The Moody diagram is a graph that gives you the friction factor for fluid flowing through a pipe, based on two values you calculate beforehand: the Reynolds number (plotted on the horizontal axis) and the relative roughness of the pipe (plotted as individual curves). Once you know how to locate these two values on the chart, reading it takes about 30 seconds.
What the Axes Represent
The horizontal axis (x-axis) shows the Reynolds number, which tells you whether the flow is smooth and orderly (laminar) or chaotic (turbulent). It runs from about 600 on the left to over 100 million on the right, using a logarithmic scale. That means each major gridline represents a tenfold increase, so the spacing between 1,000 and 10,000 looks the same as between 100,000 and 1,000,000.
The vertical axis (y-axis) shows the Darcy friction factor, typically ranging from about 0.008 to 0.1. This axis is also logarithmic. The friction factor is the number you ultimately need from the diagram, and it plugs directly into the Darcy-Weisbach equation to calculate how much energy (head loss) fluid loses to friction as it moves through a pipe.
Along the right-hand side, you’ll see a secondary scale labeled “relative roughness” (ε/D). Each curved line in the turbulent region corresponds to a specific relative roughness value. This scale helps you identify which curve to follow.
Calculate Reynolds Number First
Before touching the diagram, you need the Reynolds number for your flow. The formula is:
Re = VD / ν
V is the average flow velocity, D is the pipe’s internal diameter, and ν (nu) is the kinematic viscosity of the fluid. All three must be in consistent units. In imperial units, that means feet per second for velocity, feet for diameter, and square feet per second for viscosity. The result is a dimensionless number.
If the Reynolds number comes out below about 2,100, your flow is laminar. Between roughly 2,100 and 4,000 is a transition zone where flow is unpredictable. Above 4,000, flow is fully turbulent. This distinction matters because you read the diagram differently in each region.
Determine Relative Roughness
Relative roughness is the ratio of the pipe wall’s absolute roughness (ε) to its internal diameter (D). Both must be in the same units. Absolute roughness values depend on the pipe material:
- PVC or glass tubing: 0.0015 mm (very smooth)
- Commercial or welded steel: 0.045 mm
- Cast iron: 0.26 mm
- Concrete: 0.3 to 3.0 mm (varies with finish quality)
Divide the absolute roughness by the pipe diameter to get relative roughness. For example, a 100 mm diameter commercial steel pipe has a relative roughness of 0.045 / 100 = 0.00045. This value tells you which curve on the Moody diagram to use.
Reading the Laminar Region
The left portion of the diagram, where Reynolds numbers fall below 2,100, has a single straight diagonal line sloping downward from left to right. Pipe roughness doesn’t matter here. In laminar flow, the friction factor follows a simple formula: f = 64 / Re. The line on the diagram is just a graphical representation of that equation.
To read it, find your Reynolds number on the x-axis, draw a vertical line up to the diagonal, then move horizontally to the y-axis. That’s your friction factor. At Re = 1,000, the friction factor is 0.064. At Re = 2,000, it’s 0.032. You can also just calculate 64/Re directly and skip the chart entirely for laminar flow.
Reading the Turbulent Region
This is where the Moody diagram earns its keep. Above Re = 4,000, the single laminar line fans out into a family of curves, each one representing a different relative roughness. The lowest curve (closest to the bottom) corresponds to a perfectly smooth pipe, while higher curves correspond to rougher pipes.
Here’s the step-by-step process:
- Step 1: Find your Reynolds number on the x-axis.
- Step 2: Locate your relative roughness value on the right-hand scale, and identify which curve it belongs to. If your value falls between labeled curves, interpolate visually.
- Step 3: Follow that curve horizontally until you’re directly above your Reynolds number.
- Step 4: From that intersection point, move straight left to the y-axis and read the friction factor.
The curves in the turbulent region are based on the Colebrook-White equation, which relates friction factor to both Reynolds number and relative roughness. This equation is implicit, meaning it can’t be solved in one step algebraically. The Moody diagram exists precisely to give you a visual shortcut around that iterative math.
The Transition Zone and Fully Rough Flow
Between Reynolds numbers of about 2,100 and 4,000, the diagram shows a shaded or dashed region. Flow here is unstable, oscillating between laminar and turbulent behavior. Friction factor values in this zone are unreliable, and the diagram reflects that uncertainty. If your Reynolds number lands here, expect some imprecision in your result.
At the far right of the diagram, you’ll notice the curves flatten out and become horizontal. This is the “fully rough” zone, where the friction factor depends only on relative roughness and no longer changes with Reynolds number. In practical terms, at very high flow velocities, increasing the speed further doesn’t change the friction factor. The pipe’s surface texture dominates. In this region, the Colebrook-White equation simplifies to f depending on ε/D alone.
Darcy vs. Fanning Friction Factor
One major source of error when using any friction factor chart: there are two different friction factors in common use. The Darcy friction factor (also called the Moody friction factor) is exactly four times the Fanning friction factor. Most Moody diagrams use the Darcy version, but not all. If you pull a friction factor from one type of chart and plug it into an equation expecting the other, your answer will be off by a factor of four.
Check the axis labels. A Darcy-based diagram typically shows friction factors ranging from about 0.008 to 0.1. A Fanning-based chart will show values roughly one-quarter of that range, from about 0.002 to 0.025. If in doubt, verify by checking the laminar line: at Re = 1,000, the Darcy friction factor is 0.064 (from f = 64/Re), while the Fanning friction factor would be 0.016 (from f = 16/Re).
Using the Friction Factor
Once you’ve read the friction factor from the diagram, it goes into the Darcy-Weisbach equation to calculate head loss:
h_f = f × (L/D) × (V² / 2g)
Here, f is the friction factor you just found, L is the pipe length, D is the internal diameter, V is the flow velocity, and g is gravitational acceleration (9.81 m/s² or 32.2 ft/s²). Head loss (h_f) comes out in units of length, representing the height of a column of fluid equivalent to the energy lost to friction. You can convert this to a pressure drop by multiplying by the fluid’s density and gravitational acceleration.
This is the core application. Engineers use this calculation to size pumps, design piping systems, and predict pressure drops across long runs of pipe. The Moody diagram is simply the tool that bridges the gap between your flow conditions and the friction factor the equation requires.
Tips for Accurate Readings
Because both axes are logarithmic, small visual distances represent large numerical differences, especially at the upper end of each scale. When interpolating between gridlines, remember that the midpoint visually is not the midpoint numerically. On a log scale, the visual midpoint between 1,000 and 10,000 corresponds to roughly 3,000, not 5,500.
If your relative roughness value falls between two labeled curves, estimate the curve’s position proportionally, keeping the logarithmic spacing in mind. For precision work where visual interpolation isn’t accurate enough, use the Colebrook-White equation directly with an iterative solver or one of the many explicit approximations available (the Swamee-Jain equation, for instance, gives results within 1% of the Colebrook-White equation without iteration).
Finally, double-check your units before calculating Reynolds number and relative roughness. Mixing metric and imperial values, or using pipe diameter in inches when the formula expects feet, is the most common source of wildly wrong friction factors.