Friction loss. FL = C × Q² × L, where Q = gpm ÷ 100 and L = hose length in feet ÷ 100. The standard fire-service coefficients C are 1½" = 24, 1¾" = 15.5, 2" = 8, 2½" = 2, 3" = 0.8 (0.67 if it is fitted with 3" couplings), 3½" = 0.34, 4" = 0.2, 5" = 0.08. These are the values in the IFSTA and NFA handbooks and the ones NFPA 1002 candidates are expected to work with.

Pump discharge pressure. PDP = NP + FL ± EL + AL. Nozzle pressure is 100 psi for a fog nozzle, 75 psi for a low-pressure fog, 50 psi for a smooth-bore handline and 80 psi for a master-stream smooth bore. Appliance losses are conventionally 5 psi for a wye, 10 psi for a siamese, 20 psi for a master stream device and 25 psi for a standpipe; a relay's receiving pumper is generally held at 20–30 psi. Add them all together.

Elevation. The physics gives 0.434 psi per foot of head; the fireground rule of thumb is 0.5 psi per foot, or 5 psi per floor excluding the ground floor. This tool uses 0.5 psi/ft for an entered height and 5 psi/floor for an entered storey count, and subtracts when the nozzle is below the pump.

Solid stream flow and nozzle reaction. gpm = 29.83 × c × d² × √NP, with c ≈ 0.97 for a well-made tip. Nozzle reaction is 0.0505 × Q × √NP for a fog nozzle and 1.57 × d² × NP for a smooth bore, both in pounds — the force the nozzle firefighter is actually holding.

The hand methods. The condensed Q formula is a supply-line shortcut, not an attack-line one: per 100 ft, 3" is Q², 4" is Q² ÷ 5 and 5" is Q² ÷ 15. It runs roughly 20 % above the coefficient method for 3" hose, erring towards more pressure rather than less. For 2½" the traditional Underwriters' formula is 2Q² + Q per 100 ft — at 250 gpm that is 15 psi against 12.5 from the chart, and again deliberately high. There is no clean mental shortcut for 1¾": the coefficient is large enough that a small flow error moves the answer a long way, so use the table.

Worked example. 200 ft of 1¾" at 150 gpm to a second-floor nozzle, fog, one floor above grade. Q = 1.5, L = 2, so FL = 15.5 × 2.25 × 2 = 69.75 psi — about 35 psi per 100 ft, the canonical 1¾" figure. PDP = 100 + 69.75 + 5 + 0 = 174.75 ≈ 175 psi. Nozzle reaction = 0.0505 × 150 × √100 = 75.8 lb. Cross-check the supply side the other way: 500 gpm through 600 ft of 5" is 0.08 × 25 × 6 = 12 psi by the table, and Q² ÷ 15 × 6 = 1.67 × 6 = 10 psi by the condensed Q formula — close enough to set a pump in your head.

Where it stops being true. The coefficient table assumes smooth, new, clean, correctly coupled hose. Old rubber-lined hose, kinks, a partially closed bail valve, an undersized nozzle gasket or a stretched lay can add 10–30 % more friction loss than the table predicts, and the table cannot see any of it. The flow you entered is the flow at the nozzle; if the pump cannot hold the calculated PDP you will not get it. Above about 250 psi you are past what most appliances and hose are rated to be safely worked at, and the tool says so rather than quietly giving you a number. Always back any calculated pressure off against a flow meter and a pressure gauge — the gauge wins.

Disclaimer. A training and drill aid. Do not substitute it for your department's SOPs, your manufacturer's nozzle data, or the pressure gauge on the pump panel. Sources: IFSTA Pumping and Aerial Apparatus Driver/Operator Handbook · National Fire Academy Fire and Emergency Services Hydraulics · NFPA 1002. Last reviewed: 2026-09-21.