Darcy Friction Factor Calculator
Solve the Darcy friction factor f from the Reynolds number Re and relative roughness ε/D — exact f = 64/Re for laminar flow, iterated Colebrook–White for turbulent flow — or run it in reverse to find Re from f. Includes explicit Haaland / Swamee–Jain comparison and an interactive Moody chart.
Scope boundary
This tool solves the Darcy friction factor f itself — from Re and ε/D, or Re from f — and plots the Moody chart. It does not compute flow rate, head loss, or pipe diameter.
- Need flow rate Q from head loss, or pipe diameter from flow rate (uses Colebrook internally)? Use the Pipe Flow Calculator.
- Need head loss from a known flow rate? Use the Darcy–Weisbach head loss calculator.
- Need friction loss in a fire hose (NFPA)? Use the fire hose friction loss calculator — a different formula for a different job.
Dimensionless. Laminar ≤ 2300, transitional 2300–4000, turbulent ≥ 4000.
Must be between 0 (smooth) and 0.05.
Solves the turbulent branch (Re ≥ 4000) by bisection. If a laminar solution also exists (Re = 64/f ≤ 2300), it is shown too.
Interactive Moody chart
The red marker shows your latest calculation. Curves are computed live with the same Colebrook–White iteration as the calculator.
Pipe roughness table
Absolute roughness ε for common pipe materials. Click Use to fill ε into the calculator (then enter your diameter D).
| Material | ε (mm) | |
|---|---|---|
| PVC / plastic, drawn copper | 0.0015 | |
| Stainless steel | 0.002 | |
| Commercial steel | 0.045 | |
| Galvanized iron | 0.15 | |
| Cast iron | 0.26 | |
| Concrete | 0.30 |
How it works
The friction factor depends only on the Reynolds number and the relative roughness:
f = 64/Re (laminar, Re ≤ 2300 — exact)1/√f = −2·log10( ε/3.7D + 2.51/(Re·√f) ) (Colebrook–White, turbulent, iterated)The Colebrook–White equation is implicit in f, so the calculator seeds a fixed-point iteration with the explicit Haaland approximation and repeats until f stops changing (tolerance 1e-12). The 2300–4000 transitional band linearly blends the laminar and turbulent values. For a fixed roughness, turbulent f decreases strictly with Re — which is what makes the reverse solver (bisection on Re) possible.
Worked example
Re = 50,000 with relative roughness ε/D = 0.002 (for example, commercial steel ε = 0.045 mm in a 22.5 mm pipe):
| Quantity | Value |
|---|---|
| Flow regime | Turbulent (Re > 4000) |
| Darcy friction factor f (Colebrook–White, iterated) | 0.0265056 |
| Haaland explicit approximation | 0.0262832 |
| Swamee–Jain explicit approximation | 0.0267711 |
| Smooth-pipe check: Re = 100,000, ε/D = 0 | f = 0.0179898 (on the Moody smooth curve) |
| Laminar check: Re = 1000 | f = 64/1000 = 0.064 |
Frequently asked questions
What does this Darcy friction factor calculator compute?
It solves the Darcy friction factor f from the Reynolds number Re and the relative roughness ε/D, using the exact f = 64/Re relation for laminar flow and the iterated Colebrook-White equation for turbulent flow. It also runs in reverse — finding Re from a known f and ε/D — compares the explicit Haaland and Swamee-Jain approximations, and plots your point on an interactive Moody chart.
What is the Darcy friction factor?
The Darcy friction factor f is the dimensionless number in the Darcy-Weisbach equation, hf = f·(L/D)·(v²/2g), that captures how much energy flowing fluid loses to wall friction. For a straight pipe it depends only on the Reynolds number and the relative roughness ε/D: typically 0.008 to 0.1, higher for rougher pipes and lower Reynolds numbers.
How is the friction factor calculated for laminar flow?
For laminar flow (Re at or below 2300) the friction factor is exact and independent of roughness: f = 64/Re. For example, at Re = 1000, f = 0.064 exactly. This is the straight dashed line on the left of the Moody chart.
How does the Colebrook-White equation work?
The Colebrook-White equation, 1/√f = −2·log10(ε/3.7D + 2.51/(Re·√f)), is implicit — f appears on both sides — so it cannot be solved directly. This tool solves it by fixed-point iteration: it seeds the iteration with the explicit Haaland approximation, then repeatedly evaluates the right-hand side until f stops changing (tolerance 1e-12, usually within a handful of iterations).
What are the Haaland and Swamee-Jain approximations?
They are explicit (non-iterative) approximations of the Colebrook-White equation: Haaland, 1/√f = −1.8·log10((ε/3.7D)^1.11 + 6.9/Re), and Swamee-Jain, f = 0.25/(log10(ε/3.7D + 5.74/Re^0.9))². Both are within about 1–2% of the iterated Colebrook value — the results table shows all three side by side so you can compare. For the worked example (Re = 50,000, ε/D = 0.002), Colebrook gives 0.0265056, Haaland 0.0262832 and Swamee-Jain 0.0267711.
How do I read the Moody chart?
Find your Reynolds number on the horizontal (log) axis and move up to the curve matching your relative roughness ε/D, then read the friction factor f on the vertical (log) axis. The dashed line on the left is the laminar region (f = 64/Re); the nearly horizontal curves on the right are the fully rough zone where f stops depending on Re. The red marker shows your latest calculation.
What relative roughness should I use for my pipe?
Divide the absolute roughness ε by the pipe diameter D (same units). Typical ε values: drawn copper or PVC 0.0015 mm, stainless steel 0.002 mm, commercial steel 0.045 mm, galvanized iron 0.15 mm, cast iron 0.26 mm, concrete 0.30 mm. The roughness table fills ε in for you — just enter D, or enter ε/D directly.
How does the inverse solver find Re from f?
For a fixed relative roughness, the turbulent friction factor decreases strictly as Re increases, so exactly one Reynolds number matches a given f. The solver brackets Re between 4,000 and 10^9 and bisects the interval until Re stops changing (tolerance 1e-10). If your f is outside the feasible turbulent band for that roughness, the tool reports the valid band instead of guessing.
How is this different from the pipe flow calculator?
This tool solves for the Darcy friction factor f itself — from Re and ε/D, or Re from f — and draws the Moody chart. The pipe flow calculator at nrtechstudio.com/tools/pipe-flow/ uses the Colebrook equation internally but solves a different problem: flow rate Q from head loss, or pipe diameter from flow rate. Use this tool when f or Re is the unknown; use that one when Q or D is the unknown.
Is this the Darcy or the Fanning friction factor?
This tool uses the Darcy-Weisbach friction factor (sometimes called the Darcy, Moody or Blasius factor). It is exactly 4 times the Fanning friction factor used in some chemical-engineering and heat-transfer texts. If a reference gives you a Fanning factor, multiply it by 4 before comparing with this tool's output.
What is the fully rough zone?
At very high Reynolds numbers, the friction factor stops decreasing and flattens to a constant that depends only on roughness: 1/√f = −2·log10(ε/3.7D). For example, with ε/D = 0.01 the asymptote is f = 0.0379037, and at Re = 10^7 the Colebrook value is already 0.0379098 — essentially fully rough. On the Moody chart these are the flat curves on the right.
What assumptions and limits apply?
Steady, incompressible, Newtonian flow in a straight circular pipe running full, with uniform roughness. Relative roughness ε/D must be between 0 and 0.05, and Re should be positive (the chart spans 10^3 to 10^8). Between Re 2300 and 4000 the tool linearly blends the laminar and turbulent values — a documented approximation of the unstable transitional zone, not a physical law. Do not use it for compressible flow, open channels, or non-Newtonian fluids.
Free tool by NRTechStudio