US (1 yd³ ≈ 0.765 m³) and cubic-metre increments elsewhere. Always double-check with the supplier before pouring.

Why does my fish tank volume differ from the manufacturer's spec?

Three reasons. First, the spec is usually the gross internal volume; you lose 5–10% to gravel, decor, and the gap below the rim. Second, glass thickness shrinks the usable volume — a tank with external 60×30×30 cm has only about 56×26×26 cm of water-fillable space. Third, US gallon vs UK gallon vs litre confusion accounts for a lot of imported-spec mismatches.

Guide

Volume Formulas for Every Common Solid Shape (With Examples)

Eight formulas cover almost every real-world volume problem — and the unit conversions cause more errors than the geometry.

By Buğra SözeriPublished May 31, 2026

Volume is one of the most useful pieces of school maths because the real world is full of moments when you need it — pouring concrete, sizing a fish tank, ordering gravel, costing a barrel of fuel. The formulas are not difficult, but they are easy to confuse, and unit conversions cause more errors than the geometry ever does. This guide gives you the eight formulas that cover almost everything, with worked examples and the conversion traps clearly marked.

Before you start: pick one unit and stick to it

The single largest source of volume errors is mixing units. A cube with sides of 1 m has a volume of 1 m³, which is 1,000,000 cm³, not 100. If you measure length in metres and width in centimetres, the answer is meaningless. Convert all dimensions to the same unit before applying any formula.

Useful conversions:

1 m³ = 1,000 litres = 1,000,000 cm³ = 1,000,000 mL
1 m³ ≈ 264.17 US gallons ≈ 219.97 imperial gallons
1 m³ ≈ 35.31 cubic feet ≈ 1.308 cubic yards
1 ft³ ≈ 7.481 US gallons

Run the numbers in our volume calculator if you want to check any of the worked examples below.

1. Sphere

V = (4/3) π r³

Derivation hint:the formula falls out of integrating thin disks stacked from the equator to the pole, in spherical coordinates. Archimedes proved it in the third century BCE without calculus, by showing a sphere's volume is exactly two-thirds the volume of the enclosing cylinder.

Example: a basketball with a 12 cm radius.

V = (4/3) × π × 12³ = (4/3) × π × 1728 ≈ 7,238 cm³ ≈ 7.24 litres.

2. Cylinder

V = π r² h

Derivation hint: a cylinder is a circle stretched perpendicular to its plane. Volume = base area × height; the base is a circle, so the area is π r².

Example: a steel drum 60 cm tall with a 30 cm radius (about a US 55-gallon barrel).

V = π × 30² × 60 = π × 900 × 60 ≈ 169,646 cm³ ≈ 169.6 litres ≈ 44.8 US gallons.

The difference between a 44.8-gallon and a 55-gallon drum is the rim and the headspace; manufacturer nominal capacity is always lower than gross volume.

3. Cone

V = (1/3) π r² h

Derivation hint: a cone is exactly one-third of its enclosing cylinder. Three identical cones fill the matching cylinder; you can verify with rice and cardboard models.

Example: an ice-cream cone, 12 cm tall with a 3 cm radius at the top.

V = (1/3) × π × 3² × 12 = (1/3) × π × 9 × 12 ≈ 113.1 cm³ ≈ 113 mL.

4. Pyramid

V = (1/3) × base area × h

Derivation hint: like the cone, a pyramid is one-third of its enclosing prism. The same one-third factor appears because both are linearly tapering solids.

Example: the Great Pyramid of Giza, approximately 230 m on each side at the base and 139 m tall (current height; original was 146 m).

V = (1/3) × (230 × 230) × 139 ≈ 2,450,633 m³ ≈ 2.45 million cubic metres of stone.

5. Rectangular prism (cuboid)

V = l × w × h

Derivation hint: the cuboid is the canonical volume shape — width times depth times height, the same way you tile a floor and then stack tiles to the ceiling.

Example: a concrete slab for a small patio, 4 m × 3 m × 0.15 m thick.

V = 4 × 3 × 0.15 = 1.8 m³.

Order 2.0 m³ to allow for spillage and uneven sub-grade. Concrete suppliers will not split a delivery below the minimum drum size; verify the minimum order before scheduling.

6. Cube

V = s³

Derivation hint: a cube is a cuboid where all three sides are equal, so the formula simplifies.

Example:a Rubik's cube, 5.7 cm per side.

V = 5.7³ = 185.2 cm³.

Most of the “volume” is mechanism, not solid plastic — the manufactured material volume is much less.

7. Torus (doughnut shape)

V = 2 π² R r²

where R is the distance from the centre of the tube to the centre of the torus, and r is the radius of the tube itself.

Derivation hint:Pappus's centroid theorem — the volume of a solid of revolution is the area of the rotating shape times the distance travelled by its centroid. A circle of area π r² traced around a path of circumference 2 π R gives the formula.

Example: a bicycle inner tube with R = 30 cm and r = 2 cm.

V = 2 × π² × 30 × 2² = 240 π² ≈ 2,369 cm³ ≈ 2.37 litres.

8. Ellipsoid

V = (4/3) π a b c

where a, b, and c are the semi-axis lengths (half of the three principal axes).

Derivation hint: the ellipsoid is a sphere scaled by different factors along each axis. A sphere of radius r has volume (4/3) π r³; replacing r³ with the product of the three semi-axes gives the ellipsoid formula.

Example: a chicken egg, approximately 6 cm × 4.5 cm × 4.5 cm (long axis 6, two equal short axes 4.5). Semi-axes are 3, 2.25, 2.25.

V = (4/3) × π × 3 × 2.25 × 2.25 ≈ 63.6 cm³ ≈ 64 mL.

A large chicken egg is about 60 mL, so the model is close.

Archimedes' water-displacement method

For an irregular shape — a sculpture, a rock, an engine block — no formula applies. The classical solution is displacement: submerge the object in a container of water and measure how much the water level rises. The displaced volume equals the object's volume.

Practical procedure:

Fill a container of known cross-sectional area with enough water to fully submerge the object.
Mark the water level.
Submerge the object completely (use a thin wire if it floats).
Mark the new water level.
Volume of object = container cross-section × height difference.

For floating objects (less dense than water), weigh the object dry in grams, submerge it on a string while it hangs from a kitchen scale, and the difference in weight readings equals the weight of displaced water. Divide by 1 g/cm³ to get volume in cm³.

Real-world uses

Concrete pour. Rectangular prism formula, then add 5–10% waste. Use cubic metres or yards; never centimetres.
Fish tank capacity. Internal dimensions only. Subtract gravel, decor, and 10% headspace from the gross to get fish-loading capacity.
Fuel tank. Cylinder formula for horizontal or vertical cylindrical tanks. Account for the fact that a horizontal cylinder is not linearly filled — half full by depth is half full by volume only at exactly the centreline.
Shipping volume.Cuboid formula. Carriers charge by “dimensional weight,” computed by dividing volume in cm³ by a divisor (5,000 or 6,000 depending on carrier).
Cooking and baking.Cylinder for a round pan, rectangular prism for a sheet pan. Recipe says “9-inch round pan” — that is a 23-cm-diameter cylinder; if you only have a 20-cm pan, scale the recipe by the ratio of volumes.

The unit-conversion trap, one more time

Volume scales with the cube of length. If you double every linear dimension, the volume increases by a factor of 8, not 2. This is why scaling a model up to full size — or converting a fluid-ounce recipe to litres — is rarely a simple multiplication. When in doubt, compute the volume in your starting unit, then convert the final volume value once; do not convert dimensions one at a time mid-formula.

The honest takeaway

Eight formulas cover almost every real-world volume problem. The geometry is straightforward; the failure modes are almost always (a) mixed units, (b) confusing radius with diameter, or (c) forgetting that volume scales with the cube of length. Verify any tricky calculation with our volume calculator, double- check your unit conversions before ordering material, and when in doubt, use Archimedes' displacement method for irregular shapes — it has worked for 2,300 years and shows no sign of stopping.

Frequently asked questions

How do I convert m³ to litres or gallons?: 1 cubic metre is exactly 1,000 litres. To convert to US gallons, multiply litres by 0.2642 (so 1 m³ ≈ 264.17 US gal). For UK/imperial gallons, multiply by 0.2200 (so 1 m³ ≈ 219.97 imp gal). The most common error is mixing centimetres and metres in the same calculation — 1 m³ is 1,000,000 cm³, not 100.
Why does the cone formula have ⅓ in it?: Because a cone is exactly one-third of the cylinder that would enclose it. The full derivation uses integration — slicing the cone into thin disks and summing — but the intuition is that three identical cones with the same base and height fill the matching cylinder exactly. The same one-third factor applies to pyramids for the same reason.
How do I find the volume of an irregular shape?: Archimedes' displacement method: submerge the object in a container of water, measure the volume of water displaced, and that equals the object's volume. Works for anything that does not absorb water and is denser than water. For porous or floating objects, weigh the object dry, weigh it submerged on a string, and divide the difference (in grams) by the water's density (1 g/cm³).
What is the difference between volume and capacity?: Volume is the space an object occupies; capacity is the space a container can hold. For a solid object they are the same. For a container, the capacity is the internal volume — calculated from internal dimensions, which differ from external dimensions by the wall thickness. A 1-litre bottle has more than 1 litre of external volume because the glass takes up space.
How much concrete do I order for a slab?: Calculate the volume in cubic metres or cubic yards (length × width × thickness, all in the same unit), then add 5–10% for waste. A 4×3×0.15 m slab is 1.8 m³; order 2.0 m³. Concrete is sold in cubic-yard increments in the US (1 yd³ ≈ 0.765 m³) and cubic-metre increments elsewhere. Always double-check with the supplier before pouring.
Why does my fish tank volume differ from the manufacturer's spec?: Three reasons. First, the spec is usually the gross internal volume; you lose 5–10% to gravel, decor, and the gap below the rim. Second, glass thickness shrinks the usable volume — a tank with external 60×30×30 cm has only about 56×26×26 cm of water-fillable space. Third, US gallon vs UK gallon vs litre confusion accounts for a lot of imported-spec mismatches.

Sources & references

Authoritative references cited by this piece. Verified by Buğra Sözeri on the dates shown and re-checked at every deploy.

Stewart — Calculus: Early Transcendentals (9th ed.) — Standard calculus reference for the derivations of solid-of-revolution volume formulas (cone, sphere, torus, ellipsoid)(as of 2026-05-31)
NIST — Reference on Constants, Units, and Uncertainty — Authoritative SI definitions and unit-conversion factors used in this guide(as of 2026-05-31)
Wolfram MathWorld — Solid Geometry — Reference for the canonical formulas, including the torus and ellipsoid(as of 2026-05-31)
NRMCA — National Ready Mixed Concrete Association: ordering guide — Background for the concrete-volume worked example(as of 2026-05-31)

Published May 31, 2026