Free Volume Calculator

This online volume calculator offers a fast, accurate way to determine the capacity of the most common three‑dimensional solids. It handles cube volume, sphere volume, cylinder volume, cone volume, rectangular prism volume, pyramid volume, and hemisphere volume—all within a single interface. The tool also functions as a volume unit converter, allowing you to switch between metric units (cubic meters, liters, milliliters) and imperial units (cubic inches, cubic feet, gallons) instantly.

What Is Volume?

Volume measures the three‑dimensional space occupied by an object, substance, or container. It is fundamentally different from area, which is a two‑dimensional measure. The SI standard unit of volume is the cubic meter (m³), but in everyday use you will also encounter liters, milliliters, cubic feet, cubic inches, and gallons. In practical terms, the volume of a container is often called its capacity—the amount of fluid or gas it can hold.

Volume Units and Conversion Table

This calculator supports a broad range of volume units. Popular metric units include cubic centimeters (cm³), cubic meters (m³), liters (L), and milliliters (mL). In the US customary and imperial systems, common units are fluid ounces (fl oz), cubic inches (in³), cubic feet (ft³), cups, pints (pt), quarts (qt), and gallons (gal). The table below provides conversion factors for some of the most frequently used units, enabling quick comparison.

Unit	m³	L	ft³	gal (US)
1 cubic meter (m³)	1	1,000	35.3	264.2
1 liter (L)	0.001	1	0.0353	0.2642
1 cubic foot (ft³)	0.02832	28.317	1	7.481
1 US gallon (gal)	0.003785	3.785	0.1337	1
1 cubic inch (in³)	1.639×10⁻⁵	0.01639	5.787×10⁻⁴	4.329×10⁻³

For a complete unit‑to‑unit reference, you can use the tool’s built‑in volume converter, which handles dozens of combinations instantly.

Volume Formulas for Common 3D Shapes

Each shape has a specific geometric formula that the calculator applies automatically. The table below summarizes the key formulas.

Shape	Volume Formula	Variables
Cube	$V = s^{3}$	$s$ = side length
Rectangular prism (box)	$V = l \times w \times h$	$l$ = length, $w$ = width, $h$ = height
Cylinder	$V = \pi r^{2} h$	$r$ = radius, $h$ = height
Cone	$V = \dfrac{1}{3} \pi r^{2} h$	$r$ = radius, $h$ = height
Sphere	$V = \dfrac{4}{3} \pi r^{3}$	$r$ = radius
Hemisphere	$V = \dfrac{2}{3} \pi r^{3}$	$r$ = radius
Pyramid (general)	$V = \dfrac{1}{3} A h$	$A$ = base area, $h$ = height
Pyramid (regular polygon)	$V = \dfrac{n}{12} h s^{2} \cot\left(\dfrac{\pi}{n}\right)$	$n$ = sides, $s$ = side length, $h$ = height
General prism	$V = A h$	$A$ = base area, $h$ = height

Quick Examples

• A cube with side 5 cm has a volume of $5^{3} = 125\ \text{cm}^{3}$.
• A sphere with radius 10 cm has a volume of $\dfrac{4}{3} \pi (10)^{3} \approx 4,188.8\ \text{cm}^{3}$.
• A rectangular box measuring 3 ft × 2 ft × 4 ft has a volume of $3 \times 2 \times 4 = 24\ \text{ft}^{3}$.

These calculations are performed instantly by the tool once the dimensions are entered.

How to Use the Volume Calculator

1. Select the shape from the dropdown menu. The available choices include cube, sphere, cylinder, cone, rectangular prism, pyramid, and hemisphere.
2. Enter the required dimensions in the input fields. You can change the unit of each dimension by clicking the unit label next to the field.
3. Read the result—the volume is displayed immediately in the default unit.
4. Convert units if needed: click the volume unit to open a list and pick another unit (e.g., from cubic feet to liters). The numeric value updates automatically.

If you need a shape that is not listed here, a collection of specialized calculators is available for more complex geometries.

Measuring the Volume of Solids, Liquids, and Gases

Regular Solids

For objects with a regular shape (cube, sphere, cylinder, etc.), the simplest approach is to measure the relevant dimensions and apply the corresponding formula. The volume calculator automates this process, eliminating manual calculation errors.

Irregular Solids

The classic water displacement method, pioneered by Archimedes, works for any insoluble irregular object. Fill a graduated container with water, record the initial level, fully submerge the object, and record the new level. The difference between the two measurements equals the object’s volume.

Liquids

Measuring a liquid’s volume is straightforward: use a graduated cylinder, measuring cup, or volumetric flask. The choice depends on the required accuracy and the amount of liquid.

Gases

Gases expand to fill their container, so special techniques are needed:

• Use a gas syringe to collect a known volume from a reaction.
• Inflate a balloon with the gas and measure the displaced water volume (another application of Archimedes’ principle).
• Calculate the volume from the gas’s mass and density with $V = \dfrac{m}{\rho}$, or apply the ideal gas law if pressure and temperature are known.

Common Misconception: Volume of a Rectangle

Two‑dimensional shapes like rectangles, squares, and circles do not have volume—they have area. When people refer to the “volume of a rectangle,” they usually mean the volume of a rectangular prism (a box), which is a 3D object. The box volume is simply $V = l \times w \times h$. For example, a box that is 10 in long, 5 in wide, and 3 in tall has $10 \times 5 \times 3 = 150\ \text{in}^{3}$.

Real‑World Applications

Volume calculations are essential in many fields:

• Construction: Determining concrete volume for slabs and footings.
• Gardening: Estimating soil or mulch needed for planters and raised beds.
• Cooking: Converting between milliliters, cups, and tablespoons when following international recipes.
• Shipping: Computing cubic volume for freight pricing and container space planning.
• Science & medicine: Preparing solutions, dosing medication, and conducting experiments with precise volume measurements.

Whether you are a student, engineer, builder, or hobbyist, this volume calculator simplifies both common and advanced volume‑related tasks.