Why use this calculator
Low flow at a shower or a hose tap is one of the most common plumbing complaints, and it usually comes down to three things: the pipe is too small for its length, there is not enough pressure to push water up to the outlet, or the fittings add more resistance than anyone allowed for.
This calculator puts those three together. It takes the pressure you have, subtracts what the fixture needs and what the lift costs, and tells you how much water the pipe can then carry. It also flags velocity, because water moving faster than about 2.4 to 3 metres per second is noisy and causes water hammer.
It is an estimating aid for planning and troubleshooting. Pipe sizing for a real installation follows AS/NZS 3500.1 in Australia and New Zealand, the plumbing codes adopted locally in the US, or BS EN 806 in the UK, and is signed off by a licensed plumber.
How to use it
- Choose metric or imperial units first.
- Pick the pipe material, which sets how rough the bore is.
- Enter the internal diameter, which is the bore rather than the nominal size printed on the pipe.
- Enter the pipe length along the run from the supply point to the outlet.
- Enter a fittings allowance, with 20 per cent typical for a domestic run with several elbows.
- Enter the available pressure from a gauge or the water authority.
- Enter the minimum pressure the fixture needs at the outlet.
- Finally enter how much higher the outlet sits than the start, or a negative figure if it is lower.
What each result means
- Flow rate
- The most water the pipe can carry with the outlet fully open at the pressure you specified. Real fixtures restrict flow below this.
- Velocity
- How fast water moves through the bore. Above about 2.4 m/s it gets noisy, and above 3.0 m/s AS/NZS 3500.1 is exceeded.
- Velocity check
- A plain verdict on the velocity against the common design limits. Too fast means go up a pipe size for this run.
- Most flow inside the 3.0 m/s limit
- The highest flow this bore can carry without the water moving faster than 3.0 metres a second, the AS/NZS 3500.1 limit above which noise and water hammer set in.
- Head available for friction
- The pressure left to push water along the pipe after the outlet requirement and the lift are paid for, as metres or feet of water.
- Friction loss gradient
- Head lost per 100 units of pipe at this flow. It lets you compare runs and check against pipe friction charts.
- Equivalent pipe length
- The actual length plus your fittings allowance, which is the length the friction calculation really uses.
- Hazen-Williams C factor
- The roughness coefficient for the chosen material. Higher numbers are smoother pipes that carry more water at the same pressure.
The formula
Head for friction
h (m) = (P - Pr) / 9.807 - z
- P
- supply pressure in kPa
- Pr
- required outlet pressure in kPa
- z
- lift in metres
Equivalent length
L (m) = actual length x (1 + fittings % / 100)
Hydraulic gradient
S = h / L
Flow Q (m³/s) = 0.2785 x C x D^2.63 x S^0.54
- C
- the Hazen-Williams coefficient
- D
- the bore in metres
Velocity (m/s) = Q divided by the bore area, pi x D² / 4
Imperial inputs are converted at 6.895 kPa per psi and 0.3048 m per foot.
How this number is used in practice
In practice the pipe rarely runs at the full flow shown, because taps, shower heads and valves throttle it. The useful reading is the other way round: if the pipe can only deliver 12 L/min at the pressure a shower needs, and the shower wants 9 L/min while a kitchen tap wants 6 L/min at the same time, the shower will drop off when someone runs the tap.
Plumbers size supply lines for the simultaneous demand of the fixtures likely to run together, using loading unit tables in AS/NZS 3500.1, the US plumbing codes or BS EN 806, not for the maximum a pipe could carry.
Pressure matters at both ends. Australian water authorities typically supply between about 200 and 800 kPa, and AS/NZS 3500.1 caps static pressure at 500 kPa at any outlet inside a building, which is why many homes have a pressure limiting valve at the meter. In the US, 40 to 80 psi is the normal residential range and a pressure reducing valve is required above 80 psi in the International Plumbing Code.
Hot water systems also set their own limits. A two-storey house loses about 30 kPa, or 4 psi, just lifting water to the upper bathroom.
Old galvanised steel is the classic cause of falling pressure over the years. Corrosion shrinks the bore and roughens it, and because flow depends on diameter to the power 2.63, losing a few millimetres of bore can halve the flow. Replacing it with copper or PEX of the same nominal size often transforms a house.
Worked examples
20 mm bore copper, 30 m run, 20% fittings, 350 kPa supply, 50 kPa at the tap, 3 m lift
About 68.9 L/min at 3.66 m/s fully open, above the 3.0 m/s limit, so a tap should throttle it well below that
The same run in 25 mm bore PEX
About 132.8 L/min at 4.51 m/s, nearly double the flow, which shows how much capacity one size up adds
A US 3/4 inch copper line, 100 ft long, 50 psi supply, 8 psi needed, 10 ft rise
About 15.5 US gpm at 11.28 ft/s fully open, well above the 8 ft/s guide, so fixtures must limit the flow
When people use it
- Checking whether a long run to a garden tap or granny flat will deliver enough water
- Seeing how much going up one pipe size improves flow before quoting
- Diagnosing low pressure at an upstairs bathroom
- Comparing old galvanised pipe with a copper or PEX replacement
- Estimating flow for irrigation lines and tank-fed pump systems
Tips
- Measure pressure at an outside tap with a cheap gauge. It is more reliable than an authority's average figure.
- Use the bore, not the nominal size. Nominal DN20 copper, US 3/4 inch type L and 20 mm PEX all have different bores.
- If velocity is flagged, go up a size. Fast water is noisy, erodes copper at elbows and causes water hammer.
- Keep the fittings allowance honest. A run with ten elbows and a few valves can easily add 30 per cent or more.
- Allow about 9.8 kPa per metre, or 0.43 psi per foot, of height between the supply and the outlet.
- For tank and pump systems use the pump's pressure at your target flow from its curve, not its maximum pressure.
What it assumes, and where it stops being accurate
- Hazen-Williams applies to cold water in full-bore flow at ordinary velocities. It is less accurate for hot water, very small bores and very high velocities.
- Fittings are handled as a percentage of length rather than individual equivalent lengths or K values.
- The supply pressure is treated as steady. Mains pressure falls at peak times and when neighbours draw water.
- Meters, filters, backflow devices and pressure limiting valves add losses that are not included unless you raise the fittings allowance.
- The flow shown is the pipe's maximum at the stated outlet pressure, not the flow any particular fixture will draw.
- This is an estimating aid. Real pipe sizing is done by a licensed plumber to AS/NZS 3500, the local US plumbing code or BS EN 806.
Terms used on this page
- Head
- Pressure expressed as the height of a water column. One metre of head equals about 9.8 kPa.
- Hydraulic gradient
- Head lost to friction per unit length of pipe, the slope term in the Hazen-Williams equation.
- Bore
- The internal diameter of a pipe, which governs flow. It differs from the nominal size.
- Equivalent length
- The length of straight pipe that would cause the same friction loss as a set of fittings.
- Water hammer
- A pressure surge and banging noise when fast-moving water is stopped suddenly by a closing valve.
Questions people ask
- What is the Hazen-Williams C factor?
- It is an empirical roughness coefficient. Smooth plastic pipe such as PVC, PE and PEX is around 150, new copper about 140, new steel 120, and old corroded galvanised or cast iron pipe 100 or less. Higher numbers mean less friction and more flow at the same pressure.
- What velocity is too fast for water pipes?
- AS/NZS 3500.1 limits velocity in water services to 3.0 metres per second. Many designers aim for 1 to 2.4 m/s for cold water and lower for hot water, and US guidance commonly limits cold water to about 8 feet per second and hot water to about 5 feet per second.
- Why does a slightly bigger pipe carry so much more water?
- Flow depends on diameter raised to the power 2.63 in the Hazen-Williams equation. Going from a 20 mm to a 25 mm bore increases diameter by 25 per cent but increases flow by roughly 80 per cent at the same pressure and length.
- How much pressure do I lose going upstairs?
- About 9.8 kPa for every metre of height, or 0.433 psi per foot. A bathroom 6 metres above the meter loses roughly 59 kPa before any friction is counted, which is often why upstairs showers feel weaker than downstairs ones.
- Can I use this to size pipes for my house?
- Use it to understand and estimate. Actual pipe sizing uses loading units for simultaneous demand, specific fitting losses and the minimum pressures in the relevant code, and the work must be carried out and certified by a licensed plumber in most jurisdictions.
Use this with
Plumbing Pipe Flow Calculator answers one part of the question. These pick up where it stops: Water Tank & Dam Volume Calculator, Swimming Pool Volume Calculator, Irrigation Water Calculator and HVAC BTU Calculator.
Where these figures come from
This calculation is jurisdiction-neutral arithmetic. No country-specific rules are applied.
- Australian Building Codes Board: Plumbing Code of Australia. Plumbing Code of Australia and referenced AS/NZS 3500 series
- International Code Council. International Plumbing Code pressure and velocity requirements
- Standards Australia. AS/NZS 3500.1 water services
Plumbing Pipe Flow Calculator produces an estimate for general information. It is not financial, tax, medical, legal or engineering advice. read the full disclaimer. Spotted a wrong number? Report it and it gets fixed. The form picks up this calculator and the inputs you used.