Inputs

Use a known Reynolds number, or calculate it from velocity, inside diameter, and kinematic viscosity.

Reynolds number input

Reynolds number

Roughness input

Relative roughness, ε/D

Pipe roughness values and ε/D helper ↗

Liquid-water properties reference ↗ · Pure water, 0–99°C at 100 kPa absolute.

Results

Enter inputs and calculate.

Method

Re = VD/ν
Laminar (Re ≤ 2300): f = 64/Re
Transition (2300 < Re < 4000): Churchill estimate
Turbulent (Re ≥ 4000): 1/√f = −2 log₁₀(ε/(3.7D) + 2.51/(Re√f))

The reported Darcy factor is used in the standard straight-pipe pressure-loss form. The Fanning factor is one quarter of the Darcy factor. Roughness affects turbulent flow but not the laminar relation.

What the Darcy friction factor represents

The Darcy friction factor is the dimensionless coefficient used in the Darcy-Weisbach equation for straight-pipe loss. In laminar flow it depends only on Reynolds number. In turbulent flow it depends on both Reynolds number and relative roughness, ε/D. This calculator reports both the Darcy factor and the Fanning factor so the convention is explicit.

For turbulent flow the calculator solves the Colebrook-White equation iteratively. In the transition region it uses the Churchill correlation to provide a continuous engineering estimate. Because transitional flow is inherently uncertain, the numerical answer should not be interpreted as greater physical certainty than the flow regime allows.

When to use it

Darcy-Weisbach straight-pipe pressure-drop calculations.
Converting K values to equivalent length when the operating friction factor is known.
Checking the effect of roughness, Reynolds number, or pipe aging on line loss.
Verifying a friction factor from another calculator, spreadsheet, or Moody chart.

Assumptions and inputs

For fully developed flow in a full, circular pipe. This page supports 1 ≤ Re ≤ 10⁸ and 0 ≤ ε/D ≤ 0.05. Transition results are estimates, not reliable design limits.

The reported factor is the Darcy friction factor.
Absolute roughness is converted to relative roughness using the actual inside diameter.
For laminar flow, the calculator uses f = 64/Re and roughness does not enter the relation.
Roughness is an engineering representation of the internal surface. Actual aged, scaled, corroded, lined, or fouled pipe may differ from handbook values.

Common mistakes

Confusing Darcy and Fanning factors. Darcy f = 4 × Fanning f. Using the wrong convention creates a fourfold error in the friction term.
Entering absolute roughness as ε/D. Relative roughness must be dimensionless.
Using outside or nominal diameter to compute relative roughness. Use inside diameter.
Expecting one friction factor to apply at every flow rate. Reynolds number changes with flow and fluid properties.
Overstating precision in transition flow. A correlation can provide a smooth estimate without making the physical regime perfectly predictable.

Benchmark: at Re = 100,000 and ε/D = 0.001, the Colebrook solution is about f = 0.02217 Darcy.

Using f in a pressure-drop calculation

Insert the Darcy factor into ΔP = f(L/D)(ρV²/2), or use the Pipe Friction Loss Calculator to calculate Reynolds number, f, straight-pipe loss, and fitting losses together. If you are working from an equivalent-length table, use the K Factor ↔ Equivalent Length Calculator.

Reference background: the U.S. Department of Energy fluid-flow handbook describes friction factors, Moody-chart behavior, and Darcy head loss. DOE fluid-flow handbook.

Darcy or Fanning?

Darcy vs. Fanning reference ↗ · Compare the definitions, convert friction factors, and check which equation to use.

Equation values and input guide

Enter Reynolds number directly or calculate it from velocity, diameter and kinematic viscosity. Choose absolute or relative roughness to match your source data. Use the resulting Darcy factor in a Darcy pressure-loss equation.

f: Darcy friction factor, dimensionless. It equals four times the Fanning friction factor.
Re: Reynolds number VD/ν, dimensionless.
V, D, ν: Average velocity (m/s), actual inside diameter (m), and kinematic viscosity (m²/s) after conversion.
ε: Absolute wall roughness, a length describing the pipe material and condition. Use a supported value from the roughness reference or supplier.
ε/D: Relative roughness, dimensionless; divide roughness and bore expressed in the same length unit.
log₁₀: Base-10 logarithm. The turbulent equation is implicit because f occurs on both sides; the calculator solves it iteratively.

Use the unit selectors beside the inputs. Units shown in the equations must be consistent when checking the math by hand.