Moody Chart Friction Factor Calculator

The Moody chart is a graph that plots the Darcy friction factor f against Reynolds number Re for a family of relative roughness (ε/D) curves. Engineers historically read f off the chart by locating Re on the x-axis and following the curve for their pipe's relative roughness. This calculator solves the same underlying Colebrook-White equation numerically instead of reading a graph, then plots the result on the chart for reference.

The Darcy friction factor f is a dimensionless number that quantifies pipe wall friction in the Darcy-Weisbach pressure drop equation, deltaP = f x (L/D) x (rho v^2 / 2). It depends on the Reynolds number and, for turbulent flow, on the pipe's relative roughness ε/D. It is not the same as the Fanning friction factor, which is exactly one quarter of the Darcy value.

The Colebrook-White equation is the implicit formula that defines the turbulent friction factor: 1/sqrt(f) = -2 log10(ε/D/3.7 + 2.51/(Re sqrt(f))). It cannot be solved algebraically for f because f appears on both sides, so this calculator solves it by fixed-point iteration, starting from an initial guess of f = 0.02 and iterating until the value converges.

For laminar flow, defined as Reynolds number below 2,300, the friction factor follows the exact analytical formula f = 64/Re. No iteration or roughness data is needed because laminar flow is smooth and layered, with friction determined entirely by viscous effects near the pipe wall, not by wall roughness.

This is the transitional zone, where flow can be intermittently laminar and turbulent and no single formula is reliably accurate. This calculator extrapolates the Colebrook-White turbulent formula into this range and labels the result as transitional, but real pipe flow in this regime is unpredictable and engineers typically avoid designing systems to operate here.

Relative roughness is ε/D, the pipe's absolute wall roughness ε divided by its internal diameter D, both in the same units. This calculator accepts roughness in millimetres and diameter in millimetres and divides them internally. A relative roughness of 0.000225 (commercial steel at 200 mm) is very different from the same 0.045 mm roughness in a 20 mm pipe, where ε/D = 0.00225, ten times rougher relative to the flow.

The Darcy-Weisbach pressure drop calculator and pipe flow calculator compute pressure loss or flow rate for a complete pipe system (length, flow rate, fluid properties) and use a friction factor internally as one step. This Moody chart calculator isolates just that one step, the friction factor itself, and visualizes it against the full family of Moody chart curves so you can see where your flow sits relative to laminar, transitional, and turbulent regimes at any roughness.

At very high Reynolds number in a rough pipe, the flow becomes fully rough turbulent: the roughness elements protrude through the thin viscous sublayer near the wall, and further increases in velocity no longer change the friction factor meaningfully. The curve becomes nearly horizontal, friction factor depends only on relative roughness in this regime, not on Re.

Yes. New pipes have roughness close to the manufactured value (drawn copper or PVC around 0.0015 mm, new steel around 0.045 mm), but corrosion, scaling, and biofilm buildup increase effective roughness over the service life of a pipe, sometimes by an order of magnitude for old cast iron or corroded steel. Engineers often design with an aged roughness value rather than the as-manufactured value for long-life systems.

Approximate absolute roughness ε: drawn copper or glass about 0.0015 mm, commercial steel or wrought iron about 0.045 mm, galvanized steel about 0.15 mm, cast iron about 0.26 mm, concrete 0.3 to 3 mm depending on finish, and riveted steel up to 3 to 9 mm. These values are the standard references used to populate Moody chart curves in engineering textbooks.

Colebrook-White is a semi-empirical curve fit to experimental turbulent pipe flow data, not a first-principles derivation, but it is widely accepted as the most accurate general-purpose turbulent friction factor formula, typically within a few percent of measured values across a very wide range of Reynolds numbers and roughness ratios. Explicit approximations like Swamee-Jain trade a small amount of accuracy for avoiding the iterative solve.