The water demand calculator above estimates the peak instantaneous flow a building's supply must carry, using the probability method that underlies plumbing design. It treats each fixture as either running or idle at any instant, computes the chance that a given number are running together, and reports the flow that is exceeded only for the percentage of time you choose. It also reports the long-run average demand, which is a completely different and much smaller number.
Arb Digital builds free calculators that keep code tables out of the arithmetic. This page takes flow rates and usage frequencies as your inputs rather than publishing a fixture-unit table, and it states its boundary plainly: the water usage calculator estimates how much water a household consumes over a day, a month or a year, which is a volume. This page produces a peak design flow rate for sizing pipes, pumps and storage. Consumption and peak flow are not related by any simple factor.
Why Peak Demand Is Not the Sum of the Fixtures
A building with fifty fixtures never runs fifty fixtures at once. If you size the supply for the sum of every rated flow, you specify a main several times larger than anything the building will draw, at large cost and with the side effect of low velocities that allow sediment to settle and water to stagnate. If instead you size for the average, the supply collapses every morning.
The design question is therefore statistical: what flow is high enough that it is only exceeded rarely? Roy B. Hunter answered it for plumbing in the National Bureau of Standards report Methods of Estimating Loads in Plumbing Systems, published as Building Materials and Structures Report BMS 65 in 1940 and still the basis of fixture-unit methods in modern plumbing codes. The NIST publication record for Hunter's work on water-distributing systems for buildings holds the original reports.
Hunter's insight was to treat each fixture as a Bernoulli trial. A fixture that runs for t seconds and is used every T seconds during the busy period is running with probability p = t/T at any instant. For n identical fixtures the number running follows a binomial distribution, and the design load is the smallest number m such that the probability of more than m running at once falls below one per cent.
How to Use It
- Group your fixtures by behaviour. Fixtures with similar flow rates and usage patterns belong together: flush valves in one group, basins in another, showers in a third.
- Enter the rated flow per fixture. Use the discharge rate for the fitting actually specified, since water-efficient fittings change this substantially.
- Enter duration and interval for the busy period. The interval is the mean time between uses of one fixture during the peak, not across the whole day.
- Leave the percentile at 99 unless you have a reason. That is Hunter's criterion and it is what code tables were built on.
- Compare the peak with the average. The gap between them is what storage exists to absorb, and it drives the choice between a direct-fed and a stored system.
The Method and a Worked Example
For each group, the probability that any one fixture is in use is duration divided by interval. The tool then accumulates the binomial distribution from zero upwards and stops at the first count whose cumulative probability reaches the design percentile. That count is the number of fixtures assumed to be running simultaneously, and the group's contribution to peak flow is that count multiplied by the flow per fixture. Group contributions are added.
Work the defaults. Group one is 20 fixtures at 3 GPM, used for 60 seconds every 300, so p = 0.2. The binomial with n = 20 and p = 0.2 reaches a cumulative 0.99 at 8, so eight fixtures are assumed running, giving 24 GPM. Group two is 15 fixtures at 1.5 GPM with p = 0.05, which reaches the percentile at 3, giving 4.5 GPM. Group three is 10 fixtures at 2 GPM with p = 0.1667, which reaches it at 5, giving 10 GPM. The peak design demand is 38.5 GPM.
The average is the expected value, which is simply the sum of n × p × flow across the groups: 12 + 1.125 + 3.333, or 16.46 GPM. The peak is 2.3 times the average here, and that ratio grows as the building gets smaller. In a single dwelling the peak can exceed the average many times over, which is precisely why small systems feel the most strain.
Diversity: Why Bigger Buildings Are Easier
The interesting behaviour of this calculation is how slowly peak demand grows with size. Double a group from 20 fixtures to 40 at the same usage probability and the simultaneous count rises by much less than double, because the binomial distribution concentrates around its mean as n grows. The standard deviation grows with the square root of the count while the mean grows linearly, so the tail allowance shrinks in relative terms.
That is the diversity effect, and it is why per-apartment design flows in a tower are far lower than the design flow for a single house. It is also why fixture-unit tables are non-linear: they rise steeply at first and then flatten. Any rule of thumb that multiplies a per-fixture figure by the count is wrong in both directions — oversizing large buildings and undersizing small ones.
The same reasoning explains why grouping matters. Putting all fixtures into one group when they have genuinely different usage patterns distorts the result, because the method assumes fixtures within a group are identical and independent. Splitting them into behavioural groups and summing the group peaks is conservative but reasonable, since the group peaks will not in reality coincide exactly.
What This Does Not Size
A flow rate is not a pipe size. Converting one into the other requires a target velocity, and then a pressure-loss calculation over the full run including fittings, height and the residual pressure needed at the least favoured outlet. The flow rate calculator relates flow, bore and velocity, and the PSI to GPM calculator deals with the pressure side.
Nor does it size storage. A tank is sized from the volume drawn during a peak period and the rate at which the incoming supply refills it, which needs a demand profile over time rather than a single instantaneous figure. Once you have a volume, the tank volume calculator and the pipe volume calculator convert between dimensions and capacity.
Hot water is a separate calculation again, since only part of the demand is hot and the recovery rate of the heater matters as much as its storage volume. Drainage is separate once more, with its own fixture-unit system on the discharge side; the wastewater loading calculator covers the treatment end of that. And none of this is code compliance: plumbing codes prescribe their own method, and the authority having jurisdiction decides what is acceptable.
Where the Method Struggles
Hunter's assumptions were drawn from 1940s fixtures and 1940s behaviour. Modern water-efficient fittings, such as those carrying the EPA WaterSense label, use less water per use, and some use it for longer, which changes both the flow and the probability in ways the original tables never anticipated. Codes and research bodies have revised the underlying data more than once for that reason, and several alternative methods now exist.
The independence assumption also breaks in buildings with synchronised behaviour. A stadium at half time, a school between lessons or a factory at shift change produces genuine simultaneity that no independence-based model captures, and those buildings are designed from measured or scheduled profiles instead. If your building has a bell, the binomial is the wrong tool.
Finally, the result is only as good as the interval you entered. That figure is a behavioural estimate, not a specification, and it swings the answer more than any other input. Try halving it and watch the peak move: that sensitivity is worth knowing before quoting a design flow to anyone.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Summing every fixture's rated flow — that is a flow no building ever draws, and designing to it wastes money and leaves velocities too low.
- Sizing to the average — the average is what a meter records over time, not what the pipe must deliver at eight in the morning.
- Putting unlike fixtures in one group — the method assumes fixtures in a group are identical and independent, so mixed groups distort the tail.
- Using an all-day interval — the interval must describe the busy period, since that is when the peak occurs.
- Treating the output as code compliance — plumbing codes prescribe their own fixture-unit method and the authority having jurisdiction decides.
Related Free Tools From Arb Digital
Turn a design flow into a pipe size with the flow rate calculator and check the pressure side with the PSI to GPM calculator. Size vessels with the tank volume calculator and the pipe volume calculator. For consumption rather than design flow use the water usage calculator, for hot water the water heating calculator, and for the discharge side the wastewater loading calculator. The full free online tools hub lists everything.
Frequently Asked Questions
The instantaneous flow rate the supply must be able to deliver during the busiest period, rather than the total volume used. It is a flow in gallons per minute or litres per second, and it is what determines pipe sizes, pump duty and storage recovery.
Each fixture is treated as running with probability equal to its duration of use divided by the interval between uses. The number running at once then follows a binomial distribution, and the design flow is set at the count that the distribution reaches at the chosen percentile, usually 99 per cent.
Roy B. Hunter, in the National Bureau of Standards report Methods of Estimating Loads in Plumbing Systems, published as Building Materials and Structures Report BMS 65 in 1940. The fixture-unit tables in modern plumbing codes descend from that work.
Because the binomial distribution concentrates around its mean as the group grows. The mean rises in proportion to the count while the spread rises with its square root, so the allowance for simultaneous use shrinks in relative terms. That is the diversity effect.
No. Codes prescribe their own method and their own tables, and the authority having jurisdiction decides what is acceptable. This page computes the underlying probability directly so you can see how the numbers behave, but a submitted design must follow the applicable code.
Not reliably. The method assumes fixtures are used independently, and buildings with synchronised breaks produce genuine simultaneity that no independence-based model captures. Those buildings are designed from measured or scheduled demand profiles instead.
The water usage calculator estimates household consumption as a volume over a day, month or year. This page produces a peak instantaneous flow rate for sizing pipework and storage. A volume and a design flow are different quantities and neither can be derived from the other by a simple factor.
This tool is provided for educational and preliminary estimating use. It is not a plumbing design, a code calculation or a compliance check. Water supply systems must be designed by a qualified engineer or licensed plumber to the plumbing code adopted by the authority having jurisdiction.
