A Volume Calculator finds the three-dimensional space contained inside a selected solid.

Choose the shape, enter the required dimensions, and the calculator applies the appropriate formula. Results are reported in cubic units such as:

ft³

m³

cm³

or:

in³

Volume calculations are useful for containers, tanks, concrete forms, storage spaces, geometric solids, material estimates, and many other three-dimensional problems.

Identify the solid first, use compatible dimensions, and make sure the formula uses the correct radius, height, and other measurements.

Volume adds a third dimension

Area measures two-dimensional space.

Volume measures three-dimensional space.

For a rectangular box:

Volume = Length × Width × Height

If a box measures:

4 cm × 3 cm × 2 cm

then:

Volume = 4 × 3 × 2

= 24 cm³

The result uses:

cubic centimetres

because three length dimensions were multiplied together.

Common volume formulas

Solid	Volume formula
Rectangular prism	V = l × w × h
Cube	V = s³
Cylinder	V = πr²h
Cone	V = πr²h ÷ 3
Sphere	V = 4πr³ ÷ 3
Prism	V = Base area × perpendicular height
Pyramid	V = Base area × perpendicular height ÷ 3

The dimensions required depend on the selected solid.

Do not substitute a slant height when the formula requires a perpendicular height.

How to use the Volume Calculator

1. Select the solid.
2. Identify the dimensions required by its formula.
3. Convert all measurements to compatible units.
4. Enter the dimensions.
5. Calculate the volume.
6. Confirm the answer is reported in cubic units.
7. For hollow or composite shapes, calculate each part separately and add or subtract as required.

A quick sketch with labeled dimensions can help prevent radius, height, and orientation mistakes.

Rectangular prism volume

For a rectangular prism:

V = l × w × h

Suppose a storage box measures:

6 ft long

4 ft wide

and:

3 ft high

Then:

V = 6 × 4 × 3

= 72 ft³

This formula works for rectangular boxes, rooms, pits, tanks, and other rectangular solids when the entered dimensions represent the relevant interior or exterior geometry.

Cube volume

A cube has equal:

length

width

and:

height

So:

V = s³

If each side is:

5 cm

then:

V = 5³

= 125 cm³

Doubling the side length does much more than double the volume because all three dimensions change.

Cylinder volume

For a cylinder:

V = πr²h

where:

r = radius

and:

h = perpendicular height

Suppose:

Radius = 3 m

Height = 5 m

Then:

V = π × 3² × 5

= 45π

≈ 141.37 m³

Keep the calculator’s full value of:

π

until the final rounding step.

Radius is half the diameter

If a cylinder has:

diameter = 10 ft

then:

radius = 5 ft

The volume formula uses the radius:

V = π × 5² × h

Using:

10

as the radius would make the circular base area four times too large.

Always check whether the input field requests:

radius

or:

diameter

Cone volume

For a cone:

V = πr²h ÷ 3

A cone with the same base radius and perpendicular height as a cylinder has exactly:

one-third

of the cylinder’s volume.

For example, if:

r = 3 m

and:

h = 5 m

the corresponding cylinder has:

45π m³

The cone has:

45π ÷ 3 = 15π m³

or approximately:

47.12 m³

Cone volume does not use slant height

A cone may have both:

vertical height

and:

slant height

The volume formula needs the perpendicular distance from the base plane to the apex.

It does not use the sloping side directly.

Entering the slant height as:

h

can overstate the volume.

Sphere volume

For a sphere:

V = 4πr³ ÷ 3

Suppose:

r = 4 cm

Then:

V = 4π × 4³ ÷ 3

= 256π/3

≈ 268.08 cm³

Again, use the radius rather than the diameter.

Prism volume follows a simple pattern

For any prism with a constant cross-section:

Volume = Base area × Perpendicular height

A rectangular prism is one example.

If the base is triangular:

Base area = b × h ÷ 2

Then multiply that area by the prism length.

This same idea works for many solids with a constant cross-section.

Pyramid volume follows a related rule

For a pyramid:

V = Base area × Perpendicular height ÷ 3

A pyramid occupies one-third the volume of a prism with the same base and perpendicular height.

This relationship is similar to the cylinder-cone comparison.

Compatible units are essential

Do not multiply:

4 ft × 30 in × 2 ft

without converting the dimensions first.

Convert:

30 in = 2.5 ft

Then:

4 × 2.5 × 2 = 20 ft³

Or convert every dimension to inches.

The important point is that all three lengths must use the same unit before multiplication.

Cubic-unit conversion is not the same as length conversion

If:

1 ft = 12 in

then:

1 ft³ = 12³ in³

So:

1 ft³ = 1,728 in³

not:

12 in³

The linear conversion factor is cubed because volume has three dimensions.

Another cubic conversion example

Since:

1 m = 100 cm

then:

1 m³ = 100³ cm³

which is:

1,000,000 cm³

A seemingly simple length conversion becomes much larger when applied to volume.

Converting inputs first is often easier

Suppose a container measures:

2 ft × 18 in × 12 in

Convert everything to feet:

18 in = 1.5 ft

12 in = 1 ft

Then:

V = 2 × 1.5 × 1

= 3 ft³

This approach is often less error-prone than calculating in mixed units and trying to repair the cubic result afterward.

Area and volume should not be confused

A floor measuring:

10 ft × 8 ft

has area:

80 ft²

If the space extends:

6 ft high

then its volume is:

10 × 8 × 6 = 480 ft³

Square units describe surfaces.

Cubic units describe enclosed three-dimensional space.

Volume scales with the cube of length

If every dimension of a solid doubles:

Volume scale factor = 2³ = 8

For example, a cube with:

side = 2

has:

volume = 8

A cube with:

side = 4

has:

volume = 64

And:

64 = 8 × 8

Doubling every dimension makes the volume eight times larger.

Tripling dimensions multiplies volume by 27

If every length is multiplied by:

3

then:

Volume scale factor = 3³ = 27

So a model with:

10 cm³

of volume becomes:

270 cm³

when every linear dimension is tripled.

This cubic scaling is one reason size changes can have large effects on storage, material use, and mass.

Composite solids can be split into simpler pieces

Suppose a stepped object is made from two rectangular prisms.

Prism A:

5 m × 4 m × 2 m

Volume:

40 m³

Prism B:

2 m × 4 m × 3 m

Volume:

24 m³

Total:

40 + 24 = 64 m³

The pieces should not overlap unless the overlap is subtracted separately.

Hollow spaces are subtracted

Suppose a rectangular block measures:

10 cm × 8 cm × 6 cm

Outer volume:

10 × 8 × 6 = 480 cm³

It contains a rectangular hollow section measuring:

6 cm × 4 cm × 6 cm

Inner volume:

6 × 4 × 6 = 144 cm³

Material volume:

480 − 144 = 336 cm³

This method can be used for hollow boxes, pipes, shells, and other shapes where an inner region is removed.

Wall thickness changes internal capacity

Suppose a box has outside dimensions:

10 × 8 × 6 cm

with walls:

1 cm thick

The inside dimensions are not:

10 × 8 × 6

They become:

8 × 6 × 4 cm

assuming 1 cm thickness on both opposite sides.

Internal volume:

8 × 6 × 4 = 192 cm³

The outer volume and usable internal capacity are different.

A hollow cylinder uses outer minus inner volume

For a cylindrical pipe:

Material volume = Outer cylinder volume − Inner cylinder volume

So:

V = πR²h − πr²h

which can be written:

V = πh(R² − r²)

where:

R

is the outer radius

and:

r

is the inner radius.

This is useful for pipe walls, sleeves, and cylindrical shells.

Geometric volume is not always usable capacity

A tank may have a geometric volume of:

1,000 L

but its usable working capacity may be lower.

Reasons can include:

• freeboard;
• fittings;
• internal components;
• overflow level;
• outlet elevation;
• safety margin;
• irregular walls.

The Volume Calculator gives geometric volume from the dimensions entered.

It does not automatically know operational capacity.

Total tank volume and fill volume are different

A tank’s total dimensions describe its maximum geometric space.

If it is only partly full, the contents depend on:

fill depth

and:

container orientation

For a vertical rectangular tank, partial volume is simple:

Volume = Length × Width × Fill depth

provided the cross-section remains constant.

Partial vertical cylinders are also straightforward

For a vertical cylinder with liquid depth:

h

the partial liquid volume is:

V = πr²h

as long as:

h

does not exceed the tank height.

The circular cross-section stays constant throughout the fill depth.

Horizontal cylinders need different geometry

A horizontal cylindrical tank behaves differently.

When partly full, the liquid cross-section forms a circular segment.

The relationship between:

fill depth

and:

liquid volume

is nonlinear.

A half-full horizontal cylinder has half its volume, but a quarter of its diameter in liquid depth does not mean one-quarter of the volume.

Use a horizontal-tank formula or dedicated calculator for that situation.

Orientation can change partial-fill calculations

The same cylindrical tank has the same total geometric volume whether it stands upright or lies horizontally.

But partial fill behaves differently.

Vertical orientation:

cross-sectional area stays constant

Horizontal orientation:

liquid cross-sectional area changes with depth

So orientation matters whenever the container is not completely full.

Irregular containers may need measured capacity

Not every container has a simple geometric interior.

Real vessels can include:

• rounded corners;
• sloped bottoms;
• internal baffles;
• fittings;
• ribs;
• tapered walls;
• irregular heads.

Manufacturer capacity data or direct measurement may be more reliable than a simple geometric approximation.

Displacement can measure irregular objects

For a waterproof object that fits inside a measuring vessel, volume can be measured by liquid displacement.

Suppose water initially reads:

500 mL

After fully submerging the object, it reads:

650 mL

The displaced volume is:

650 − 500 = 150 mL

So the object’s submerged volume is approximately:

150 mL

Since:

1 mL = 1 cm³

that is:

150 cm³

Displacement measurements can have error

Possible sources include:

• trapped air;
• water absorption;
• meniscus reading;
• splashing;
• incomplete submersion;
• coarse measurement marks.

Displacement is a physical measurement rather than a purely geometric calculation.

Its accuracy depends on the procedure and equipment.

Volume can be converted to mass using density

Once volume is known:

Mass = Density × Volume

For example, if a material has density:

800 kg/m³

and occupies:

2 m³

then:

Mass = 800 × 2

= 1,600 kg

The units must be compatible.

Density units must match volume units

If density is:

kg/m³

use volume in:

m³

If density is:

lb/ft³

use volume in:

ft³

Mixing cubic metres with pounds per cubic foot directly will produce an incorrect result.

Convert one side first.

Bulk density can differ from solid-material density

Materials such as:

• soil;
• gravel;
• sand;
• mulch;
• grain;
• foam;
• packed products

contain varying amounts of:

air

void space

or:

moisture

Their bulk density may therefore differ from the density of the solid material itself.

Use a supplier or project-specific bulk-density value when estimating mass from bulk volume.

Packing changes usable storage

A container may have:

100 ft³

of geometric volume but hold less than 100 ft³ of individual objects efficiently.

Unused voids can remain between:

• boxes;
• spheres;
• irregular objects;
• bags;
• loose goods.

Geometric capacity and practical storage capacity are different concepts.

Volume does not automatically tell you material quantity

Suppose a trench has:

20 yd³

of geometric volume.

The quantity of soil, gravel, concrete, or another material required can differ because of:

• compaction;
• settlement;
• bulking;
• waste;
• packaging;
• moisture;
• placement method.

Use the material-specific calculator after finding the geometric volume.

Concrete volume is only the starting quantity

A slab volume can be calculated geometrically.

For example:

20 ft × 10 ft × 0.5 ft = 100 ft³

Convert to cubic yards:

100 ÷ 27 ≈ 3.70 yd³

But actual concrete ordering can also involve:

• waste;
• form variation;
• subgrade irregularity;
• supplier increments.

Use the Concrete Calculator for concrete-specific planning.

Irregular solids may need approximation

An object with curved or irregular boundaries may not match any standard solid exactly.

Possible approaches include:

• dividing it into approximate solids;
• coordinate geometry;
• integration;
• 3D modeling;
• displacement;
• manufacturer specifications.

The basic Volume Calculator works best when the shape matches a known geometric formula.

Frustums need their own formula

A truncated cone or pyramid is called a:

frustum

It cannot be calculated accurately by treating it as a full cylinder or ordinary cone.

The volume depends on both end areas and perpendicular height.

For a frustum of a cone:

V = πh(R² + Rr + r²) / 3

where:

R

is the larger radius

and:

r

is the smaller radius.

Use a shape-specific formula when the calculator supports it.

Slanted prisms still use perpendicular height

For a prism:

Volume = Base area × Perpendicular height

If the sides lean, the sloping edge is not necessarily the height.

The height is the perpendicular distance between the parallel base planes.

Using a sloping edge can overstate the volume.

Bounding boxes provide a quick check

Suppose an irregular object fits completely inside a:

10 cm × 8 cm × 6 cm

box.

The bounding-box volume is:

480 cm³

The irregular object’s volume cannot exceed that amount.

If your calculated result is:

650 cm³

the setup should be checked.

Compare cone and cylinder results

A cone and cylinder with the same:

radius

and:

perpendicular height

have:

Vcone = 1/3 × Vcylinder

If your calculation gives the cone more volume than the cylinder, an input or formula is wrong.

This is a useful independent check.

Compare a sphere with its bounding cube

A sphere of radius:

r

fits inside a cube with side:

2r

Sphere volume:

4πr³/3

Cube volume:

8r³

The sphere’s volume must therefore be smaller than the cube’s.

Simple geometric comparisons like this can reveal unrealistic results.

Measurement uncertainty affects volume strongly

Because volume depends on three dimensions, small measurement errors can combine.

For:

V = lwh

uncertainty in:

length

width

and:

height

all contribute to uncertainty in the final volume.

Avoid reporting excessive decimal precision from rough measurements.

Rough dimensions do not justify many decimal places

Suppose a box is measured as:

4.2 ft × 3.1 ft × 2.8 ft

The direct calculation is:

4.2 × 3.1 × 2.8 = 36.456 ft³

But if each measurement was only approximate to the nearest tenth of a foot, reporting:

36.456000 ft³

would imply more precision than the inputs support.

Round the final result appropriately.

Keep π precise until the end

For cylinders, cones, and spheres, avoid replacing:

π

with:

3.14

too early.

Use the calculator’s built-in value of π.

Then round the final answer according to the required precision.

This prevents avoidable error from propagating through the calculation.

Common volume calculation mistakes to avoid

Reporting square units

Volume uses cubic units such as:

ft³

not:

ft²

Using diameter as radius

Divide the diameter by 2 before using formulas containing:

r

Using slant height as perpendicular height

Cone, pyramid, and prism formulas normally require perpendicular height.

Mixing units

Convert dimensions before multiplication.

Using outside dimensions for internal capacity

Wall thickness can significantly reduce usable volume.

Treating geometric capacity as working capacity

Headspace and fittings can reduce usable contents.

Ignoring orientation for partial tanks

A horizontal cylinder needs different partial-fill geometry from a vertical one.

Assuming volume directly gives mass

Density is required.

Ignoring packing or compaction

Bulk materials and stored objects may not fill space perfectly.

Quick volume examples

Solid	Dimensions	Volume
Rectangular prism	4 × 3 × 2 cm	24 cm³
Cube	s = 5 cm	125 cm³
Cylinder	r = 2 cm, h = 5 cm	≈ 62.83 cm³
Cone	r = 2 cm, h = 5 cm	≈ 20.94 cm³
Sphere	r = 3 cm	≈ 113.10 cm³

These results assume compatible dimensions and use the appropriate perpendicular height.

When to use another calculator

Use the Area Calculator when the problem involves two-dimensional surface area rather than three-dimensional volume.

Use the Concrete Calculator when the calculated volume needs to be converted into a concrete material order.

For ordinary arithmetic and unit checks, use the Basic Calculator.

FAQ

What is the volume of a box?

Multiply its length, width, and height:

V = l × w × h

Use inside dimensions if you are calculating internal capacity.

What is the volume of a cylinder?

Use:

V = πr²h

where:

r

is the radius and:

h

is the perpendicular height.

What is the volume of a sphere?

Use:

V = 4πr³/3

What is the volume of a cone?

Use:

V = πr²h/3

Does a cone use slant height?

No.

The ordinary cone-volume formula uses perpendicular height.

Why are volume units cubed?

Volume multiplies three length dimensions.

For example:

m × m × m = m³

How many cubic inches are in one cubic foot?

Since:

1 ft = 12 in

then:

1 ft³ = 12³ = 1,728 in³

Can I mix feet and inches?

Not directly.

Convert every dimension to a common unit before applying the formula.

How do I calculate a hollow object’s material volume?

Calculate the outer volume and subtract the inner hollow volume.

Is container volume the same as usable capacity?

Not always.

Internal fittings, freeboard, wall thickness, and irregular geometry can reduce usable capacity.

How do I find mass from volume?

Use:

Mass = Density × Volume

Make sure the density and volume units are compatible.

Can I calculate a partly filled tank?

Yes for some simple orientations.

A vertical rectangular or cylindrical tank can use fill depth directly, but a horizontal cylinder requires circular-segment geometry.

Can displacement measure volume?

Yes.

For a fully submerged waterproof object, the increase in liquid volume equals the displaced object volume, subject to measurement error.

What happens if every dimension doubles?

The volume becomes:

2³ = 8 times

as large.

Does the calculator include material waste or compaction?

No.

It calculates geometric volume. Material-specific allowances should be added separately where appropriate.

Mathematics reference

For additional explanations and worked examples involving volume, geometric solids, units, and measurement, see:

OpenStax — Prealgebra 2e

Match the volume to the solid and the purpose

A Volume Calculator can give a precise geometric result only when the correct shape and dimensions are used.

A rectangular prism needs three perpendicular lengths.

A cylinder needs radius and height.

A cone needs radius and perpendicular height.

A sphere needs radius.

For hollow solids, subtract the internal volume. For composite objects, calculate each nonoverlapping part separately. For liquid capacity, confirm that internal geometry and fill level match the formula being used.

Finally, keep geometric volume separate from mass, usable storage, material ordering, and partial-fill capacity. Those questions may require density, packing, freeboard, compaction, or another specialized calculation.