Calculate pipe head loss, flow rate, diameter, length, or friction factor from the other four values using common engineering units.
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Head Loss Formula
The calculator uses the Darcy-Weisbach head loss relationship and rearranges it to solve for the one field you leave blank. Inputs are converted internally to base units before calculation: flow rate in GPM, diameter in inches, length in feet, and head loss in feet.
h_L = f*(L/(D/12))*V^2/(2*g)
V = 4*Q/(pi*D^2)
Q = 448.831*A*sqrt((2*g*h_L)/(f*(L/D)))
A = pi*(D/12)^2/4
D = ((8*f*L*Q^2)/(g*pi^2*h_L))^(1/5)
L = h_L*2*g*(D/12)/(f*V^2)
f = h_L*2*g*(D/12)/(L*V^2)
- hL = head loss, in feet before final unit conversion
- f = Darcy friction factor, unitless
- L = pipe length, in feet
- D = pipe diameter, in inches unless shown as D/12, which converts inches to feet
- V = flow velocity used in the calculation
- Q = flow rate, converted to GPM
- A = pipe cross-sectional area, in square feet
- g = acceleration due to gravity, 32.174 ft/s²
If you leave Head Loss blank, the calculator finds hL from flow rate, diameter, pipe length, and friction factor. If you leave Flow Rate blank, it solves velocity from the head loss equation, then converts the flow to your selected flow unit. If you leave Diameter, Length, or Friction Factor blank, it uses the rearranged version of the same relationship for that missing value.
Friction Factor and Unit Reference
Use the friction factor table as a rough reference only. The correct value depends on Reynolds number, pipe roughness, fluid properties, and whether the flow is laminar or turbulent.
| Pipe or flow condition | Typical Darcy friction factor | Notes |
|---|---|---|
| Laminar flow | 64 / Re | Applies when Reynolds number is below about 2,000 |
| Smooth pipe, turbulent flow | 0.008 to 0.015 | Common for very smooth tubing at higher Reynolds numbers |
| PVC or copper water pipe | 0.012 to 0.020 | Often used as an estimate for clean water systems |
| Commercial steel pipe | 0.015 to 0.030 | Depends strongly on age and roughness |
| Rough or aged pipe | 0.025 to 0.050+ | Scaling, corrosion, or deposits can increase losses |
| Input type | Supported units | Internal base unit |
|---|---|---|
| Flow rate | GPM, LPM, m³/h | GPM |
| Diameter | in, cm, m | inches |
| Length | ft, m, yd | feet |
| Head loss | ft, m, in | feet |
Head Loss Examples
Example 1: Calculate head loss
Suppose you enter a flow rate of 100 GPM, a diameter of 4 in, a pipe length of 100 ft, and a friction factor of 0.020. Leave head loss blank.
V = 4*100/(pi*4^2) = 7.9577
h_L = 0.020*(100/(4/12))*7.9577^2/(2*32.174) = 5.9047 ft
The calculated head loss is about 5.9047 ft.
Example 2: Calculate friction factor
Using the same pipe and flow, enter a flow rate of 100 GPM, a diameter of 4 in, a length of 100 ft, and a head loss of 5.9047 ft. Leave friction factor blank.
f = 5.9047*2*32.174*(4/12)/(100*7.9577^2) = 0.0200
The calculated friction factor is about 0.020000.
Head Loss Calculator FAQ
What does head loss mean?
Head loss is the loss of mechanical energy in a flowing fluid, expressed as an equivalent height of fluid. A result of 5 ft of head loss means the system loses energy equal to lifting the fluid 5 ft. It is not the same as pressure drop, but it can be converted to pressure drop if you know the fluid density or specific weight.
Should I use Darcy friction factor or Fanning friction factor?
Use the Darcy friction factor. The Darcy friction factor is four times the Fanning friction factor. If you enter a Fanning value by mistake, the calculated head loss will be too low by a factor of about 4.
Why do I need to leave exactly one field blank?
The calculator solves for one unknown at a time. Enter values for four of the five fields: flow rate, diameter, length, friction factor, and head loss. Leave only the value you want to calculate blank.
