To describe the same pipe friction, the Darcy and Fanning friction factors differ by exactly a factor of 4. Enter either value to compute both coefficients along with the pressure drop ΔP and head loss, and see — and avoid — the 4x conversion mistake that is so common in pipe design.
Parameters
Friction factor convention
Enter either one; the other is converted automatically
Friction factor value f
Friction factor in the convention selected above
Pipe inner diameter D
mm
Pipe length L
m
Mean velocity U
m/s
Fluid density ρ
kg/m³
About 998 kg/m³ for water at 20°C
Results
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Darcy friction factor f_D
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Fanning friction factor f_F
—
Pressure drop ΔP (kPa)
—
Head loss h_L (m)
—
Dynamic pressure ½ρU² (kPa)
—
L/D ratio
—
Pressure drop along the pipe and the ×4 link
A colour gradient shows pressure high at the inlet and low at the outlet. The Darcy and Fanning values sit side by side in the ×4 relationship.
Pressure drop vs mean velocity U
Pressure drop vs pipe length L
Theory & Key Formulas
$$f_{Darcy}=4\,f_{Fanning}$$
Relation between the Darcy (Moody) and Fanning friction factors. They describe the same flow but use different definition bases, so they differ by exactly a factor of 4.
Pressure drop ΔP from the Darcy-Weisbach equation. L: pipe length, D: inner diameter, ρ: fluid density, U: mean velocity. When using the Fanning factor, the factor of 4 must always be applied.
$$h_{L}=\frac{\Delta P}{\rho g}$$
The pressure drop converted to head loss (a height of fluid column). g: gravitational acceleration. Always confirming which convention a chart or correlation uses is the key to avoiding a 4x blunder.
What are the Darcy and Fanning Friction Factors?
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I tried to calculate the pressure drop in a pipe and ran into two things — the "Darcy friction factor" and the "Fanning friction factor". They are both "friction factors", so why are there two of them?
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Great question — this is a pitfall everyone who studies fluid mechanics hits at least once. Both are dimensionless numbers that describe how much energy a fluid loses to friction against the pipe wall. The only difference is the basis of the definition. The Darcy friction factor is defined so it gives the whole-pipe pressure drop directly, while the Fanning friction factor is defined as the wall shear stress divided by the dynamic pressure. As a result, even for the same flow, the numbers differ by exactly a factor of 4 — through the wonderfully simple relation f_Darcy = 4·f_Fanning.
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Wait — a factor of 4? Couldn't getting that wrong cause a serious accident?
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That is exactly the scary part. The pressure-drop equation, the Darcy-Weisbach equation, is ΔP = f·(L/D)·(ρU²/2), and the f used there is the Darcy friction factor. If you accidentally plug in a Fanning value — one quarter of the Darcy value — the pressure drop comes out four times too small. You size a pump and then find it cannot deliver nearly enough pressure. Try the mode switch on the left between "Enter the Darcy factor" and "Enter the Fanning factor". Even with the same 0.02, entering it as Darcy versus as Fanning makes ΔP differ by a factor of 4.
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You're right — ΔP jumped from 79.84 kPa to about 319 kPa. So which one should I use?
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Either one gives the same correct answer, as long as you match it to the equation. The key is to keep the equation and the definition of the coefficient consistent. Use the Darcy friction factor with the Darcy-Weisbach equation; use the Fanning friction factor with the Fanning form ΔP = 4·f_Fanning·(L/D)·(ρU²/2). By convention, mechanical, piping and civil engineers tend to use Darcy, while chemical-process engineers use Fanning. That is why disagreements arise when numbers are passed between departments.
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I see. Is there an easy way to tell them apart?
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Yes. The quickest test is to look at the laminar-flow formula. In laminar flow (Reynolds number below 2300) the Darcy friction factor is 64/Re and the Fanning friction factor is 16/Re. With 64 and 16, again exactly a factor of 4. If someone says "the laminar friction factor is 64/Re" they think in Darcy; "16/Re" means Fanning. When reading a paper or textbook, checking whether the laminar formula is 64 or 16 instantly tells you which definition the source uses. This trick is genuinely useful both in practice and when reading the literature.
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I often hear about the Moody chart — which one is that?
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The Moody chart you usually see is drawn with the Darcy friction factor. But don't relax — chemical-engineering textbooks also include Fanning-friction-factor charts. If the vertical axis reads 64/Re in the laminar region it is Darcy; 16/Re means Fanning. The Colebrook equation (the turbulent friction-factor equation) also exists in both a Darcy and a Fanning form. So "whenever you see a chart or correlation, first check the definition with the laminar formula" — make that a habit and you will be free of the 4x blunder for life.
Frequently Asked Questions
Both describe the same pipe friction, but they are defined on different bases, so their numbers differ by a factor of 4: f_Darcy = 4·f_Fanning. The Darcy (Moody) friction factor is the coefficient used in the Darcy-Weisbach equation ΔP = f·(L/D)·(ρU²/2), which gives the pressure drop directly; it is standard in mechanical and civil engineering. The Fanning friction factor is the wall shear stress non-dimensionalised by the dynamic pressure and is widely used in chemical-engineering correlations. For example, a flow with a Darcy factor of 0.02 has a Fanning factor of 0.005.
The Darcy-Weisbach equation ΔP = f_Darcy·(L/D)·(ρU²/2) assumes the Darcy friction factor. However, many chemical-engineering textbooks, some Moody charts and correlations (such as the Fanning form of the Colebrook equation) return the Fanning friction factor. If a Fanning value is plugged straight into the Darcy-Weisbach equation, the pressure drop is underestimated by a factor of 4. The reverse mistake makes pump head or energy loss four times too large. Always confirming which definition a chart or correlation uses is the only reliable way to avoid this 4x blunder.
Either one gives the correct answer. What matters is matching the equation to the definition of the coefficient. If you use the Darcy-Weisbach equation, use the Darcy friction factor; if you use the Fanning form ΔP = 4·f_Fanning·(L/D)·(ρU²/2), use the Fanning friction factor. In practice, mechanical and piping engineers tend to use Darcy while chemical-process engineers use Fanning, so disagreements arise when numbers cross between departments. This tool switches the input mode and shows both values at once, so conversion mistakes are physically prevented.
In laminar flow (Reynolds number Re < 2300) the friction factor is set by theory: the Darcy friction factor is f_Darcy = 64/Re and the Fanning friction factor is f_Fanning = 16/Re. Here too the factor of 4 holds exactly, since 64 = 4×16. Whether someone remembers 64/Re or 16/Re tells you whether they think in Darcy or Fanning. In turbulent flow you use the Moody chart or the Colebrook equation, but every correlation also exists in a Darcy and a Fanning form, so checking the definition of the coefficient remains essential in turbulent flow as well.
Real-World Applications
Process-plant piping design: In chemical plants and oil refineries, the pressure drop of the whole piping network is summed up to size the pump head. Chemical-engineering convention uses the Fanning friction factor, so the f_Fanning obtained from a correlation must either be multiplied by 4 before going into the Darcy-Weisbach equation, or the Fanning form of the equation must be used directly. Mixing up the definition here makes the pump capacity four times too large or too small, with direct consequences for equipment cost and operating stability.
Building services and water-supply systems: For the water-supply and HVAC piping of a building, the Darcy friction factor and the Darcy-Weisbach equation are standard, following mechanical-services convention. Importing a Fanning friction factor from a foreign reference or a chemical-process software leads to a 4x conversion error and a wrong pipe diameter or pump selection. In design reviews, "is that friction factor Darcy or Fanning?" should always be a checklist item.
Validating CFD results: After solving a pipe flow with CFD, you compare the wall shear stress or compare against the Moody chart to check plausibility. Unless you know whether the friction factor output by the CFD solver, or computed by a post-processing script, follows the Darcy or the Fanning definition, you cannot separate a "calculation error" from a "definition mix-up" when a 4x discrepancy appears during validation.
Education and engineer-to-engineer communication: University fluid-mechanics courses and in-house training adopt either Darcy or Fanning depending on the textbook. When engineers with different educational backgrounds design together, exchanging only the numerical value of a friction factor produces a 4x discrepancy. Quoting both values side by side, as this tool does, is the basis of error-free communication.
Common Misconceptions and Pitfalls
The biggest misconception is assuming there is only one friction factor. Early in a fluid-mechanics course it is easy to believe that the friction factor in your textbook is the one and only definition. In reality, the Darcy (Moody) and Fanning friction factors are both used in parallel, related by f_Darcy = 4·f_Fanning. When you use a foreign paper or software from another discipline, failing to confirm which definition the other side uses means you may proceed with a design while a 4x error goes unnoticed. If a value feels "oddly small or large", suspect the definition first.
Next is the assumption that there is only one form of a correlation or Moody chart. The Colebrook equation and the Moody chart that give the turbulent friction factor both exist in Darcy and Fanning forms. Because the equations look similar, you cannot easily tell them apart from the coefficient alone. The reliable test is to look at the laminar region: a laminar formula of 64/Re means Darcy, 16/Re means Fanning. Before quoting a chart or equation, make it a habit to verify the definition with this "laminar test". The origin of the equation — mechanical-engineering versus chemical-engineering — is another clue.
Finally, confusing pressure drop with head loss. The pressure drop ΔP has units of Pa (pascal), while the head loss h_L has units of m (metres, a height of fluid column). They convert through h_L = ΔP/(ρg), but the result changes with the fluid density ρ. Water and oil have different densities, so the same ΔP gives a different head loss. Pump datasheets are usually written in head (metres), while pipe calculations often work in pressure (Pa), so handling this unit conversion carelessly creates another source of error. Together with the factor-of-4 friction-factor problem, always keeping units and definitions consistent is what underpins reliable pipe design.
How to Use
Enter the Fanning friction factor (f_F) or select from the range 0.004–0.08 for turbulent flow in commercial steel pipe
Input pipe diameter (dNum) in mm and relative roughness range, or use 0.045 mm for Schedule 40 steel
Set flow velocity (uNum) in m/s (typical range 1–4 m/s for process piping) and pipe length (lNum) in meters
The simulator automatically calculates Darcy friction factor (f_D = 4 × f_F), pressure drop via ΔP = f_D(L/D)(ρU²/2), and equivalent head loss in meters of fluid column
Worked Example
For a 50 mm Schedule 40 carbon steel pipe carrying water at 2.5 m/s over 15 m length with Fanning friction factor f_F = 0.0064: Darcy factor f_D = 0.0256; L/D = 300; dynamic pressure ½ρU² = 3.13 kPa; pressure drop ΔP = 0.0256 × 300 × 3.13 = 24.1 kPa; head loss h_L = 24.1/(9.81 × 1.0) = 2.46 m. This represents moderate friction loss typical in moderate-velocity industrial circulation systems.
Practical Notes
Darcy–Weisbach applies to any incompressible fluid; multiply calculated ΔP by 1.25–1.5 for compressible gas flows (Mach < 0.3) to account for density variation along the pipe
For rough pipe (worn cast iron ε ≈ 0.25 mm), Fanning friction may climb 40–60% above smooth pipe values; always validate with Colebrook–White iteration or Moody chart
Head loss exceeding 10 kPa per 100 m of pipe indicates undersized diameter or excessive velocity; consider upsizing to DN65 minimum for process water distribution