Fire-service hydraulics · NFPA-style coefficients
Fire Hose Friction Loss Calculator
Calculate friction loss in fire hose with the standard fire-service formula FL = C × (Q/100)² × (L/100), then roll it into pump discharge pressure (PDP) with nozzle pressure, elevation and appliance losses. Includes the full coefficient table, a smooth-bore flow finder, and an FL-per-100-ft quick reference — in imperial or metric, 100% in your browser.
Friction Loss & Pump Discharge Pressure
Live results — change any input and the numbers update instantly.
Your department's flow-tested value.
Positive = nozzle above the pump (adds pressure). Negative = below (reduces).
Wyes, siamese, reducers, etc.
Total friction loss
— psi
Pump discharge pressure (PDP)
— psi
FL per 100 ft
— psi
Nozzle reaction (est.)
— lbs
Smooth Bore Flow Finder
Estimate nozzle flow from tip size and nozzle pressure: GPM = 29.7 × d² × √NP.
Estimated flow
— GPM
Standard references: 1" tip at 50 psi ≈ 210 GPM; 7/8" tip at 50 psi ≈ 161 GPM.
Friction Loss Coefficient Table (C)
Empirical fire-service coefficients per hose diameter. Used directly by the calculator above.
| Hose diameter | Coefficient C |
|---|
Sources: fire-department hydraulics training material (sacweedvfd.org) and fire-hose friction loss coefficient charts; 3" listed with 2 1/2" couplings. Plain 3" hose charts list 0.667–0.677 — enter either value in the custom field. Published values are empirical averages; hose age and liner material shift them.
Quick Reference: Friction Loss per 100 ft (psi)
FL/100 ft = C × (Q/100)² — the numbers pump charts are built from. Multiply by your number of 100-foot sections.
| Hose \ GPM |
|---|
Computed live from the same engine as the calculator — always consistent.
How the Math Works
The friction loss formula
FL (psi) = C × (Q / 100)² × (L / 100)C is the friction loss coefficient for the hose diameter, Q is the flow in gallons per minute, and L is the hose length in feet. Because flow is squared, doubling the GPM quadruples the friction loss in the same hose.
Pump discharge pressure (PDP)
PDP = Nozzle Pressure + FL + Elevation Pressure + Appliance LossElevation pressure is ±0.433 psi per foot of height difference between the nozzle and the pump (exact: 62.4 lb/ft³ ÷ 144 in²/ft² = 0.4333 psi/ft). Add it when the nozzle is above the pump; subtract when below. A common field shortcut rounds it to 0.5 psi/ft (EP = 0.5H). Appliance loss covers wyes, siameses, reducers and valves — a few psi each.
Nozzle reaction
NR (lbs) = 0.0505 × GPM × √NPThe backward force on the firefighter holding the line.
Metric mode
Metric inputs are converted to imperial first (1 GPM = 3.78541 L/min, 1 ft = 0.3048 m), the same formula runs, and the result is converted to kilopascals (1 psi = 6.89476 kPa). One formula, one source of truth — metric and imperial can never disagree.
Standard presets used in this calculator
This friction loss calculator fire hose crews rely on for drills uses the nozzle pressures firefighters train with: fog nozzle pressure 100 psi for handline combination nozzles, smooth bore nozzle pressure 50 psi for handline tips, and 80 psi for smooth bore master streams. The smooth bore GPM formula is GPM = 29.7 × d² × √NP. Typical attack lines are 1.5 inch, 1.75 inch, 2 inch and 2.5 inch hose; supply lines are 3 inch, 4 inch, 5 inch or 6 inch large-diameter hose (LDH).
Worked Examples
FL = 15.5 × (150/100)² × (200/100) = 15.5 × 2.25 × 2 = 69.75 psi
PDP = 100 + 69.75 + 0 + 0 = 169.75 psi
FL = 15.5 × 2.25 × 2.5 = 87.19 psi; elevation = 20 × 0.433 = 8.66 psi
PDP = 100 + 87.19 + 8.66 + 10 = 205.85 psi
FL = 0.08 × (1000/100)² × (1000/100) = 0.08 × 100 × 10 = 80 psi — this is why LDH replaced multiple 3" lines for supply.
Scope: which tool do you need?
This calculator covers flexible fire hose and LDH with NFPA-style empirical coefficients. It is not the right method for other systems:
- Rigid pipe systems (plumbing, irrigation mains, industrial pipe): use the Darcy-Weisbach calculator — head loss from the Colebrook equation and Reynolds number, with minor (fitting) losses.
- Drip irrigation / sprinkler hydraulics: see the drip irrigation calculator (pipe + pump sizing with Hazen-Williams).
- Household water demand planning: see the water demand calculator.
Do not mix methods: hose coefficients for hose, Darcy-Weisbach for pipe.
Frequently Asked Questions
What is the friction loss formula for fire hoses?
The standard fire-service formula is FL = C x (Q/100)^2 x (L/100), where FL is friction loss in psi, C is the friction loss coefficient for the hose diameter, Q is the flow rate in gallons per minute (GPM), and L is the hose length in feet. For example, 200 feet of 1 3/4-inch hose (C = 15.5) flowing 150 GPM gives FL = 15.5 x 1.5^2 x 2 = 69.75 psi. This fire hose friction loss calculator applies that formula for you, with the coefficient table built in.
What are the friction loss coefficients for common fire hose diameters?
The widely used fire-service coefficients (C) are: 3/4-inch booster 1100, 1-inch booster 150, 1 1/4-inch booster 80, 1 1/2-inch 24, 1 3/4-inch 15.5, 2-inch 8, 2 1/2-inch 2, 3-inch (with 2 1/2-inch couplings) 0.8, 3 1/2-inch 0.34, 4-inch 0.2, 4 1/2-inch 0.1, 5-inch LDH 0.08, and 6-inch LDH 0.05. Some charts round 1 3/4-inch to 15, and plain 3-inch hose (no reducing couplings) to 0.667. This calculator uses 15.5 and 0.8 and also offers a custom coefficient field for your department's tested values.
How do I calculate pump discharge pressure (PDP)?
Pump discharge pressure is PDP = nozzle pressure + friction loss + elevation pressure + appliance loss. Elevation adds or subtracts about 0.433 psi per foot: add when the nozzle is above the pump, subtract when it is below. A typical appliance (wye, siamese, reducer) costs a few psi each. Enter your values above and this calculator totals all four parts into the pump discharge pressure you should set on the panel.
What is the elevation pressure in fire hose calculations?
Water exerts 0.433 psi per foot of elevation (62.4 lb/ft^3 divided by 144 in^2/ft^2). A nozzle 100 feet above the pumper needs about 43.3 psi extra; a nozzle 100 feet below the pumper needs about 43.3 psi less. A common field rule of thumb simplifies this to 0.5 psi per foot (EP = 0.5H), which is close enough for rough estimates but this calculator uses the exact 0.433 value.
What nozzle pressure should I use: 50 psi or 100 psi?
Standard fire-service nozzle pressures are 50 psi for a smooth bore handline tip, 100 psi for a fog/combination nozzle handline, and 80 psi for a smooth bore master stream device. This calculator includes presets for all three plus a custom field, because the nozzle pressure is the starting point of every pump discharge pressure calculation.
Why does friction loss rise so fast when I increase flow?
Friction loss grows with the square of the flow: doubling the GPM quadruples the friction loss in the same hose. That is why upgrading from a 1 3/4-inch line to a 2 1/2-inch line (coefficient 15.5 down to 2) is so effective — the bigger hose cuts friction loss to roughly one-eighth at the same flow. The quick-reference table above shows this squared relationship at a glance.
Can I calculate friction loss in metric units (kPa, L/min, meters)?
Yes. Switch to metric mode and enter flow in liters per minute and length in meters. The calculator converts your inputs to the imperial formula internally (1 GPM = 3.78541 L/min, 1 ft = 0.3048 m), computes the loss, and converts the result to kilopascals (1 psi = 6.89476 kPa). There is only one formula in the engine, so metric and imperial results always agree.
What is friction loss per 100 feet of hose?
Friction loss per 100 feet is FL/100 = C x (Q/100)^2 — the middle of the formula, and the number most cheat sheets and pump charts are built from. For example, 1 3/4-inch hose at 150 GPM loses 34.875 psi per 100 feet (15.5 x 2.25). Multiply by your number of 100-foot sections to get total friction loss.
What is nozzle reaction and how is it calculated?
Nozzle reaction is the backward force the firefighter feels: NR = 0.0505 x GPM x sqrt(nozzle pressure), in pounds of force. A 1-inch smooth bore tip at 50 psi flows about 210 GPM, so its reaction is roughly 75 lbs. This calculator shows the estimate next to your results so you can judge line control needs.
How do I find the flow of a smooth bore nozzle?
Use GPM = 29.7 x d^2 x sqrt(NP), where d is the tip diameter in inches and NP is the nozzle pressure in psi. A 1-inch tip at 50 psi gives 29.7 x 1 x 7.07 = 210 GPM. A 7/8-inch tip at 50 psi gives about 161 GPM. The smooth bore flow finder above applies this formula with common tip sizes.
Does this calculator handle relay pumping?
For relay pumping, the attack pumper needs PDP = friction loss + residual intake pressure for the next pumper (commonly 20 psi, though departments may require more). Compute the friction loss for the supply line above, then add your department's required residual pressure. The main calculator covers forward lays; the relay concept is explained here for training context.
Are these coefficients exact for my hose?
No. Friction loss coefficients are empirical averages; published tables differ slightly because liner material, hose age, and manufacturing vary. Some departments flow-test their own hose and publish their own C values. The coefficient table here follows two fire-service references, but the Fire Protection Research Foundation notes modern hose may have lower loss than older rules of thumb. Use the custom coefficient field with your department's tested values for the most accurate pump pressures, and always verify with gauges.
Is this friction loss calculator only for fire hoses?
Yes — this tool covers flexible fire hose and large-diameter hose (LDH) with NFPA-style fire-service coefficients. For rigid pipes and fittings, use the Darcy-Weisbach calculator (https://nrtechstudio.com/tools/darcy-weisbach/), which solves head loss from the Colebrook equation and Reynolds number — the right method for pipe systems.
How is fire hose friction loss different from pipe friction loss?
Fire hose uses empirical per-diameter coefficients (C) with the formula FL = C x (Q/100)^2 x (L/100) because hose stretches, flexes, and couples differently than pipe. Pipe friction uses the Darcy-Weisbach equation hf = f x (L/D) x (v^2/2g) with a friction factor from the Colebrook equation and the pipe's roughness. Do not mix the methods: hose coefficients for hose, Darcy-Weisbach for pipe. See the scope box above for which tool to use.
Can friction loss be too high to pump through?
Yes. Friction loss can exceed the pump's practical discharge pressure on long, small-diameter lays at high flow — for example, 500 feet of 1 1/2-inch hose at 250 GPM loses 24 x 6.25 x 5 = 750 psi, which no pumper can supply. When the calculator shows an extreme number, the fix is a larger hose diameter, a shorter lay, or splitting the flow across multiple lines. Always sanity-check against your department's maximum operating pressures.