Volume Calculator: Calculate the Volume of 3D Shapes

The Volume Calculator helps you quickly find how much three-dimensional space an object occupies. Select a shape, enter its dimensions, and the calculator applies the appropriate volume formula to give you the result.

Different 3D shapes require different formulas. A rectangular prism uses length, width, and height, while a cylinder uses its radius and height. Spheres, cones, pyramids, frustums, capsules, tori, and polygon-based prisms each have their own method of calculating volume.

This calculator supports a range of common and specialized 3D shapes. You can also work with different length and volume units, including cubic units as well as capacity units such as liters and US gallons. If you already know the desired volume, you can also work backward to find a missing dimension when enough information is available.

What Is Volume?

Volume is the amount of three-dimensional space occupied by an object or enclosed inside a container.

Area measures a two-dimensional surface, while volume measures three dimensions. That’s why volume is normally expressed in cubic units, such as cubic centimeters (cm³), cubic meters (m³), cubic feet (ft³), or cubic yards (yd³).

For example, consider a rectangular box that is 2 meters long, 1 meter wide, and 0.5 meters high:

2 × 1 × 0.5 = 1 m³

The volume of the box is therefore 1 cubic meter.

In everyday situations, volume is also commonly used to describe how much liquid a container can hold. This is why units such as liters, milliliters, gallons, quarts, pints, and fluid ounces are often used when talking about containers and liquids.

How to Calculate Volume

There is no single volume formula that works for every 3D shape. The correct formula depends on the geometry of the object.

The basic process is:

1. Identify the 3D shape.
2. Measure the dimensions required for that shape.
3. Make sure the measurements are interpreted with the correct units.
4. Apply the appropriate volume formula.
5. Convert the result to your preferred volume unit if needed.

For simple shapes, calculating volume by hand may take only a few seconds. With more complicated shapes, however, it is easy to use the wrong formula, overlook a measurement, or make an error during unit conversion.

A volume calculator simplifies the process by applying the appropriate formula and handling the calculation for you.

Example: Calculating the Volume of a Box

Suppose a storage box is 80 cm long, 40 cm wide, and 30 cm high.

For a rectangular prism:

Volume = length × width × height

Substituting the measurements:

80 × 40 × 30 = 96,000 cm³

Since:

1,000 cm³ = 1 L

the same volume can also be expressed as:

96,000 cm³ = 96 L

This is a good example of why converting between cubic units and capacity units can be useful in everyday calculations.

Volume Formulas by Shape

The Volume Calculator supports the following 3D shapes. Rather than simply memorizing each equation, it helps to understand what the measurements represent and why the formula works.

Cube

A cube has six equal square faces, so all three dimensions are represented by the same side length.

Volume = side³

For example, if the side length is 5 cm:

V = 5³ = 125 cm³

Because all sides are equal, a cube requires only one measurement to calculate its volume.

Rectangular Prism

A rectangular prism, sometimes called a cuboid, has three independent dimensions: length, width, and height.

Volume = length × width × height

This is the standard formula for boxes, rooms, storage containers, rectangular tanks, packages, and many construction materials.

For example, a rectangular prism measuring 2 m × 1.5 m × 0.8 m has a volume of:

2 × 1.5 × 0.8 = 2.4 m³

Cylinder

A cylinder has a circular base and a constant cross-section along its height.

Volume = π × r² × h

Here, r is the radius of the circular base and h is the height.

The expression π × r² calculates the area of the circular base. Multiplying that area by the height gives the cylinder’s volume.

For example, a cylinder with a radius of 0.5 m and a height of 2 m has a volume of approximately:

π × 0.5² × 2 ≈ 1.57 m³

This formula is useful for cylindrical tanks, cans, containers, pipes, and other round structures.

Cone

A cone has a circular base that narrows to a single point.

Volume = 1/3 × π × r² × h

The formula is similar to the cylinder formula, but the result is multiplied by one-third. A cone with the same base radius and height as a cylinder occupies exactly one-third of the cylinder’s volume.

For example, a cone with a radius of 3 m and a height of 4 m has a volume of approximately:

1/3 × π × 3² × 4 ≈ 37.70 m³

When measuring a cone, remember that the height is the perpendicular distance from the base to the tip, not the length of the sloping side.

Sphere

A sphere is a perfectly round three-dimensional shape in which every point on its surface is the same distance from the center.

Volume = 4/3 × π × r³

Here, r is the radius, measured from the center of the sphere to its surface.

For example, a sphere with a radius of 1 m has a volume of approximately:

4/3 × π × 1³ ≈ 4.19 m³

This formula can be used for balls, spherical containers, tanks, and other objects that can reasonably be modeled as spheres.

Because the radius is cubed, even a relatively small change in radius can produce a significant change in volume.

Hemisphere

A hemisphere is exactly half of a sphere.

Volume = 2/3 × π × r³

The formula is simply half the volume of a sphere with the same radius.

Hemisphere calculations can be useful for domes, half-spherical containers, and other objects with a rounded half-sphere shape.

Triangular Prism

A triangular prism has a triangular cross-section that extends along a length.

To calculate its volume, first find the area of the triangular base and then multiply it by the prism’s length:

Volume = 1/2 × base × height × length

The height of the triangle is the perpendicular distance from the base to the opposite vertex.

This formula can be useful for triangular structural components, wedges, packaging, and certain construction materials.

Pyramid

A pyramid has a base of a particular shape, with its sides meeting at a common point called the apex.

Volume = 1/3 × base area × height

The base does not necessarily have to be a square. The key measurements are the area of the base and the perpendicular height from the base to the apex.

This general formula can therefore be used for pyramids with different base shapes.

Square Pyramid

A square pyramid has a square base, which makes the base area especially simple to calculate.

Volume = 1/3 × base side² × height

If the side length of the square base is s, the base area is s². Multiply that area by the height and divide by 3 to obtain the volume.

For example, a square pyramid with a base side of 3 m and a height of 4 m has a volume of:

1/3 × 3² × 4 = 12 m³

Frustum

A frustum is the portion of a cone that remains after its tip has been cut off by a plane parallel to the base.

Because it has two circular bases with different radii, its volume requires both radii:

Volume = 1/3 × π × h × (R² + Rr + r²)

Where:

• R is the larger radius
• r is the smaller radius
• h is the perpendicular height

For example, if the larger radius is 3 m, the smaller radius is 1 m, and the height is 2 m:

1/3 × π × 2 × (3² + 3 × 1 + 1²) ≈ 27.23 m³

This formula is useful for tapered containers, truncated cones, and certain architectural and construction components.

Ellipsoid

An ellipsoid is a three-dimensional shape that can be thought of as a stretched or flattened sphere.

Volume = 4/3 × π × A × B × C

Here, A, B, and C are the three semi-axis lengths.

A sphere is a special case of an ellipsoid. When all three semi-axes are equal, the formula becomes the familiar sphere volume formula.

Capsule

A capsule consists of a cylindrical middle section with a hemisphere at each end.

Its volume is:

Volume = π × r² × L + 4/3 × π × r³

Here, r is the radius and L is the length of the cylindrical middle section.

The formula can be understood as the volume of one cylinder plus one complete sphere, because the two hemispherical ends together form a sphere.

For example, a capsule with a radius of 1 m and a cylindrical section 2 m long has a volume of approximately:

π × 1² × 2 + 4/3 × π × 1³ ≈ 10.47 m³

There is also a useful special case: if the cylindrical section has a length of zero, the capsule becomes a sphere. The formula then reduces to the standard sphere volume formula.

Torus

A torus is the doughnut-shaped 3D object familiar from geometry and everyday objects.

Its volume is:

Volume = 2 × π² × R × r²

Here:

• R is the major radius, measured from the center of the torus to the center of its tube
• r is the minor radius, which is the radius of the tube itself

For example, a torus with a major radius of 5 cm and a minor radius of 1 cm has a volume of approximately:

2 × π² × 5 × 1² ≈ 98.70 cm³

For this shape, the major radius must be greater than the minor radius.

Regular Prism

A regular prism has a regular polygon as its base and a constant height.

Its volume is the area of the polygonal base multiplied by the prism’s height:

Volume = [n × s² / (4 × tan(π / n))] × h

Where:

• n is the number of sides of the regular polygon
• s is the side length
• h is the prism height

The number of sides must be an integer between 3 and 100.

For example, a regular hexagonal prism with a side length of 2 m and a height of 3 m has a base area of approximately 10.39 m² and a volume of approximately:

10.39 × 3 ≈ 31.18 m³

The same general formula can be used for regular triangular, square, pentagonal, hexagonal, octagonal, and other polygon-based prisms within the supported range.

Irregular Prism

An irregular prism has a base that does not need to be a regular polygon.

Its volume is:

Volume = base area × height

The important step is determining the area of the base first. Once the base area is known, multiply it by the prism’s height to obtain the volume.

This method works for prisms whose cross-sections are irregular or whose sides are not all equal.

How to Use the Volume Calculator

Using the calculator is straightforward.

First, select the 3D shape that best matches the object you want to measure. Different shapes require different measurements, so the calculator uses the appropriate formula for the selected shape.

Next, enter the dimensions required for that shape. Depending on the object, these may include:

• Side length
• Length
• Width
• Height
• Radius
• Major radius
• Minor radius
• Base dimensions
• Number of polygon sides

The calculator then applies the corresponding formula and displays the calculated volume.

For shapes that depend on a base area, such as pyramids and prisms, the calculation takes the base area and height into account automatically. You don’t need to manually calculate every intermediate step.

Different Input and Output Units

The unit you use for your measurements does not have to be the same as the unit you want for the final answer.

For example, you might measure a water tank in meters but want to know its capacity in liters. Or you might measure a small object in millimeters and prefer to see its volume in cubic centimeters.

The calculator handles these conversions for you. Your measurements are first interpreted using a consistent standard, and the final volume is then converted to the unit you select.

This makes it easier to compare measurements and results without performing separate manual conversions.

Common Cubic Volume Units

Common geometric volume units include:

• mm³ — cubic millimeters
• cm³ — cubic centimeters
• m³ — cubic meters
• ft³ — cubic feet
• yd³ — cubic yards

Cubic units are commonly used in geometry, engineering, construction, manufacturing, packaging, and material estimation.

Common Capacity Units

For liquids and containers, capacity units are often easier to understand:

• mL — milliliters
• L — liters
• US gal — US gallons
• US qt — US quarts
• US pt — US pints
• US fl oz — US fluid ounces

Being able to switch between geometric volume and capacity units is particularly useful when working with tanks, bottles, storage containers, and liquid measurements.

Cubic Units vs. Liquid Volume Units

Cubic units and liquid-capacity units both describe volume, but they are commonly used in different contexts.

Cubic meters, cubic centimeters, cubic feet, and cubic yards describe geometric volume. They relate directly to the dimensions of a three-dimensional object.

Liters, milliliters, gallons, quarts, pints, and fluid ounces are commonly used when describing the capacity of containers or the amount of liquid.

For example:

1 L = 1,000 cm³

So a container with an internal volume of 5,000 cm³ has a capacity of:

5,000 cm³ = 5 L

This type of liquid volume conversion is useful when moving between geometric measurements and practical capacity measurements.

Remember that different systems may use different definitions for certain capacity units. For example, a US gallon is different from an imperial gallon, which is why the calculator specifically identifies US capacity units where applicable.

Finding a Missing Dimension From a Known Volume

A Volume Calculator can also be useful when the volume is already known.

Instead of calculating:

dimensions → volume

you may sometimes need to work backward:

volume → missing dimension

For example, suppose you know the volume of a rectangular container, its length, and its width, but you need to determine its height.

Starting with:

V = length × width × height

you can rearrange the equation:

height = volume ÷ (length × width)

If the target volume is 2.4 m³, the length is 2 m, and the width is 1.5 m:

height = 2.4 ÷ (2 × 1.5) = 0.8 m

The same basic idea can be applied to other supported shapes when the available information is sufficient to determine the unknown dimension.

Keeping Known Dimensions Fixed

When working backward from a target volume, you can keep the dimensions you already know fixed and solve for another dimension.

For example, if the length and width of a storage container are already determined, you can use the desired capacity to calculate how tall the container needs to be.

There must, however, be at least one relevant dimension that can be determined. If all dimensions are already fixed, there is no remaining dimension to calculate.

Likewise, if the known information is insufficient to uniquely determine the missing value, the calculator cannot produce a meaningful reverse result.

What Measurements Do I Need?

The required measurements depend on the shape you select.

If a required measurement is missing, the volume cannot be calculated for that shape.

Most dimensions should also be valid positive numbers. A negative physical dimension does not represent a meaningful size, and zero is generally not valid for a dimension that defines the size of a shape.

There are a few shape-specific cases to keep in mind:

• The cylindrical length of a capsule can be 0. In that case, the capsule becomes a sphere.
• A regular prism must have between 3 and 100 sides, and the number of sides must be a whole number.
• For a torus, the major radius must be greater than the minor radius.
• Reverse calculations require enough known information to determine the requested dimension.

How the Calculator Helps

Calculating the volume of a simple box by hand is usually easy. The process becomes more complicated when you are working with several different shapes, decimal measurements, unfamiliar formulas, or multiple unit systems.

The Volume Calculator helps by bringing these steps together in one place.

Automatically Applying the Appropriate Formula

You don’t need to remember whether a particular shape uses 1/3, 2/3, 4/3, or another coefficient. Select the shape and the corresponding volume formula is applied automatically.

Reducing Manual Calculation Errors

Manually entering measurements into a formula, calculating intermediate values, and then converting the result can create several opportunities for mistakes. Using one calculator for the process can make the calculation more consistent.

Working With Different Units

You can use the units that match your measurements and view the result in another volume unit when that is more convenient.

Connecting Geometry With Real-World Capacity

A geometric volume such as cubic meters or cubic centimeters can be viewed in a capacity unit such as liters or US gallons. This is especially useful when working with tanks, containers, and liquids.

Solving Backward From a Target Volume

The calculator can also help when the volume is already known. When the available information is sufficient, you can use the target volume to determine a missing dimension rather than calculating the volume from fixed dimensions.

Real-World Uses of Volume Calculations

Volume calculations are useful far beyond geometry homework. They appear in construction, manufacturing, packaging, storage, liquid measurement, and everyday planning.

Tanks and Containers

For cylindrical and rectangular tanks, volume calculations can estimate how much liquid the container can hold.

For example, the volume of a cylindrical tank can be calculated with:

V = π × r² × h

The result can then be expressed in cubic meters or converted into liters.

When estimating the actual capacity of a physical container, use its internal dimensions whenever possible. The walls, fittings, and other components take up space and can make the usable capacity smaller than the external volume suggests.

Boxes and Packaging

Packaging designers need to know how much space a box provides and whether an item is likely to fit inside.

Rectangular prisms are especially common because shipping boxes, cartons, and many storage containers have rectangular dimensions.

Pipes and Cylindrical Objects

Cylinder volume calculations can help estimate the space inside or occupied by cylindrical objects, depending on which dimensions are being measured.

The same basic geometry is useful for cans, tanks, cylindrical components, and similar structures.

Cones and Tapered Containers

Cones and frustums appear in funnels, tapered containers, architectural structures, and other objects that become narrower toward one end.

When an object has two circular ends of different sizes, the frustum formula is often more appropriate than the standard cone formula.

Construction

Construction projects often require estimates for materials such as concrete, soil, gravel, or other fill.

Depending on the shape of the area, rectangular prisms, triangular prisms, cylinders, pyramids, and other geometric models can be used to estimate volume.

Manufacturing and Engineering

Manufacturers and engineers may need to estimate the volume of components with cylindrical, spherical, ellipsoidal, toroidal, or other geometric forms.

For objects with more complicated overall designs, breaking the object into simpler geometric sections can make volume estimation easier.

Storage Planning

Knowing the volume of a storage box, container, tank, or enclosed space can help estimate how much material it can hold.

Keep in mind that theoretical geometric volume is not always the same as usable storage capacity. Walls, lids, fittings, supports, and other internal structures can reduce the actual usable space.

Volume, Area, and Length Are Different

It is easy to confuse length, area, and volume because all three describe measurements of physical space.

Length measures one dimension.

Examples include:

• meters
• centimeters
• feet
• inches

Area measures a two-dimensional surface.

Examples include:

• m²
• cm²
• ft²

Volume measures three-dimensional space.

Examples include:

• m³
• cm³
• ft³

The distinction matters when converting units because volume involves three dimensions.

For example:

1 m = 100 cm

Therefore:

1 m² = 10,000 cm²

and:

1 m³ = 1,000,000 cm³

The conversion factor is cubed for volume because length is being converted in three separate dimensions.

Tips for Getting an Accurate Volume

A calculator can apply the correct formula, but the result still depends on the measurements you enter.

Measure the Correct Dimension

For circles, cylinders, cones, and related shapes, make sure you know whether a measurement represents the radius or diameter.

If you have the diameter, divide it by 2 to obtain the radius.

Use Perpendicular Height

For cones, pyramids, frustums, and triangular prisms, the height used in the volume formula is generally the perpendicular distance between the relevant base and the opposite point or plane.

A sloping edge is not necessarily the same as the geometric height.

Check Your Units

Use the units that match your actual measurements. If you measure one dimension in centimeters and another in meters, make sure the calculator is interpreting those units correctly.

The final result can then be displayed in your preferred volume unit.

Use Internal Dimensions for Capacity

If your goal is to determine how much a container can actually hold, measure the internal dimensions whenever possible.

Using external dimensions may overestimate the usable capacity because the walls and other physical components occupy space.

Avoid Unnecessary Rounding

Some formulas involve π and can produce long decimal results. Rounding too early can slightly affect the final answer.

For the most accurate result, keep your measurements as precise as practical and round the final value rather than intermediate calculations.

Final Thoughts

Calculating the volume of a 3D object is straightforward once you know its shape and the measurements required by the corresponding formula. The challenge is that different shapes use different equations, and real-world calculations often involve decimals, unit conversions, or a need to work backward from a desired capacity.

The Volume Calculator brings these calculations together in one place. Select the shape, enter the required dimensions, choose your units, and the calculator applies the appropriate formula to calculate the result.

Whether you’re checking the capacity of a water tank, estimating the volume of a package, planning construction materials, measuring a storage container, or working backward from a target volume, understanding how to find volume makes these problems much easier to handle.