Calculate the Darcy friction factor from velocity, flow rate, or Reynolds number and relative roughness; infer absolute roughness from a target factor. Optional pipe length and density add straight-pipe loss estimates.

Darcy factor for steady, fully developed circular-pipe flow. Uses 64/Re for laminar flow; no estimate in the 2,300–4,000 transition range. Pipe losses exclude fittings and elevation.

Enter 0 for a smooth-pipe estimate.

Use the fluid property at its operating temperature.

Pipe losses (blank: omit)

Blank omits head loss and pressure drop.

Blank omits pressure drop. Head loss needs no density.

Related Calculators

Haaland Equation Formula

The Haaland equation is an explicit correlation used to estimate the Darcy-Weisbach friction factor for turbulent flow in pipes and ducts. It is popular because it avoids iteration while still giving a close approximation to the Colebrook relationship in many engineering calculations.

f = [- 1.8log₁₀[((ε / D) / (3.7))1.11 + (6.9) / (Re)]]⁻²
Quantity Meaning Practical note
Friction factor The Darcy-Weisbach friction factor returned by the calculator Use this value for head loss and pressure drop calculations.
Relative roughness Pipe roughness compared with internal diameter It is dimensionless. If you compute it yourself, roughness and diameter must use the same length unit.
Reynolds number A dimensionless indicator of flow regime Higher values generally mean stronger turbulence and a different friction response.

How to Use the Haaland Equation Calculator

  1. Select a solve mode. In the direct Reynolds mode, enter relative roughness ε/D and Reynolds number.
  2. Velocity and flow modes instead use inside diameter, absolute roughness and kinematic viscosity. Inverse mode also needs a target Darcy factor. Enter pipe length only if head loss is needed, and density only for pressure drop.
  3. Calculate the Darcy friction factor.
  4. Use the result in downstream pipe-flow equations such as head loss or pressure drop.

Velocity and flow modes compute relative roughness from absolute roughness and inside diameter using consistent units. Direct mode accepts the dimensionless ratio. Unit changes convert entered quantities; select Calculate to update a previous result.

What the Inputs Tell You

  • Relative roughness: Higher roughness means more wall drag and usually a larger friction factor.
  • Reynolds number: As Reynolds number increases, the friction factor often drops for smoother pipes, but roughness becomes increasingly important at high turbulence levels.
  • Friction factor: This is a resistance coefficient used to quantify how much energy the fluid loses as it moves through a pipe.

Example

For a relative roughness of 0.0005 and a Reynolds number of 100000, the Haaland equation gives a friction factor of about 0.020. That value can then be inserted directly into head-loss or pressure-drop calculations for the pipe section being analyzed.

Using the Result in Pipe Flow Calculations

After finding the friction factor, the most common next step is to calculate head loss or pressure loss along the pipe.

hf = f(L) / (D)(V²) / (2g)
Δ P = f(L) / (D)(ρ V²) / (2)
  • Head loss: Useful in pump sizing, piping system design, and energy balance calculations.
  • Pressure drop: Useful when evaluating system resistance, compressor load, or available pressure at downstream equipment.
  • System comparison: A small change in friction factor can materially change loss estimates over long pipe runs.

When the Haaland Equation Is Appropriate

  • Steady, fully developed turbulent flow in circular pipes within the stated model range; noncircular ducts require an appropriate separate model
  • Fast engineering estimates where an explicit equation is preferred over iteration
  • Applications with appropriate fluid properties and negligible compressibility; this tool does not model changing gas density
  • Spreadsheet, hand-calculation, or calculator-based pressure loss workflows

Limitations and Flow-Regime Notes

The Haaland equation is intended for turbulent-flow friction factor estimation. It should not be treated as the default choice for every Reynolds number.

f = (64) / (Re)
  • Laminar flow: For Reynolds numbers below about 2300, use the laminar relation shown above instead of Haaland.
  • Transitional flow: From Re 2300 up to 4000, this tool rejects a friction-factor estimate because the transition is uncertain. Turbulent calculations here support Re 4000–100,000,000 and relative roughness 0–0.05.
  • Factor convention: This calculator uses the Darcy friction factor, not the Fanning friction factor. The Darcy value is four times the Fanning value.
  • Model choice: For highly sensitive design work, engineers may compare Haaland results with Colebrook-based solutions or software output.

Common Input Mistakes

  • Confusing absolute roughness in velocity/flow modes with relative roughness in the direct mode
  • Using outside diameter instead of the pipe’s inside diameter
  • Mixing Darcy and Fanning friction factor conventions
  • Applying the equation to clearly laminar flow
  • Using a Reynolds number that was calculated with inconsistent units or incorrect fluid properties

Haaland correlation: S. E. Haaland, Simple and Explicit Formulas for the Friction Factor in Turbulent Pipe Flow (1983). Pipe-loss outputs omit fittings, elevation, entrance effects and compressibility; inverse roughness is a model estimate, not a measurement.

Why Engineers Like the Haaland Equation

The main advantage of the Haaland equation is speed. It captures the influence of both Reynolds number and wall roughness in a single explicit expression, making it ideal for calculators, quick design checks, and repeated evaluations across many pipe segments. When you need a fast estimate of pipe friction without solving an implicit equation, it is one of the most practical tools available.