Sprinkler K-factor calculator (flow and pressure)

Every sprinkler, nozzle and hydraulic node follows the same relationship between discharge and pressure: Q = K√P. If you know two of flow, pressure and K-factor, you know the third. This page explains the formula and gives you a free calculator for the two questions that come up most: how much a head flows at a given pressure, and what pressure it needs to deliver a required flow.

The formula

1. Flow from pressure: Q = K × √P, with Q in gpm, P in psi and K in gpm/psi^½.
2. Pressure for a required flow: P = (Q / K)².
3. K-factor from a test point: K = Q / √P.
4. Required flow at the most remote head is usually the design density times the area each sprinkler covers (for example 0.10 gpm/ft² × 130 ft² = 13 gpm).
5. Check the result against the minimum operating pressure. 7 psi is the common general minimum for standard sprinklers, but many listed sprinklers (storage, extended coverage, residential) have higher minimums. Use the higher of the calculated pressure and the listed minimum.
6. Metric K-factors are in L/min/bar^½. Multiply a US K-factor by about 14.4 to convert (K5.6 is about K80).

Free calculator

Worked example

A light hazard design at 0.10 gpm/ft² with 130 ft² per sprinkler needs 13 gpm at the most remote head. With a K5.6 sprinkler, P = (13 / 5.6)² ≈ 5.4 psi. That is below the 7 psi minimum, so the head is calculated at 7 psi instead, and it actually flows 5.6 × √7 ≈ 14.8 gpm. That higher flow carries back through the rest of the hydraulic calculation.

Next step is the friction loss from that head back to the source. The Sprinkler Pipe Friction Loss Calculator workbook runs Hazen-Williams loss, fittings, elevation and velocity segment by segment, or start with the free Hazen-Williams calculator.