Volume Calculator

Use this free Volume Calculator to find the volume of a box, rectangular prism, cylinder, cube, sphere, cone, pipe, tank, or aquarium. Enter the dimensions, choose the shape that matches your problem, and the calculator will return the volume along with useful conversions such as cubic metres, cubic feet, litres, millilitres, and US gallons.

The calculator is designed for common searches such as volume calculator, cylinder volume formula, volume of a cylinder, volume of a cube, length × width × height, tank capacity calculator, and pipe volume calculator. The guide below also explains the main volume formulas, how to find volume step by step, and how to convert cubic measurements into practical liquid-capacity units.

How to Use the Volume Calculator

Choose the shape or container that matches your problem, enter the requested dimensions, and select the unit used for those measurements. The Volume Calculator calculates the cubic volume and then converts it into practical capacity measurements such as litres, millilitres, cubic feet, and US gallons.

The Box / Rectangle mode is ideal when the problem gives length, width, and height. Cylinder mode works for cans, drums, tanks, and other cylindrical objects. Cube, Sphere, and Cone modes use the standard geometric volume formulas. Pipe mode estimates the internal space inside a pipe, while Tank / Aquarium mode calculates both full capacity and a partially filled volume.

If you are working with two-dimensional measurements before calculating a three-dimensional volume, our Area Calculator can help calculate the base area first.

What Is Volume?

Volume is the amount of three-dimensional space occupied by an object or contained inside a shape. Area measures a two-dimensional surface, while volume adds a third dimension. That is why volume is normally expressed in cubic units such as cubic inches, cubic feet, cubic centimetres, or cubic metres.

For containers that hold liquids, the same space can also be expressed as capacity. Cubic metres can be converted to litres, and litres can be converted to millilitres or gallons. One cubic metre equals 1,000 litres, which makes metric volume conversions especially straightforward.

The meaning of volume stays the same whether you are calculating a shipping box, concrete form, cylinder, water tank, aquarium, pipe, sphere, or cone. What changes is the formula used to describe the shape.

Volume Formula

There is no single volume formula for every possible shape. The correct equation for volume depends on the geometry. A rectangular prism uses length × width × height, while a cylinder uses the area of a circular base multiplied by height.

These are the core formulas behind most searches for a volume calculator, equation for volume, formula for volume, or how to calculate volume. More complicated shapes can often be broken into several simple shapes and calculated separately.

Length × Width × Height

The most common volume calculation is length × width × height, often shortened to L × W × H or LxWxH. This formula applies to boxes, rectangular prisms, rooms, storage bins, rectangular tanks, and many shipping or construction measurements.

If a box measures 10 feet long, 6 feet wide, and 4 feet high, the calculation is:

10 × 6 × 4 = 240 cubic feet

The same formula works with inches, centimetres, metres, or any consistent unit. The final answer is expressed in the cube of that unit. If the dimensions are in centimetres, the answer is cubic centimetres. If they are in metres, the answer is cubic metres.

Keeping all three dimensions in the same unit before multiplying is important. If one dimension is in feet and another is in inches, convert them first. The Simple Math Calculator can help with arithmetic after you have converted the measurements.

Volume of a Rectangle vs Volume of a Box

A rectangle itself is two-dimensional, so technically it has area rather than volume. When people search for a volume of rectangle formula, formula of volume for rectangle, or rectangle formula for volume, they usually mean a rectangular prism or box. That three-dimensional formula is length × width × height.

Cylinder Volume Formula

The cylinder volume formula is one of the most searched volume equations:

V = πr²h

The radius is the distance from the centre of the circular base to its edge, and h is the cylinder height. The formula works because πr² calculates the area of the circular base and multiplying by height extends that area through the cylinder.

If you know the diameter instead of radius, divide the diameter by 2 first. For a cylinder with diameter 8 cm and height 12 cm, the radius is 4 cm. The calculation becomes π × 4² × 12, which is approximately 603.19 cm³.

This same cylinder volume equation is used for many practical objects, including drums, pipes, round tanks, columns, cans, silos, and storage vessels. The Cylinder mode above works as both a volume of cylinder calculator and a cylinder volume calculator because it accepts either radius or diameter.

How to Calculate the Volume of a Cylinder

• Measure the radius, or measure the diameter and divide it by 2.
• Square the radius.
• Multiply the squared radius by π.
• Multiply by the cylinder height.
• Write the result in cubic units.

This process answers common questions such as how to find volume of a cylinder, how to calculate volume of a cylinder, how to determine cylinder volume, and what is the formula for volume in a cylinder.

Cylinder Volume Example

Suppose a cylinder has a radius of 3 feet and a height of 10 feet:

V = π × 3² × 10 = 90π ≈ 282.74 ft³

If you are checking the multiplication, powers, or π calculation manually, our Scientific Calculator is useful for verifying the result.

Volume of a Cube

A cube has equal length, width, and height, so its volume formula is especially simple:

V = s³

If each side of a cube is 5 cm, the volume is 5 × 5 × 5 = 125 cm³. This is equivalent to using length × width × height, but because all three dimensions are equal, the formula can be shortened to s³.

Searches such as volume of a cube, volume of cube, volume of a cube formula, and how to calculate volume of a cube all refer to this same relationship.

Sphere Volume Calculator

The volume of a sphere is calculated with:

V = 4/3 × πr³

A sphere has no length, width, or height in the rectangular sense. Its size is described by radius or diameter. If you know the diameter, divide it by 2 to get the radius before using the formula.

For a sphere with radius 3 metres, the volume is 4/3 × π × 3³, which is approximately 113.10 m³. The Sphere mode performs this calculation automatically and accepts either radius or diameter.

Cone Volume Calculator

A cone uses a circular base like a cylinder, but it tapers to a point. Its volume is one-third of the volume of a cylinder with the same base radius and height:

V = 1/3 × πr²h

For a cone with radius 3 cm and height 8 cm, volume is 1/3 × π × 3² × 8, or approximately 75.40 cm³.

Pipe Volume Calculator

A pipe volume calculator estimates how much space or liquid fits inside the pipe. For a straight pipe with a constant inside diameter, the internal space is simply a cylinder. Use the inside radius and pipe length:

Pipe Volume = πr²L

The key measurement is the inside diameter. Outside diameter includes the pipe wall and will overstate internal capacity. If a 4-inch inside-diameter pipe is 20 feet long, convert the dimensions to the same unit before calculating or use the Pipe mode above with a consistent unit.

Pipe volume is useful for estimating water capacity, flushing volume, chemical quantity, and the amount of fluid held in plumbing or process piping. Actual system volume may be higher when fittings, valves, vessels, and connected equipment are included.

Tank Capacity Calculator

A tank capacity calculator converts internal dimensions into usable volume. For a rectangular tank, the basic formula is length × width × height. Once the cubic volume is known, it can be converted into litres or gallons.

The Tank / Aquarium mode also includes a fill percentage. A tank filled to 80% contains 80% of its full geometric capacity. This is useful for storage tanks that require freeboard, liquid tanks that are intentionally not filled to the top, and aquariums where the water level is below the rim.

Tank size calculator and tank capacity calculator searches often refer to slightly different needs. Tank size usually means the physical dimensions, while capacity refers to the volume those dimensions can hold. The calculator above shows both together.

Aquarium Volume Calculator

An aquarium volume calculator is essentially a rectangular tank calculation when the aquarium has straight sides. Measure the inside length, inside width, and water height, then multiply the dimensions. Converting that cubic volume to litres or gallons gives the approximate water capacity.

Actual aquarium water volume is usually lower than the outside dimensions suggest because glass thickness, substrate, rocks, decorations, filters, and an unfilled space at the top reduce the amount of water. For a more realistic estimate, use inside dimensions and enter the approximate fill percentage.

Pool Volume Calculator

A rectangular swimming pool can also be estimated with length × width × average depth. If the pool has a shallow and deep end, a simple approximation is to add the shallow depth and deep depth and divide by 2 to get the average depth.

Irregular pools may require a more specialized pool volume calculator because curves, sloped floors, steps, and variable widths affect capacity. Breaking the pool into simple sections can improve an estimate.

How Many Gallons?

Once the geometric volume is calculated, the result can be converted to gallons. The calculator uses US liquid gallons. One US gallon equals approximately 3.78541 litres.

This is why a gallon calculator is often part of a volume calculation. First determine the physical volume, then convert the cubic unit into liquid capacity.

Convert Volume to Millilitres

To convert a volume into millilitres, it is often easiest to convert into litres first. One litre equals 1,000 millilitres. One cubic centimetre is also equal to one millilitre, which is a useful relationship for small metric measurements.

For example, 2.5 litres equals 2,500 mL. A box measuring 10 cm × 10 cm × 10 cm has a volume of 1,000 cm³, which equals 1,000 mL or 1 litre.

How to Find Volume

The general process for finding volume is straightforward:

• Identify the three-dimensional shape.
• Measure the dimensions required by that shape’s formula.
• Convert all measurements into the same unit.
• Substitute the dimensions into the volume equation.
• Calculate the cubic result.
• Convert to litres, gallons, millilitres, or another unit if needed.

This process applies whether the search is how to find volume, how to calculate volume, how do I calculate the volume, how to determine volume, or find out volume. The shape tells you which measurements and formula are required.

Why Volume Uses Cubic Units

Area uses square units because it describes two dimensions. Volume uses cubic units because it describes three dimensions. Multiplying metres × metres × metres gives m³. Multiplying inches × inches × inches gives in³.

This distinction matters when converting results. A linear conversion factor must be cubed when converting cubic units. One foot equals 12 inches, but one cubic foot equals 12 × 12 × 12 = 1,728 cubic inches.

Volume of a Box

The volume of a box is one of the simplest and most useful calculations in shipping, storage, construction, and packaging. Multiply the inside length by inside width by inside height when you need internal capacity. Use outside dimensions when you need the total space the box occupies.

For a box that measures 24 in × 18 in × 12 in, volume is 5,184 in³. Converting that to cubic feet gives 3 ft³ because 5,184 ÷ 1,728 = 3.

Volume of a Cylinder vs Surface Area

Volume of a cylinder measures the space inside the cylinder, while surface area measures the amount of material covering the outside. They use different formulas. Cylinder volume is πr²h. Total cylinder surface area is 2πr² + 2πrh.

This distinction is useful when a project involves both capacity and material. A tank may require volume to determine storage capacity and surface area to estimate coating, insulation, or sheet material.

Surface Area to Volume Ratio

Surface area to volume ratio compares how much exterior surface an object has relative to the amount of space inside it. The ratio becomes especially important in biology, chemistry, heat transfer, packaging, and engineering.

Small objects often have a larger surface-area-to-volume ratio than similar larger objects. As a shape scales up, volume increases faster than surface area. That relationship affects cooling, heating, diffusion, evaporation, and material efficiency.

If you need the outside surface first, use the Area Calculator and compare that result with the volume calculated here.

Volume Formula in Chemistry

Volume in chemistry can refer to the space occupied by a solid, liquid, or gas. Laboratory volume is commonly measured in litres, millilitres, cubic centimetres, or cubic metres. The geometric formulas on this page are useful when the container has a known shape, but chemistry problems may also involve density, concentration, molarity, or gas-law equations.

A useful metric relationship is 1 mL = 1 cm³. This allows direct conversion between small geometric volumes in cubic centimetres and liquid volumes in millilitres.

Surfboard Volume Calculator: Why It Is Different

Surfboard volume is commonly listed in litres, but a surfboard is an irregular three-dimensional shape rather than a simple box or cylinder. Length × width × thickness can give only a rough bounding-box estimate because the rails, nose, tail, rocker, and foil remove a large amount of material.

A dedicated surfboard volume calculator usually relies on shape modelling or board-design data. The general Volume Calculator on this page is best for regular geometric shapes and containers where the dimensions match a standard formula.

Volume and Unit Consistency

One of the most common volume mistakes is mixing units. For example, multiplying a length in metres by a width in centimetres and a height in millimetres does not produce a useful cubic unit until the dimensions are converted to one common unit.

The calculator avoids that issue by assuming all dimensions entered for one calculation use the selected unit. If your measurements are mixed, convert them first, then enter the consistent values.

Volume and Percentage Capacity

Containers are not always filled to 100% capacity. A tank may need expansion room, a grain bin may not be filled to the exact roof line, and an aquarium usually has an air gap at the top. To estimate a partial fill, multiply full capacity by the fill percentage expressed as a decimal.

For example, a 1,000-litre tank filled to 75% contains approximately 750 litres. The Tank / Aquarium mode performs this adjustment automatically. If you need help working with percentages separately, the Percentage Calculator can calculate percentages and percentage changes.

Volume of a Hollow Cylinder

A hollow cylinder is different from a solid cylinder because material exists between an outer radius and an inner radius. The material volume is found by subtracting the inner-cylinder volume from the outer-cylinder volume:

V = πh(R² − r²)

Here, R is the outer radius and r is the inner radius. This is useful for calculating the material volume of a thick-walled pipe, sleeve, tube, or cylindrical shell. The Pipe mode above instead calculates the empty interior capacity using the inside diameter.

Volume of a Rectangular Tank

A rectangular tank uses the same L × W × H formula as a box. The main difference is that tank capacity is usually converted to litres or gallons. For example, a tank measuring 2 m × 1 m × 1 m has a full geometric volume of 2 m³, equal to 2,000 litres.

Volume of a Cylindrical Tank

A vertical cylindrical tank uses V = πr²h, just like any cylinder. A horizontal cylindrical tank that is only partially filled requires a more complex circular-segment formula because the liquid depth does not scale linearly with capacity. For a completely full horizontal cylinder, however, the normal cylinder formula still gives total volume.

Volume and Density

Volume tells you how much space something occupies, while density connects mass to volume. The basic density relationship is density = mass ÷ volume. If density and volume are known, mass can be estimated by multiplying them. Different materials can occupy the same volume while having very different masses.

Volume and Material Estimation

Volume calculations are often the first step in estimating concrete, soil, gravel, mulch, water, fuel, and other bulk materials. The geometric volume gives the theoretical amount of space, but real purchasing quantities may need extra material for waste, compaction, uneven surfaces, spillage, or a safety margin.

Volume Examples

Example 1: Box Volume

A box measuring 8 ft × 4 ft × 3 ft has a volume of 96 ft³.

Example 2: Cylinder Volume

A cylinder with radius 2 m and height 5 m has volume π × 2² × 5 = 20π, or about 62.83 m³.

Example 3: Cube Volume

A cube with a side of 7 cm has volume 7³ = 343 cm³.

Example 4: Sphere Volume

A sphere with radius 3 cm has volume 4/3 × π × 27 ≈ 113.10 cm³.

Example 5: Cone Volume

A cone with radius 4 cm and height 9 cm has volume 1/3 × π × 16 × 9 = 48π, or about 150.80 cm³.

Example 6: Tank Capacity

A rectangular tank measuring 1.5 m × 1 m × 0.8 m has a full capacity of 1.2 m³, equal to 1,200 litres. At an 80% fill level, it contains approximately 960 litres.

Common Volume Mistakes

• Using diameter where the formula requires radius.
• Mixing inches, feet, metres, and centimetres in one calculation.
• Forgetting that volume uses cubic units.
• Using outside tank dimensions when internal capacity is needed.
• Using outside pipe diameter instead of inside diameter for fluid capacity.
• Confusing area with volume.
• Forgetting the one-third factor in the cone formula.
• Using a rectangular formula for an irregular shape.

Why Use a Volume Calculator?

A volume calculator is useful because volume formulas become error-prone when several conversions are involved. A single calculation may require radius conversion, squaring or cubing, multiplication by π, and then conversion from cubic units to litres or gallons.

The calculator keeps those steps together and shows both the geometric result and practical capacity conversions. It is useful for school math, construction estimates, storage planning, tanks, aquariums, piping, packaging, and everyday measurement problems.

Additional Related Volume Keywords and Calculations

Closely related volume topics include rectangular prism volume, cubic feet calculator, cubic metre calculator, litres to gallons, gallons to litres, tank volume, container capacity, drum volume, barrel capacity, pool capacity, water volume, concrete volume, soil volume, cubic yard calculation, room volume, shipping box volume, and storage bin capacity. These are all based on the same general idea: measure a three-dimensional space and apply the formula that matches its shape.

For geometry lessons and examples covering volume of prisms, cylinders, cones, spheres, and other solids, see Khan Academy’s solid geometry lessons.

Volume Calculator Frequently Asked Questions

Final Thoughts

Volume calculations become much easier once you identify the shape and use the matching formula. Boxes and rectangular tanks use length × width × height, cubes use side cubed, cylinders and pipes use πr²h, spheres use 4/3πr³, and cones use one-third of the equivalent cylinder volume.

The Volume Calculator above brings those formulas together and automatically converts the result into practical units such as litres and gallons. Whether you are calculating the volume of a cylinder, cube, tank, aquarium, pipe, sphere, cone, or box, keep the dimensions in one consistent unit and use internal measurements whenever capacity is the goal.