CalculatorHub Search

Pump Head Pressure Calculator

Reviewed by the CalculatorHub team, edited by James Graham. Based on Bernoulli equation and Darcy-Weisbach friction formula. Last verified 14 June 2026.

Total dynamic head (TDH) is the key parameter for pump selection. It is the sum of static head (elevation change), friction head loss in the pipes, and the velocity head at the discharge point. This calculator uses the Bernoulli energy equation and Darcy-Weisbach formula to compute TDH and the corresponding discharge pressure. Enter your system parameters to find the required pump head for sizing against a manufacturer pump curve.

Vertical elevation from pump centreline to discharge point. Negative if pumping downhill.
Total pipe length including suction and discharge sides
Internal pipe diameter. Common sizes: 50, 80, 100, 150, 200 mm.
Required volumetric flow rate in litres per second
Typical range 0.01 to 0.03. Use Moody chart or Colebrook equation for your pipe roughness and Reynolds number.
Water at 20 C: 998 kg/m3. Seawater: 1,025 kg/m3.
-- m
-- m
-- m
-- kPa

Total dynamic head formula

TDH = Hz + hf + hv
hf = f × (L/D) × v2 / (2g)
hv = v2 / (2g)
v = Q / A = Q / (pi × D2 / 4)
P = rho × g × TDH

Where: Hz = static elevation head (m), hf = Darcy-Weisbach friction head (m), hv = velocity head at outlet (m), f = Darcy friction factor, L = pipe length (m), D = internal pipe diameter (m), v = flow velocity (m/s), Q = flow rate (m^3/s), g = 9.81 m/s^2, rho = fluid density (kg/m^3).

Notes on friction factor selection

  • Use the Moody chart or Colebrook-White equation to determine f for your pipe roughness and Reynolds number.
  • For commercial steel pipe (roughness 0.046 mm) at Re = 100,000, f is approximately 0.021.
  • Add minor losses (fittings, valves, bends) by converting them to equivalent lengths of straight pipe using K-factor tables.
  • ANSI/HI 9.6.1 provides guidance on pump system design and minimum flow requirements.

Pump head calculator: frequently asked questions

What is total dynamic head (TDH)?

Total dynamic head is the total equivalent height of fluid that a pump must overcome to move fluid from the suction reservoir to the discharge point. TDH = static head + friction head + velocity head. It is expressed in metres of fluid column (m) and is used to select a pump from a manufacturer's pump curve.

How does pump head relate to pressure?

Pressure (Pa) = rho * g * H, where rho is fluid density (kg/m^3), g = 9.81 m/s^2, and H is head (m). For water at 20 degrees C (rho = 998 kg/m^3), 1 metre of head equals approximately 9.79 kPa or 0.098 bar.

What is the Darcy-Weisbach equation for friction head?

Friction head loss hf = f * (L/D) * (v^2 / 2g), where f is the Darcy friction factor, L is pipe length (m), D is pipe internal diameter (m), v is flow velocity (m/s), and g = 9.81 m/s^2. For turbulent flow in steel pipes, f is typically 0.01 to 0.03 depending on roughness and Reynolds number.

What is static head?

Static head (also called elevation head) is the vertical height difference between the pump centre line and the discharge point. If pumping uphill, static head is positive. If pumping downhill, it is negative and reduces the required TDH.

How do I convert pump head to power?

Hydraulic power (kW) = rho * g * Q * H / 1000, where Q is flow rate (m^3/s) and H is TDH (m). Shaft power = Hydraulic power / pump efficiency. For a pump with 75% efficiency delivering 0.05 m^3/s at 30 m head, shaft power = 998 * 9.81 * 0.05 * 30 / (1000 * 0.75) = 19.6 kW.

Official sources

Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.