Fixture Unit Sizing Calculator

Calculator overview

Inputs and outputs

This summary comes from the calculator's published input and output contract.

Inputs

Street Pressure: About this input

The supply pressure available at the main or meter, in pounds per square inch. It is the starting pressure the whole calculation draws down from.

Unit psi Default 60 Range At least 0
Shower: About this input

The number of showers served, as a count, each converted to water supply fixture units by an illustrative loading value.

Unit count Default 8 Range At least 0
Required Fixture Pressure: About this input

The residual pressure the most demanding fixture needs at its inlet to work, in pounds per square inch, for example about 8 to 25 depending on the fixture.

Unit psi Default 8 Range At least 0
Wc Flush Valve: About this input

The number of flush-valve water closets served, as a count. Flush valves draw a high instantaneous flow and carry more fixture units than tank types.

Unit count Default 0 Range At least 0
Wc Flush Tank: About this input

The number of tank-type water closets served, as a count. Tank types refill slowly and carry fewer fixture units than flush-valve types.

Unit count Default 10 Range At least 0
Velocity Limit: About this input

The largest water velocity you will allow in the pipe, in feet per second, used to keep noise and erosion within bounds. Common ceilings are around 8 feet per second for cold water.

Unit ft/s Default 8
Meter And Fixed Losses: About this input

The pressure lost across the water meter, backflow preventer and other fixed devices, in pounds per square inch. It is subtracted from the street pressure before any pressure is left for pipe friction.

Unit psi Default 5 Range At least 0
Elevation To Highest Fixture: About this input

The vertical rise from the source to the highest fixture served, in feet. Each foot of lift costs about 0.43 pounds per square inch of the available pressure.

Unit ft Default 20
Developed Length: About this input

The total developed length of pipe from the source to the most remote fixture, in feet, following the actual routing rather than the straight-line distance. It sets how much friction the available pressure has to cover.

Unit ft Default 150 Range At least 0
Bathtub: About this input

The number of bathtubs served, as a count. Each fixture type is converted to water supply fixture units using an illustrative loading value, so confirm the units against the plumbing code adopted where the work is installed.

Unit count Default 4 Range At least 0
Lavatory: About this input

The number of lavatories, or wash basins, served, as a count, each converted to water supply fixture units by an illustrative loading value.

Unit count Default 10 Range At least 0
Kitchen Sink: About this input

The number of kitchen sinks served, as a count, each converted to water supply fixture units by an illustrative loading value.

Unit count Default 6 Range At least 0
Hazenwilliams: About this input

The Hazen-Williams roughness coefficient of the pipe, a dimensionless value near 130 to 150 for smooth plastic or copper and lower for older metal. A higher value means a smoother pipe and less friction loss.

Default 140 Range At least 0

Outputs

Recommended Nominal Size: About this output

The nominal pipe size that matches the recommended inside diameter, expressed as a trade label. Confirm the actual inside diameter for the material and schedule you will install.

No unit declared
Pressure Available For Friction: About this output

The pressure left to overcome pipe friction, in pounds per square inch, after meter losses, elevation lift and the required fixture pressure are taken from the street pressure.

Unit psi
Recommended Pipe Id: About this output

The smallest pipe inside diameter, in inches, whose friction gradient and velocity both stay within the allowable limits for the peak demand. This is a sizing aid, not a design or a substitute for the governing plumbing code and a licensed professional.

Unit in
Velocity At Chosen Size: About this output

The water velocity in the recommended size at peak demand, in feet per second. Compare it against the velocity limit.

Unit ft/s
Total Fixture Units: About this output

The sum of water supply fixture units across all fixtures, a dimensionless demand index. It is the input to the diversity relationship that estimates simultaneous flow.

No unit declared
Gradient At Chosen Size: About this output

The friction gradient the recommended size actually produces at peak demand, in feet of head per 100 feet. Compare it against the allowable gradient.

Unit ft/100ft
Allowable Gradient: About this output

The friction pressure available spread over the developed length, in feet of head per 100 feet of pipe. It is the target gradient the recommended size must not exceed.

Unit ft/100ft
Mean Continuous Flow: About this output

The average flow the fixture units imply if demand were spread evenly, in gallons per minute. It is a reference figure, not the value the pipe is sized on.

Unit gpm
Peak Demand: About this output

The estimated simultaneous demand at the 99th percentile, in gallons per minute, from an illustrative diversity relationship that converts fixture units to probable flow. Different codes and methods give different curves, so treat a divergence from another tool as a method difference, not an error.

Unit gpm
Model Status: About this output

The overall check on your entries, shown above the results. It reads OK when the inputs are usable, NOT VALID with a reason when an entry makes the model meaningless, or CHECK with a reason when a result is valid but worth a second look. Read it before you trust the numbers below.

No unit declared

What it is

The Fixture Unit Sizing Calculator estimates the peak water demand of a plumbing system and recommends a supply pipe size for it. You enter counts of each fixture type, the pressure available at the main, the developed length to the most remote fixture and the height it sits at, and the tool converts the fixtures to water supply fixture units, estimates the simultaneous demand, and finds the smallest pipe that satisfies both the pressure available and your velocity limit.

It works in United States customary units: psi for pressures, feet for lengths and elevation, gallons per minute for flow, and inches for pipe size.

Read this before using the number. The demand model here is original to this workbook. It is not the Hunter curve, and it is not an IPC or UPC table-based sizing. Its results differ from a code-table method, and on the shipped example they differ in the direction that matters; see below.

Methodology

Purpose and model boundary

This model converts a schedule of six common plumbing fixtures into a probabilistic peak water demand, then selects the smallest pipe in its embedded candidate list that meets both a Hazen-Williams friction allowance and a velocity limit. It supports first-pass water-supply sizing. It does not reproduce or enforce a plumbing code, size branches separately, calculate hot- and cold-water diversity, or replace hydraulic design for a real building.

The fixture flows, busy fractions, fixture-unit weights, and candidate copper Type L pipe sizes are explicitly labelled illustrative in the workbook and can differ from the values required by the adopted code.

Inputs and units

Fixture inputs are nonnegative counts of flush-tank water closets, lavatories, showers, kitchen sinks, bathtubs, and flush-valve water closets. The pressure basis comprises street pressure and required residual fixture pressure in psi, elevation to the highest fixture in ft, and fixed meter/device losses in psi. The sizing basis comprises developed pipe length in ft, Hazen-Williams coefficient C, and maximum velocity in ft/s.

The embedded data assigns each fixture type a flow q_i in gpm, busy fraction rho_i, and water-supply fixture-unit weight w_i. Those values are model data, not user-entered code tables.

Governing relationships

For n_i fixtures of each type, the workbook forms the instantaneous-flow mean and variance:

mu = sum(n_i × rho_i × q_i)

sigma² = sum(n_i × rho_i × (1 - rho_i) × q_i²)

The design demand is the 99th-percentile normal approximation, protected for a very small population by the largest individual flow among fixture types actually present:

Q_peak = max(mu + 2.326347874 × sqrt(sigma²), largest present q_i)

Total fixture units are sum(n_i × w_i). Available friction pressure and the equivalent allowable gradient are:

P_friction = P_street - P_required - 0.433 × elevation - P_fixed

G_allow = (P_friction / 0.433) / developed length × 100

For each candidate inside diameter d in inches, the workbook calculates:

G_HW = 0.2083 × (100 / C)^1.852 × Q_peak^1.852 / d^4.8655

velocity = 0.4085 × Q_peak / d²

Calculation sequence

Multiply the fixture counts by the workbook's illustrative flow, busy-fraction, and fixture-unit data.
Calculate mu, sigma, and the protected 99th-percentile peak demand.
Subtract residual-pressure, elevation, and fixed-loss requirements from street pressure and convert the remainder to an allowable gradient.
Evaluate the six candidate diameters in ascending order.
Select the first candidate whose Hazen-Williams gradient is no greater than G_allow and whose velocity is no greater than the entered limit.
Return none and a blank numeric pipe ID if no listed candidate qualifies, then evaluate status in the precedence below.

Outputs and interpretation

Recommended_Nominal_Size, Recommended_Pipe_Id, and Peak_Demand are the primary results. Supporting outputs show total fixture units, mean continuous flow, available friction pressure, allowable gradient, and the chosen pipe's gradient and velocity. The chart is the workbook-derived demand curve against fixture-unit loading; it is evidence of the nonlinear probability model, not a reproduced code curve.

Validation and status logic

The workbook evaluates status in this order:

Condition	Returned status
Any fixture count is negative	`NOT VALID: fixture counts cannot be negative`
The sum of all fixture counts is zero or less	`NOT VALID: enter at least one fixture`
Available pressure for friction is zero or less	`NOT VALID: no pressure available for friction; reduce elevation or losses`
Developed length is zero or less	`NOT VALID: developed length must be positive`
Hazen-Williams `C` is zero or less	`NOT VALID: Hazen-Williams C must be greater than zero`
No listed diameter satisfies both gradient and velocity criteria	`CHECK: no listed pipe size meets the allowance; add a larger size or raise pressure`
None of the preceding conditions applies	`OK`

The negative-count check precedes the zero-total check. Pressure, length, and C failures precede the no-size warning.

Assumptions and limitations

Fixture use is represented as independent Bernoulli trials with fixed busy fractions and the 99th-percentile normal approximation. Correlated use, special occupancies, flushing systems, and time-varying demand are not modelled.
The workbook intentionally runs slightly conservative relative to the published Hunter magnitude with its illustrative calibration. It does not claim exact agreement with any jurisdiction's table.
Elevation uses a fixed 0.433 psi/ft; meter and device losses are entered as one lump sum.
One C value and one developed length represent the full critical run. Fittings, branches, local loss coefficients, pressure-regulating devices, temperature, and pipe ageing are not calculated separately.
Only six embedded candidate sizes are considered. A warning can therefore mean the list is too short, not that no physical design exists.
The result depends directly on the illustrative fixture and pipe data and must be checked against the governing code and actual product dimensions.

Restrictions and non-computing states

This calculator rejects negative values for the fixture counts, street and required pressures, fixed losses, developed length, and C. The workbook additionally refuses an empty fixture schedule, exhausted friction pressure, zero developed length, and zero C. Elevation and velocity limit have no published limit; unrealistic entries can make the available pressure negative or make every candidate fail. A no-size state remains computable enough to show demand and pressure evidence but returns CHECK, none, and a blank numeric pipe ID.

Errors and warnings

A rejected entry means a submitted value violated the published input rules and the workbook did not make a sizing decision. Workbook NOT VALID means the demand or pressure basis cannot support a usable result. Workbook CHECK means demand was calculated but the finite candidate list contains no compliant size. A connection or calculation-service failure is an availability error, not a plumbing conclusion.

References

The workbook derives its relations rather than reproducing any table, chart or figure from a code, standard or agency publication. The demand model is original to it, and the friction calculation is Hazen-Williams.

The sources below are the authoritative methods this tool sits beside and does not implement:

National Institute of Standards and Technology. Methods for Estimating Loads in Plumbing Systems, Roy Hunter's demand method, the basis of code sizing tables. https://www.nist.gov/publications/methods-estimating-loads-plumbing-systems
National Bureau of Standards. Hunter's original report, BMS 65. https://nvlpubs.nist.gov/nistpubs/Legacy/BMS/nbsbuildingmaterialsstructures65.pdf
International Code Council. Sizing of Water Piping System, IRC Appendix P. https://codes.iccsafe.org/content/IRC2018/appendix-p-sizing-of-water-piping-system
Wikipedia. Hazen-Williams equation. https://en.wikipedia.org/wiki/Hazen%E2%80%93Williams_equation

Fixture unit constants shipped with the workbook are illustrative and carry no authority. The values that govern a real installation come from the plumbing code adopted where the work is built. No trademark or organisation name appearing here implies endorsement by its owner.

Additional source notes migrated from Methodology

The workbook identifies Hunter's probability method for diversified fixture demand and the US-unit Hazen-Williams relation for friction. The delivered reviewer packet links Engineering ToolBox's fixture-unit reference, ToolGrit's Hunter-curve calculator, and Engineering ToolBox's Hazen-Williams reference for independent comparison. The governing jurisdictional plumbing code remains authoritative.

Frequently asked questions

Can I use this to size pipe for a permit?

No. The demand model is original to this workbook rather than the Hunter curve behind the IPC and UPC tables, and it produces different answers. On the shipped example a code-table calculator returns about 66 fixture units and a 1-1/2 inch main where this returns 54.2 units and 1-1/4 inch, one nominal size smaller. Use this for an order-of-magnitude check and size the real system from the governing code.

Why does this give a smaller pipe than my code table?

Because it uses a different demand model. The tool estimates peak flow as the 99th percentile of a Bernoulli model of the fixture mix, floored at the largest single fixture flow, using fixture-unit constants that are illustrative rather than taken from a code. Code tables embed Hunter's method plus decades of code-body judgement and a margin this model does not carry. Smaller is the dangerous direction to be wrong in, which is why it is stated plainly rather than buried.

What is the difference between mean continuous flow and peak demand?

Mean continuous flow is what the fixtures would draw if demand were spread perfectly evenly, in the shipped example 10.45 gallons per minute. Peak demand is what they draw when several happen to run at once, estimated here at the 99th percentile: 23.44 gallons per minute, more than double. Pipes are sized for the peak, and the ratio between the two is the entire contribution of the demand model.

Which constraint is actually setting my pipe size?

Read the two pairs the page reports. If the gradient at the chosen size is far below the allowable gradient but the velocity is near your limit, velocity is binding: more pressure will not help, and only a higher velocity limit or a different fixture mix would let the pipe shrink. If the gradient is close to the allowable, pressure is binding, and a shorter run or higher street pressure would. In the shipped example velocity is binding with pressure to spare by nearly fivefold.

Why do flush valves change the answer so much?

Because they draw a large flow instantaneously rather than refilling slowly like a tank. In the demand model that raises both the mean and the spread, and it raises the floor term, the largest single fixture flow, below which the estimate is never allowed to fall. Taking the shipped example and setting 20 flush-valve water closets moves the recommendation from 1-1/4 inch to 2-1/2 inch.

Does the developed length include fittings?

Only if you add them yourself. The tool spreads the available pressure over the developed length you enter and adds no equivalent length for elbows, tees or valves. A run with many fittings loses more pressure than its measured length implies, so either add an allowance to the developed length or expect the real gradient to exceed the calculated one.

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This page is provided by LogicCommons for informational purposes only. Results are analysis outputs computed from the inputs you supply and are not engineering advice, a design, or a substitute for review by a licensed professional under the codes adopted where the work is built. Verify all inputs and results independently.

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