Pump Head Calculator (Total Dynamic Head)

Calculate total dynamic head from static lift plus pipe friction loss using the Hazen-Williams equation, with flow velocity and pressure output.

Result

Loading calculator…

—

General calculation reads

Amazon affiliate

How Not to Be Wrong

Jordan Ellenberg - math thinking

Shop on Amazon

The Joy of X

Steven Strogatz - accessible math

Shop on Amazon

Scientific calculator (Casio fx-991EX)

Shop on Amazon

As an Amazon Associate we may earn from qualifying purchases. This does not add cost for you.

How to use this calculator

Enter the static head — the vertical rise from the water source surface to the discharge point.
Enter the total pipe length; add an equivalent-length allowance for elbows and valves.
Enter the pipe inner diameter (mm) and the design flow rate (L/min).
Pick the pipe material to set the Hazen-Williams C coefficient, then read total dynamic head and velocity.

About this calculator

Total dynamic head (TDH) is the total resistance a pump must overcome, expressed as an equivalent height of water column. It is the sum of the static head — the vertical distance the water is lifted — and the friction (or dynamic) head, the pressure lost to friction as water moves through pipe and fittings. This calculator computes friction loss with the Hazen-Williams equation, the industry-standard empirical formula for water in pressurised pipes, using a roughness coefficient C that depends on pipe material. It also reports the flow velocity (which should generally stay below ~1.5–2.5 m/s to limit losses and water hammer) and converts the head to pressure in kPa, bar, and psi. Use TDH to select a pump whose head-flow curve meets your duty point.

How it works — the formula

TDH = Static head + Friction head
Friction (Hazen-Williams, SI):
  h_f = 10.67 · L · Q^1.852 / (C^1.852 · d^4.8704)
Pressure: ΔP = ρ · g · h   (ρ=1000 kg/m³, g=9.80665 m/s²)

Friction loss grows with the 1.852 power of flow and falls steeply with diameter (4.87 power), so modest pipe upsizing sharply cuts losses. Head in metres of water converts to pressure via the hydrostatic relation ΔP = ρgh.

Sources: Engineering ToolBox — Hazen-Williams equation · NIST — standard gravity g = 9.80665 m/s²

Worked examples

Example 1

100 m of 100 mm PVC (C=150) at 500 L/min, 10 m lift

Inputs:: staticHead=10, length=100, diameter=100, flow=500, cFactor=150
Output:: friction ≈ 1.04 m → TDH ≈ 11.04 m

Example 2

50 m of 50 mm steel (C=120) at 200 L/min, no lift

Inputs:: staticHead=0, length=50, diameter=50, flow=200, cFactor=120
Output:: friction ≈ 4.22 m → TDH ≈ 4.22 m

Example 3

200 m of 150 mm copper (C=130) at 1000 L/min, 20 m lift

Inputs:: staticHead=20, length=200, diameter=150, flow=1000, cFactor=130
Output:: friction ≈ 1.36 m → TDH ≈ 21.36 m

Limitations

Valid for water near 15 °C in turbulent flow; not for gases or viscous fluids.
Fittings must be added manually as equivalent pipe length.
Does not include velocity head or suction-side NPSH considerations.

Engineering estimate. Confirm pump selection against the manufacturer's certified head-flow and NPSH curves.

Frequently asked

What is total dynamic head?+

Total dynamic head (TDH) is the total equivalent height of water a pump must work against: the static lift plus all friction losses in the pipe and fittings at the design flow rate. Pump curves are published as head versus flow, so TDH is exactly the number you match against the curve to select a pump.

What is the Hazen-Williams equation?+

An empirical formula for friction head loss of water in pressurised pipe. In SI form, h_f = 10.67 · L · Q^1.852 / (C^1.852 · d^4.8704), where L is length (m), Q is flow (m³/s), d is inner diameter (m), and C is a roughness coefficient. It is simple and accurate for clean water in turbulent flow at ordinary temperatures.

What C value should I use?+

C reflects pipe smoothness: PVC/plastic ≈ 150, new steel or cement-lined ≈ 140, copper ≈ 130, galvanised/welded steel ≈ 120, and older cast iron drops toward 100 as it corrodes and scales. Lower C means more friction loss for the same flow.

How do I account for fittings and valves?+

Each fitting adds friction equivalent to a length of straight pipe. Look up the equivalent length for each elbow, tee, and valve and add the total to your pipe length input. A common rough allowance is to add 10–30% to the straight-pipe length.

Why does flow velocity matter?+

Velocity drives friction loss (loss rises steeply with flow) and high velocities cause noise, erosion, and water hammer. A typical design target is 1.0–2.0 m/s for suction and up to ~2.5 m/s for discharge. This tool reports velocity so you can check your pipe size.

When should I not use Hazen-Williams?+

It is calibrated for water around 15 °C. For hot water, viscous fluids, gases, or very cold water, use the Darcy-Weisbach equation with the Colebrook friction factor, which handles any fluid and temperature.