Calculate Water Volume: Formulas for Common Shapes

Calculate water volume by entering a container’s inside dimensions and applying the formula for its shape. This calculator uses a rectangular tank’s length, width, and water depth to return the volume in cubic metres and litres; the same method can be adapted to other shapes.

Formula

For a rectangular tank, volume equals inside length multiplied by inside width multiplied by water depth:

V = L × W × D

• V is water volume in cubic metres (m³).
• L is the inside length in metres (m).
• W is the inside width in metres (m).
• D is the water depth in metres (m).

To convert cubic metres to litres, multiply by 1,000: litres = V × 1,000. To convert litres to US liquid gallons, divide by 3.785411784. The calculator’s first result is cubic metres, followed by litres and US gallons.

Worked Example

Using the calculator’s default values—length 2 m, width 1 m, and water depth 0.5 m:

1. Multiply the dimensions: 2 × 1 × 0.5 = 1 m³.
2. Convert to litres: 1 × 1,000 = 1,000 L.
3. Convert to US gallons: 1,000 ÷ 3.785411784 = 264.172… US gal, or 264.2 US gal to one decimal place.

The volume is therefore 1 m³, equivalent to 1,000 litres or about 264.2 US liquid gallons. The gallons figure is not Imperial gallons: one Imperial gallon is larger, and 1,000 litres is about 220.0 Imperial gallons.

How to Measure a Water Container

Measure the inside dimensions, not the outside. Wall thickness reduces the space available for water, and using exterior measurements can overstate the capacity. Measure water depth from the inside bottom to the water surface; do not substitute the tank’s full height if it is only partly filled.

• For a rectangular tank, measure inside length, inside width, and current water depth.
• For a circular tank, measure the inside diameter and water depth. Radius is half the diameter.
• For a pool with a sloped or uneven bottom, divide it into sections and calculate each section separately where possible.
• Keep all dimensions in the same unit before multiplying. Convert centimetres to metres by dividing by 100, or inches to feet by dividing by 12.

If a tank is not filled to the top, calculate the water actually present using its current depth. A stated tank capacity usually describes the full interior volume; it does not tell you how much water is in it now.

Formulas for Other Common Shapes

The rectangular formula works only when the container has a level bottom and vertical sides. For other shapes, choose a formula that matches the interior geometry:

• Cylinder: V = πr²h, where r is the inside radius and h is the water depth. A round tank with a diameter of 1 m and water depth of 0.5 m holds about 0.393 m³, or 393 litres.
• Triangular prism: V = (b × hₜ ÷ 2) × L, where b and hₜ are the triangle’s base and perpendicular height, and L is the prism length.
• Sphere: A completely filled sphere has V = 4πr³ ÷ 3. A partly filled sphere requires a spherical-cap calculation, rather than treating its water depth as the sphere’s full height.

For a container with changing width or depth, a single length × width × depth calculation may not represent its true volume. Break it into simpler geometric sections or consult the container’s measured capacity. For irregular shapes, estimating from a rectangular bounding box generally gives an upper estimate, not an exact water volume.

Reading Results and Avoiding Errors

Volume is the amount of three-dimensional space occupied by water. It is not the same as surface area, which measures a two-dimensional surface, or mass, which measures how much matter is present. Water’s mass depends on its temperature and composition; this calculator reports volume only.

• Check units: Multiplying metres gives cubic metres. Multiplying centimetres gives cubic centimetres, not litres; 1,000 cm³ equals 1 L.
• Use radius correctly: The cylinder formula requires radius. If you measure diameter, divide it by two before squaring.
• Use water depth: For a partly filled vertical-sided tank, use the water level, not the container’s total height.
• Understand rounding: The displayed result is rounded. Keep unrounded values during intermediate calculations when working by hand, then round the final result to a sensible precision.
• Allow for fittings: Internal pipes, supports, filters, and other objects displace water. A geometric estimate does not subtract their volume.

Small measurement errors can noticeably affect a result, especially for a large tank. For a rectangular tank, a 1% error in each of its three measured dimensions can produce a total volume error of roughly 3% when the errors all increase the estimate by about 1% each. Precise results require careful measurements and a container shape that matches the formula.

Frequently Asked Questions

How do I calculate water volume in litres?
For a rectangular container, multiply inside length × inside width × water depth using metres, then multiply the result in cubic metres by 1,000. Alternatively, calculate in centimetres and divide cubic centimetres by 1,000 to get litres.

How many litres are in one cubic metre of water?
One cubic metre equals exactly 1,000 litres. A cubic metre is a cube measuring 1 m on each side.

How do I calculate water in a round tank?
For a vertical cylindrical tank, use π × radius² × water depth. Measure the inside diameter, divide it by two to find the radius, and use the water depth rather than the tank’s full height when it is partly filled.

How many US gallons are in a litre?
One litre is about 0.2642 US liquid gallons. Conversely, one US liquid gallon is about 3.785 litres. Do not confuse US gallons with the larger Imperial gallon.

Should I use the tank’s outside or inside dimensions?
Use inside dimensions because the water occupies the space inside the walls. Outside measurements include wall thickness and can make the calculated capacity too large.

Related

• Annulus Volume Calculator: Formula and Examples
• Absolute Minimum and Maximum Calculator Explained
• Calculate the Golden Ratio

in length | Inside length | m | 2 | 0
in width | Inside width | m | 1 | 0
in depth | Water depth | m | 0.5 | 0
out volume | Water volume | m³ | length * width * depth | 3
out litres | Water volume | L | volume * 1000 | 0
out gallons | Water volume | US gal | litres / 3.785411784 | 1