Welcome to the Haaland Equation Calculator. This tool estimates the Darcy friction factor for steady, incompressible flow in pipes. It’s designed to be quick to use: enter pipe roughness, pipe diameter, and either the Reynolds number directly or the inputs needed to compute it, and you’ll instantly get the friction factor f. The interface is simple, the inputs are standard, and the output plugs right into common head-loss and pressure-drop calculations. You can jump straight into the calculation, or keep reading to learn the formula, see a worked example, and review what each parameter means.
Understanding the formula
Haaland Equation
f = [ 1 / ( −1.8 × log10( (ε / (3.7D))^1.11 + 6.9 / Re ) ) ]^2
Variables:
f: Darcy friction factor (dimensionless)
ε: absolute roughness of the pipe
D: internal diameter of the pipe
Re: Reynolds number
If you don’t already have Re, compute it from the flow conditions:
Reynolds number
Re = (V × D) / ν
Variables:
Re: Reynolds number (dimensionless)
V: mean fluid velocity
D: internal diameter
ν: kinematic viscosity
What the equation is doing in plain language: it blends two effects that drive friction in turbulent pipe flow. The first term uses ε and D to capture how roughness matters more as the pipe gets rougher or smaller. The second term uses Re to capture how turbulence level changes with flow speed and viscosity. The log10 and the exponent 1.11 are part of an empirical fit that closely matches the widely used Colebrook relation without needing iteration.
Parameters explained
ε (absolute roughness)
A measure of the average height of surface bumps inside the pipe. Real pipes are never perfectly smooth; ε tells the calculator how bumpy the wall is. Use meters for this value (you can convert from millimeters or micrometers if your data is in those units).
D (internal diameter)
The clear inside diameter of the pipe, not the nominal size on a catalog page. Use meters. Accurate D matters because roughness is compared to D in the formula.
Re (Reynolds number)
A dimensionless indicator of flow regime. Large Re usually means turbulent flow, which is when the Haaland equation applies best. If you don’t have Re, the calculator can compute it from V, D, and ν.
V (mean velocity)
Average fluid speed in the pipe, typically in meters per second. If you know volumetric flow rate Q and cross-sectional area A, then V = Q / A.
ν (kinematic viscosity)
Fluid viscosity divided by density, in m²/s. It depends on fluid type and temperature. For water near room temperature, ν is about 1.0×10⁻⁶ m²/s.
f (Darcy friction factor)
The final output. It is dimensionless and is used in the Darcy–Weisbach equation to estimate head loss or pressure drop.
How to use the Haaland Equation Calculator — step-by-step example
Goal
Find the Darcy friction factor for water flowing through a new commercial steel pipe.
Given
ε = 0.045 mm (new commercial steel). Convert to meters: ε = 4.5×10⁻⁵ m
D = 0.10 m
V = 2.0 m/s
ν = 1.0×10⁻⁶ m²/s (water at about 20°C)
Step 1: Compute Reynolds number
Re = (V × D) / ν = (2.0 × 0.10) / 1.0×10⁻⁶ = 200,000
Step 2: Evaluate the Haaland terms
Compute the inside of the logarithm: (ε / (3.7D))^1.11 + 6.9 / Re
ε / (3.7D) = 4.5×10⁻⁵ / (3.7 × 0.10) ≈ 1.216×10⁻⁴
(ε / (3.7D))^1.11 ≈ 1.216×10⁻⁴ ^ 1.11 ≈ 9.62×10⁻⁵
6.9 / Re = 6.9 / 200,000 = 3.45×10⁻⁵
Sum ≈ 9.62×10⁻⁵ + 3.45×10⁻⁵ = 1.307×10⁻⁴
Step 3: Apply the log and outer operations
log10(1.307×10⁻⁴) ≈ −3.884
−1.8 × log10(…) ≈ 6.991
1 / 6.991 ≈ 0.143
Square it: f ≈ 0.020
A more precise computation gives f ≈ 0.0184. In practice, values around 0.018–0.020 are typical for these conditions. You can now use f in Darcy–Weisbach: head loss per length is hf/L = f × (V² / (2gD)).
Additional information
Typical absolute roughness values (ε)
| Pipe material / condition | ε (m) | Notes |
|---|---|---|
| Glass, drawn tubing | ~0 | effectively smooth |
| Copper, brass, polyethylene | 1.5×10⁻⁶ to 3×10⁻⁶ | smooth plastics and metals |
| New commercial steel | 4.5×10⁻⁵ | commonly assumed default |
| Galvanized iron | 1.5×10⁻⁴ | rougher steel |
| Cast iron (unlined) | 2.6×10⁻⁴ | older systems |
| Concrete | 3×10⁻⁴ | depends on finish |
Flow regime guide
| Re range | Regime | Notes |
|---|---|---|
| Re < 2,000 | Laminar | Use f = 64 / Re, not Haaland |
| 2,000–4,000 | Transitional | Results less reliable; check carefully |
| Re > 4,000 | Turbulent | Haaland is intended for this range |
Tip on units
Keep ε and D in the same length unit (the calculator assumes meters). If you enter ε in millimeters by accident, f will be wrong by orders of magnitude.
FAQs
Haaland is a fast, non-iterative approximation to Colebrook. Use Haaland when you need a quick, accurate estimate for turbulent flow without solving an implicit equation. For detailed standards work, you may compare both; the results are usually very close.
It’s intended for turbulent flow (typically Re > 4,000). For laminar flow, use f = 64 / Re. In the transitional zone, results from any turbulent correlation are uncertain; try to increase Re or verify with experiments.
Use SI consistently: ε and D in meters, V in m/s, ν in m²/s. If you keep units consistent, Re is dimensionless and f is dimensionless. If you work in other unit systems, convert to SI first for the best reliability.