What is the Moody diagram?

The Moody diagram (Moody, 1944) plots the Darcy friction factor f against Reynolds number Re on log-log axes, with one curve for each value of relative roughness ε/D. It is a graphical solution of the Colebrook equation for turbulent flow, plus the laminar line f = 64/Re. Reading f from it and inserting f into the Darcy-Weisbach equation gives pipe friction head loss.

How do I read a Moody chart?

Compute Re = VD/ν and relative roughness ε/D. Find Re on the horizontal axis, move up to the curve for your ε/D (interpolating between curves), then read f on the left axis. If Re is below about 2,300 use the laminar line f = 64/Re regardless of roughness. This calculator does the same thing numerically and plots your point.

How accurate are Swamee-Jain and Haaland compared with Colebrook?

Both are explicit approximations of the implicit Colebrook equation. Swamee-Jain (1976) is usually within about 1% over 5,000 ≤ Re ≤ 10⁸ and 10⁻⁶ ≤ ε/D ≤ 10⁻². Haaland (1983) is within about 2% for Re ≥ 4,000. For Re = 100,000 and ε/D = 0.0001, Colebrook gives f = 0.01851, Swamee-Jain 0.01845 (−0.3%) and Haaland 0.01827 (−1.3%).

What is the fully rough (complete turbulence) zone?

At high Reynolds numbers the curves flatten and f stops depending on Re, depending only on ε/D. The limit is the von Kármán rough-pipe equation 1/√f = 2·log₁₀(3.7/(ε/D)). For ε/D = 0.001 the fully rough friction factor is 0.0196; the dashed boundary on a Moody chart marks where this applies.

Why is the region between Re 2,300 and 4,000 left blank?

That is the critical or transitional zone, where flow can switch between laminar and turbulent and the friction factor is not uniquely defined. Neither f = 64/Re nor Colebrook is reliable there. Design either avoids the range or brackets it by checking both values and carrying the higher head loss.

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Moody Diagram Calculator

Darcy friction factor from Reynolds number and relative roughness, solved three ways — the exact Colebrook equation, Swamee-Jain and Haaland — with your operating point plotted on a live Moody chart.

Reynolds number, Re—

Relative roughness, ε/D—

Flow regime—

f — Colebrook (exact)——

f — Swamee-Jain——

Swamee-Jain error vs Colebrook—%

f — Haaland——

Haaland error vs Colebrook—%

f — fully rough limit——

Defaults: 8-inch new commercial steel pipe at 6.38 ft/s, water at 60°F — the same case as Example 1 on the Darcy-Weisbach calculator. Need Re or ε/D first? Re = VD/ν; ε/D is absolute roughness divided by inside diameter, in the same units.

Colebrook (1939), solved iteratively to 10⁻¹²:

$$ \frac{1}{\sqrt{f}} = -2\log_{10}\!\left(\frac{\varepsilon/D}{3.7} + \frac{2.51}{Re\sqrt{f}}\right) $$

Swamee-Jain (1976) and Haaland (1983), explicit:

$$ f_{SJ} = \frac{0.25}{\left[\log_{10}\!\left(\frac{\varepsilon/D}{3.7} + \frac{5.74}{Re^{0.9}}\right)\right]^2} \qquad \frac{1}{\sqrt{f_H}} = -1.8\log_{10}\!\left[\left(\frac{\varepsilon/D}{3.7}\right)^{1.11} + \frac{6.9}{Re}\right] $$

Laminar and fully rough limits:

$$ f = \frac{64}{Re} \;\; (Re < 2300) \qquad \frac{1}{\sqrt{f_{rough}}} = 2\log_{10}\!\left(\frac{3.7}{\varepsilon/D}\right) $$

f Darcy friction factor · Re Reynolds number = VD/ν · ε absolute pipe roughness · D inside diameter · ε/D relative roughness (dimensionless).

How to use the Moody diagram

The chart has two independent inputs and one output. Reynolds number tells you how turbulent the flow is; relative roughness tells you how much the pipe wall matters. Everything else about the pipe — material, age, diameter, fluid — is already folded into those two numbers. Once you have f, the Darcy-Weisbach equation turns it into head loss: h_f = f·(L/D)·V²/2g.

The same Re can give very different friction factors depending on the pipe. At Re = 10⁶, a smooth plastic pipe sits near f = 0.0117 while a pipe with ε/D = 0.01 sits near 0.038 — more than three times the head loss for identical flow. That spread is why roughness selection, not the friction-factor formula, is usually the largest uncertainty in a pipe-loss calculation. See the absolute roughness reference card for ε by material and age.

The four zones of the chart

Moody diagram flow zones
Zone	Reynolds number	What controls f	Use
Laminar	< 2,300	Viscosity only	f = 64/Re
Critical (transitional)	2,300 – 4,000	Undefined — flow can flip	Bracket both; avoid in design
Transition turbulent	> 4,000	Both Re and ε/D	Colebrook
Fully rough (complete turbulence)	High; right of dashed line	ε/D only	von Kármán rough-pipe

Fully rough friction factor by relative roughness

The flat right-hand asymptote of each curve. Once a pipe is in this zone, doubling the flow does not change f — head loss scales exactly with V².

Complete-turbulence friction factor, 1/√f = 2·log₁₀(3.7/(ε/D))
ε/D	f (fully rough)	Typical example
0.00001	0.00806	Large-diameter drawn or plastic pipe
0.0001	0.0120	Commercial steel, ~18 in diameter
0.0005	0.0167	Cast iron, ~20 in diameter
0.001	0.0196	Concrete pipe, ~12 in diameter
0.005	0.0304	Galvanized iron, ~1¼ in diameter
0.01	0.0379	Heavily tuberculated small main
0.05	0.0716	Upper limit of the chart

Values computed from the von Kármán rough-pipe equation. The "typical example" column is illustrative only; compute ε/D from the actual ε and inside diameter.

Worked examples

Example 1 — 8-inch commercial steel water main

Given: Re = 3.52×10⁵, ε/D = 0.0018 in / 8 in = 2.25×10⁻⁴.

Find: Darcy friction factor, and how much the explicit formulas differ.

Re > 4,000 → turbulent; use Colebrook.

Start from Swamee-Jain: f₀ = 0.25/[log₁₀(2.25×10⁻⁴/3.7 + 5.74/(3.52×10⁵)^0.9)]² = 0.01624

Iterate 1/√f = −2 log₁₀(6.08×10⁻⁵ + 2.51/(3.52×10⁵·√f)) until f stops changing

f = 0.01617 (Colebrook) · Swamee-Jain 0.01624 (+0.45%) · Haaland 0.01600 (−1.06%)

Example 2 — Rough pipe at high Reynolds number

Given: Re = 1.0×10⁶, ε/D = 0.001.

Find: f, and whether the pipe is in the fully rough zone.

Colebrook: f = 0.01994

Fully rough limit: 1/√f = 2·log₁₀(3.7/0.001) = 7.136 → f = 0.01964

Colebrook is within 1.6% of the rough limit — the Re term is nearly negligible here.

f = 0.01994 · Swamee-Jain 0.02003 (+0.43%) · Haaland 0.01994 (−0.01%)

Example 3 — Smooth pipe

Given: Re = 50,000, ε/D = 0 (hydraulically smooth).

With ε/D = 0 Colebrook reduces to the Prandtl smooth-pipe law, 1/√f = 2 log₁₀(Re√f) − 0.8.

f = 0.02089 (Colebrook) · Swamee-Jain 0.02076 (−0.63%) · Haaland 0.02071 (−0.85%)

Which friction factor formula should I use?

Colebrook is the reference — the Moody chart is drawn from it. Use it whenever a computer is doing the work.
Swamee-Jain is the standard explicit form for hand calculation and spreadsheets; typically within 1%.
Haaland is slightly less accurate at moderate Re but tracks Colebrook very closely in the rough zone.

The differences between the three are smaller than the uncertainty in roughness for almost any real pipe. Pick one method, state it in the calculation, and spend the saved effort on ε.

References: Moody, L.F. (1944). "Friction factors for pipe flow." Trans. ASME 66(8), 671–684. Colebrook, C.F. (1939). "Turbulent flow in pipes." J. Inst. Civil Eng. 11, 133–156. Swamee, P.K., Jain, A.K. (1976). J. Hydraulics Div., ASCE 102(5), 657–664. Haaland, S.E. (1983). J. Fluids Eng. 105(1), 89–90.

Related tools

Darcy-Weisbach head loss — turn f into friction loss
Reynolds number — compute Re from velocity, diameter and viscosity
Absolute roughness (ε) reference card
Reynolds number regimes & water viscosity
Minor loss calculator — fittings and valves