How do you calculate the volume of a pipe?

Volume of a cylindrical pipe equals pi times the inner radius squared times the length: V = pi * r^2 * L. Use the inner radius (half the inner diameter), not the outer radius. The result in cubic metres is converted to litres by multiplying by 1000 (since 1 m3 = 1000 litres).

How long does it take to fill a pipe at a given flow rate?

Fill time in minutes equals volume in litres divided by flow rate in litres per minute. For example, a pipe holding 78.54 litres at a flow rate of 10 L/min takes 78.54 divided by 10, which is about 7.85 minutes to fill. If the flow rate is zero or not entered, the fill time is shown as not applicable.

What is the difference between inner diameter and outer diameter for pipes?

For fluid volume calculations, you must use the inner diameter (bore). The outer diameter includes the pipe wall thickness, which does not carry fluid. Pipe specifications typically list the nominal bore (NB) or the actual inner diameter alongside the outer diameter and wall thickness. Using the outer diameter instead of the inner diameter will overestimate the volume.

Pipe Volume Calculator

Knowing how much fluid a pipe holds is useful in many everyday situations: estimating how long a hot water cylinder will take to fill a pipe run before hot water reaches the tap, calculating the volume of fluid in a hydraulic or refrigerant circuit before draining it for maintenance, figuring out the weight of a water-filled fire suppression system, or sizing dosing pumps that need to know the line volume before a flow switch activates. A pipe is simply a long cylinder, so the internal volume is pi times the inner radius squared times the length. The inner radius is half the inner diameter, sometimes called the bore. You must use the inner diameter, not the outer diameter, because the pipe wall does not carry fluid. Pipe datasheets always list both dimensions. This calculator asks for the inner radius in metres and the pipe length in metres, then returns the volume in litres and in cubic metres. It also lets you enter a flow rate in litres per minute and will calculate how long in minutes (and seconds) the pipe will take to fill completely at that constant flow rate. If you only need the volume, leave the flow rate at zero. The results update as you type. All figures assume the pipe runs full and that the cross-section is circular and constant throughout its length.

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Inner radius (r)

Pipe length (L)

Flow rate (optional)

L/min

78.54 L

internal pipe volume

Volume in m³0.07854 m³

Inner diameter0.10 m

Fill timeN/A

How it works

Internal pipe volume (m³) = pi times r squared times L, where r is the inner radius and L is the pipe length in metres. To convert m³ to litres, multiply by 1000 (since 1 m³ = 1000 litres). Inner diameter = 2 times r. Fill time in minutes = volume in litres divided by flow rate in litres per minute, only calculated when a flow rate greater than zero is entered.

Worked example

A pipe has an inner radius r = 0.05 m (inner diameter = 0.10 m) and a length L = 10 m. Volume = pi times 0.05 squared times 10 = pi times 0.0025 times 10 = 0.07854 m³ = 78.54 litres. If a pump delivers 10 L/min, fill time = 78.54 divided by 10 = 7.85 minutes = 7 minutes and 51 seconds. With the default flow rate of 0 the fill time shows as N/A until you enter a value.

Related calculators

Density Calculator: find the mass of a fluid in the pipe from its volume and density.
Bernoulli Equation Calculator: find pressure change in a flowing fluid using Bernoulli's principle.
Pressure Converter: convert between pascals, bar, psi, and other pressure units.
Ideal Gas Law Calculator: relate pressure, volume, temperature, and moles for a gas in a pipe or vessel.

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