Sprinkler Head Flow Rate & Pressure Calculator
Calculate sprinkler head flow rate from pressure and K-factor, or determine the required pressure for a desired flow rate using the standard sprinkler discharge formula.
Formulas Used
Sprinkler Discharge Formula (NFPA 13 / FM Global):
Q = K × √P
Where:
- Q = Flow rate (gpm or L/min)
- K = K-factor, the discharge coefficient of the sprinkler orifice (gpm/psi½ or L/min/bar½)
- P = Pressure at the sprinkler head (psi or bar)
Rearranged to find pressure:
P = (Q / K)²
Unit Conversion (K-factor):
KUS (gpm/psi½) = Kmetric (L/min/bar½) × (0.264172 / 3.80838) ≈ Kmetric / 14.4
Assumptions & References
- The formula Q = K√P is derived from Torricelli's theorem and the orifice flow equation, standardized in NFPA 13 (Standard for the Installation of Sprinkler Systems) and FM Global Data Sheet 2-0.
- The K-factor is a manufacturer-specified constant that accounts for the orifice size, geometry, and discharge coefficient of the sprinkler head. It must be obtained from the sprinkler manufacturer's data sheet.
- Common US K-factors: K2.8 (small orifice), K5.6 (standard), K8.0 (large orifice), K11.2, K14.0, K16.8, K19.6, K22.4, K25.2 (extended coverage).
- NFPA 13 specifies a minimum operating pressure of 7 psi (0.48 bar) for standard spray sprinklers and varies for ESFR and other special types.
- Maximum operating pressure is typically 175 psi (12.1 bar) unless otherwise listed by the manufacturer.
- This calculator assumes steady-state, incompressible flow with no pipe friction losses at the sprinkler head itself.
- Pressure used is the residual pressure at the sprinkler head, not the static supply pressure. Pipe friction losses must be calculated separately (Hazen-Williams equation).
- Metric conversion: 1 gpm = 3.78541 L/min; 1 psi = 0.0689476 bar = 6.89476 kPa.
- Always verify designs with a licensed fire protection engineer and comply with local Authority Having Jurisdiction (AHJ) requirements.