Friction Factor Calculator (Darcy-Weisbach)
Enter your pipe diameter, fluid velocity, kinematic viscosity and surface roughness to calculate the Darcy-Weisbach friction factor, Reynolds number and flow regime. The calculator uses the Churchill (1977) unified formula, which is valid for laminar, transitional, and turbulent flow without switching equations. Switch between metric and imperial units and see the step-by-step workings.
What is the Darcy friction factor?
The Darcy friction factor (also called the Darcy-Weisbach friction factor or the Moody friction factor) is a dimensionless number that quantifies the resistance to flow caused by friction between the fluid and the pipe wall. It appears in the Darcy-Weisbach equation: the head loss due to friction equals f times the pipe length-to-diameter ratio times the velocity head (V squared divided by twice the gravitational acceleration). A higher friction factor means more energy is lost to friction for the same flow conditions. The Darcy factor is four times larger than the Fanning friction factor, which is used in some chemical engineering contexts, so be careful not to mix them up.
How to calculate the friction factor: laminar vs turbulent flow
The approach depends on the Reynolds number. In laminar flow (Re < 2,300), friction depends only on Re and is given exactly by f = 64 / Re. No surface roughness is involved because the viscous boundary layer extends right across the pipe. In turbulent flow (Re > 4,000), both Reynolds number and the relative roughness (e/D, where e is the absolute roughness and D is the diameter) matter. The standard reference is the Colebrook-White equation: 1 / sqrt(f) = -2 log10(e/D / 3.7 + 2.51 / (Re sqrt(f))). Because this equation contains f on both sides, it must be solved iteratively, or approximated explicitly. This calculator uses the Churchill (1977) unified formula, which covers laminar, transitional, and turbulent flow without any regime-switching logic and is accurate to within 0.5% across the full practical range.
The Moody diagram
The Moody diagram is a log-log chart that plots friction factor against Reynolds number for a family of relative roughness curves, one for each e/D value. It was published by Lewis F. Moody in 1944 and became the standard reference for pipe flow calculations. The chart shows four regions: laminar flow (straight line with slope -1, valid below Re = 2,300), the uncertain transitional zone, the turbulent-smooth zone (where viscosity still matters and roughness does not yet control friction), and the fully-rough turbulent zone (where friction is constant for a given e/D and independent of Re). This calculator reproduces the Moody diagram numerically and lets you trace the f vs Re curve for your specific roughness.
Darcy-Weisbach equation and pressure drop
Once you have the friction factor, the head loss (energy loss per unit weight of fluid) for a straight pipe is h_f = f x (L / D) x V^2 / (2g), where L is the pipe length, D is the diameter, V is the mean velocity and g is 9.81 m/s^2. Pressure drop is then the product of fluid density, gravitational acceleration and head loss: Delta P = rho x g x h_f. For water at 20 deg C (density 1,000 kg/m^3) a head loss of 1 m corresponds to a pressure drop of about 9,810 Pa. These major (friction) losses must be added to minor losses at fittings and valves to get total system pressure drop.
Typical absolute roughness values by pipe material
| Pipe material | Roughness (mm) | Roughness (in) |
|---|---|---|
| Glass, drawn copper, brass | 0.0015 | 0.00006 |
| Commercial steel, wrought iron | 0.046 | 0.0018 |
| Galvanized iron | 0.15 | 0.006 |
| Cast iron | 0.26 | 0.010 |
| Asphalted cast iron | 0.12 | 0.0048 |
| Concrete (smooth finish) | 0.3 | 0.012 |
| Concrete (rough finish) | 3.0 | 0.12 |
| Riveted steel | 0.9-9.0 | 0.035-0.35 |
| PVC, smooth plastics | 0.0015 | 0.00006 |
Use these values for the surface roughness input. Source: Moody (1944) and engineering handbooks.
Frequently asked questions
What is the difference between the Darcy and Fanning friction factors?
The Darcy friction factor (used here) is exactly four times the Fanning friction factor. Both describe the same physical pipe resistance, but they appear in different forms of the head-loss equation. Chemical engineers often use the Fanning version with a factor of 4 in the denominator, while civil and mechanical engineers almost always use the Darcy version. Always check which definition a chart or equation uses: a Fanning f of 0.005 is the same as a Darcy f of 0.020.
What Reynolds number separates laminar from turbulent flow?
In a smooth, straight, circular pipe the standard critical Reynolds number is about 2,300. Below this, flow is always laminar. Above about 4,000, flow is turbulent under normal operating conditions. The range from 2,300 to 4,000 is the transitional zone, where flow can switch unpredictably between regimes and friction factor predictions are unreliable. For practical pipe design, assume turbulent flow for Re > 4,000.
Does pipe roughness affect laminar flow?
No. In laminar flow the fluid moves in smooth parallel layers and the viscous boundary layer fills the entire pipe cross-section, so the pipe wall roughness never contacts the free-flowing fluid. The friction factor is f = 64 / Re regardless of roughness. Roughness only matters once turbulent eddies carry fluid to the wall, which happens at higher Reynolds numbers.
What is the Colebrook-White equation and why is this calculator using Churchill instead?
The Colebrook-White equation (1939) is the most accurate correlation for the turbulent friction factor and is the mathematical basis of the Moody diagram. However, it is implicit: f appears on both sides, requiring an iterative (Newton-Raphson or similar) solution. The Churchill (1977) formula is an explicit approximation that is valid across the entire flow range, including laminar and transitional regions, with error below 0.5%. It avoids iteration and avoids the need to switch formulas between regimes, making it the preferred method for programmatic calculation.
How does pipe diameter affect the friction factor?
Pipe diameter affects friction factor in two ways. First, a larger diameter lowers the Reynolds number for the same flow rate (Re = V D / nu), pushing flow toward the laminar or lower-turbulence regime. Second, a larger diameter reduces the relative roughness (e/D), shifting the operating point toward the smoother-pipe curves on the Moody diagram. Both effects reduce the friction factor. Combined with the L/D term in the Darcy-Weisbach equation, doubling the diameter can reduce head loss by a factor of 30 or more.
What roughness value should I use for my pipe?
Use the reference table on this page as a starting point. Commercial steel and wrought iron pipes have an absolute roughness of about 0.046 mm. Drawn copper, brass and glass are very smooth at 0.0015 mm. PVC and smooth plastics are similarly smooth. Concrete roughness varies widely, from 0.3 mm for a smooth finish to 3 mm or more for rough poured concrete. For aged or corroded pipes, use values toward the higher end of the range, as deposits and corrosion increase roughness significantly over time.