In short: velocity head is the kinetic energy of moving water written as an equivalent height of fluid, h_v = V²/2g. At a typical service-line velocity of 5 ft/s it is about 0.39 ft (4.7 in); at 10 ft/s it climbs to about 1.55 ft, because the term grows with the square of velocity. Use the calculator above for any velocity, or any flow rate and pipe size.
These figures are planning aids for hydraulic calculations. For pump selection, pipe sizing or any safety-critical system, confirm with a licensed engineer.
How to calculate velocity head
Velocity head is one of three energy terms in Bernoulli's equation for flowing water — the other two are elevation head (height) and pressure head (static pressure). Velocity head captures the energy tied up in motion itself, and it is remarkably simple to compute once you know the flow velocity:
This calculator takes your velocity — or works one out from a flow rate and pipe diameter using the continuity equation, V = Q/A — converts it to meters per second, applies the formula, and returns the head in feet, meters, inches, centimeters and millimeters.
Worked example. Water moves through a pipe at 8 ft/s (2.438 m/s). Square the velocity: 2.438² = 5.944 m²/s². Divide by 2g (2 × 9.80665 = 19.613): 5.944 / 19.613 = 0.303 m, which converts to 0.995 ft. That's the velocity head at a fairly brisk pipe velocity — under a foot.
Why V/A instead of a lookup table. If you know a flow rate but not the velocity, the continuity equation V = Q/A (flow rate divided by pipe cross-sectional area) gets you there directly. Switch the calculator to "flow rate & pipe diameter" mode to skip the manual conversion — for pipe velocity alone without the head, see the Water Velocity Calculator.
Why velocity changes the answer so much
Because velocity is squared in the formula, small changes in speed produce much bigger changes in velocity head. Doubling the velocity quadruples the head; tripling it multiplies the head by nine. That squared relationship is also why velocity head is usually a minor player in ordinary pipe runs — at 2–5 ft/s it is a fraction of a foot — but becomes significant fast through a nozzle, an orifice, or a partly closed valve, where velocity spikes.
Velocity head shows up directly in the total dynamic head a pump must overcome, alongside static (elevation) head and friction head loss. In most building and municipal systems it is the smallest of the three terms, which is why engineers often approximate it as negligible for long, low-velocity runs — but a calculator, not a rule of thumb, is the way to confirm that for your specific numbers.
Velocity head at common pipe velocities
The values this calculator computes, from a gentle trickle to a brisk pump discharge line. Notice how the head accelerates as velocity climbs — that's the squared term at work.
| Velocity (ft/s) | Velocity (m/s) | Velocity head (ft) | Velocity head (m) |
|---|---|---|---|
| 1 | 0.305 | 0.0155 | 0.0047 |
| 2 (min flow) | 0.610 | 0.0622 | 0.0190 |
| 3 | 0.914 | 0.1399 | 0.0426 |
| 4 | 1.219 | 0.2486 | 0.0758 |
| 5 (typical) | 1.524 | 0.3885 | 0.1184 |
| 6 | 1.829 | 0.5595 | 0.1705 |
| 8 (water main) | 2.438 | 0.9946 | 0.3032 |
| 10 | 3.048 | 1.554 | 0.4737 |
| 12 (pump discharge) | 3.658 | 2.238 | 0.6821 |
| 15 (high) | 4.572 | 3.497 | 1.0658 |
| 20 | 6.096 | 6.216 | 1.8947 |
Worked examples
Backyard sprinkler line
0.39 ft
Water moving at 5 ft/s through a sprinkler supply line has a velocity head of about 0.39 ft (4.7 in) — a rounding error next to the elevation and friction head over a real run.
500 GPM through a 6-inch main
0.50 ft
500 US GPM through a 6-inch pipe works out to a velocity of about 5.67 ft/s (continuity equation), giving a velocity head of almost exactly 0.50 ft — try it with the flow-and-diameter mode above.
Pump discharge at 12 ft/s
2.24 ft
A short discharge line sized for 12 ft/s carries a velocity head of about 2.24 ft — enough to matter in a total dynamic head calculation, unlike the low-velocity examples above.
What else affects velocity head
Pipe diameter. For a fixed flow rate, a smaller pipe forces water through a smaller cross-section, raising velocity — and since velocity head scales with velocity squared, halving the diameter roughly quadruples velocity and multiplies velocity head by about sixteen. See the Pipe Size Calculator to explore that trade-off.
Where you measure it. Velocity head is a local quantity — it changes wherever the pipe's cross-section changes, such as at a reducer, a nozzle, or an open valve throat. A system with several diameters has a different velocity head at each section.
What it is not. Velocity head does not depend on water temperature, density, or pressure — only on speed and gravity. That sets it apart from pressure head, which the Pressure to Head Calculator handles, and which does depend on density.
Frequently asked questions
What is velocity head?
Velocity head is the kinetic energy of moving water expressed as an equivalent height of fluid. It equals V squared divided by 2g, where V is the flow velocity and g is the acceleration of gravity. It is one of the energy terms in Bernoulli's equation, alongside elevation head and pressure head.
Is velocity head usually significant in pipe design?
Usually not, at typical pipe velocities. At 5 ft/s, velocity head is under half a foot — small next to friction and elevation head over a real pipe run. It becomes meaningful at high velocities, such as through nozzles, orifices, or partly closed valves, where velocity — and its square — rises sharply.
How does pipe diameter affect velocity head?
A smaller diameter forces the same flow rate through a smaller area, which raises velocity by the continuity equation, V = Q/A. Because velocity head grows with the square of velocity, cutting a pipe's diameter in half roughly quadruples the velocity — and multiplies velocity head by about sixteen.
What is the difference between velocity head and pressure head?
Pressure head represents the static pressure energy in the water, converted to an equivalent column height. Velocity head represents kinetic energy from motion. Bernoulli's equation adds them, along with elevation head, to describe the total energy carried by flowing water at a point in a system.
How do I find velocity head from a flow rate instead of a velocity?
Divide the flow rate by the pipe's cross-sectional area to get velocity, then square it and divide by 2g. This calculator does that automatically — switch to "flow rate & pipe diameter" and enter your flow rate and pipe size instead of a velocity.
Does water temperature or density affect velocity head?
No. Velocity head depends only on velocity and gravity, not on the fluid's density or temperature. That is different from pressure head, which does depend on density.
Sources & references
- Bernoulli, D. (1738). Hydrodynamica. The energy-head formulation used throughout fluid mechanics.
- Crane Co. (2013). Technical Paper No. 410 — Flow of Fluids Through Valves, Fittings, and Pipe.
- Hydraulic Institute. ANSI/HI Standards for pump and system hydraulics.
John Mac, PE
Water Systems Specialist · Austin, Texas
Texas-licensed Professional Engineer with 13+ years in residential water systems and 180+ completed projects. Writes and reviews the calculators on watercalculator.us. Read full bio
Texas PE (2016) · BS Civil Engineering, Hydraulics (2013)