Swamee-Jain Equation Calculator
The Swamee-Jain equation gives you friction factor in one shot, with no iteration required. It's an explicit approximation of the Colebrook-White equation, accurate to within 3%. This calculator also runs the full iterative Colebrook-White solution so you can see how close they are.
Calculate friction factor (Swamee-Jain vs Colebrook-White)
Results
What is the Swamee-Jain equation?
The Colebrook-White equation is the standard method for turbulent pipe flow friction factor, but it's implicit: friction factor appears on both sides of the equation, so you have to solve it iteratively (as the Moody Chart Calculator does with Newton-Raphson iteration).
In 1976, Prabhata K. Swamee and Akalank K. Jain published an explicit approximation that gives nearly identical results in a single calculation. Engineers have used it since, particularly for hand calculations, spreadsheets, and embedded systems where iteration is inconvenient.
The Swamee-Jain formula
f = 0.25 / [log₁₀(ε/D/3.7 + 5.74/Re⁰·⁹)]² - f - Darcy friction factor (dimensionless)
- ε/D - relative roughness (dimensionless)
- Re - Reynolds number (dimensionless)
Valid range: Re between 5,000 and 10⁸, ε/D between 10⁻⁶ and 5×10⁻². Accuracy: within ±3% of the Colebrook-White solution.
The Colebrook-White equation (for comparison)
1/√f = -2.0 × log₁₀(ε/D/3.7 + 2.51/(Re × √f)) This implicit equation is solved iteratively. This calculator uses Newton-Raphson iteration (same as the main Moody Chart Calculator) converging to tolerance 10⁻¹⁰.
Worked example
Commercial steel pipe (ε/D = 0.0001), Re = 100,000.
f_SJ = 0.25 / [log₁₀(0.0001/3.7 + 5.74/100000⁰·⁹)]²
100000⁰·⁹ = 31,623
= 0.25 / [log₁₀(2.7027×10⁻⁵ + 5.74/31,623)]²
= 0.25 / [log₁₀(2.7027×10⁻⁵ + 1.8153×10⁻⁴)]²
= 0.25 / [log₁₀(2.0856×10⁻⁴)]²
= 0.25 / [−3.6807]² = 0.25 / 13.548
f_SJ ≈ 0.018453
Colebrook-White: f_CW ≈ 0.018514, difference −0.33%
How accurate is Swamee-Jain, and where is it worst?
"Within 3%" is the usual headline, but the error is not spread evenly. It is concentrated at the low-Reynolds, high-roughness corner of the valid range and falls away to almost nothing everywhere else. The table below gives the Swamee-Jain deviation from the iterated Colebrook-White solution, as a percentage of the Colebrook value.
| Re | ε/D = 10⁻⁶ | ε/D = 10⁻⁴ | ε/D = 10⁻³ | ε/D = 10⁻² | ε/D = 5×10⁻² |
|---|---|---|---|---|---|
| 5 × 10³ | +1.21% | +1.25% | +1.57% | +2.83% | +2.69% |
| 10⁴ | +0.29% | +0.36% | +0.88% | +2.12% | +1.68% |
| 10⁵ | −0.70% | −0.33% | +0.76% | +0.64% | +0.30% |
| 10⁶ | −0.31% | +0.49% | +0.43% | +0.12% | +0.05% |
| 10⁷ | +0.55% | +0.39% | +0.10% | +0.02% | +0.01% |
| 10⁸ | +1.14% | +0.09% | +0.02% | +0.00% | +0.00% |
Two things follow. The worst case across the whole valid domain is about +2.8%, at Re = 5,000 with ε/D = 0.01. That is the bottom-left corner, where flow has only just turned properly turbulent in a rough pipe. Across the range where real pipework operates, Re between 10⁵ and 10⁷, the deviation stays well under 1%.
A useful way to hold this: the error in your relative roughness is almost always larger than the error in Swamee-Jain. Absolute roughness values for real pipe carry ±20% or worse, and much worse for aged pipe. Against that, a sub-1% approximation error is not the thing limiting your answer.
Why the constants are 5.74 and 0.9
The Swamee-Jain equation is not derived from Colebrook-White; it is a fit to it. Colebrook's implicit form buries the friction factor inside a logarithm, and no algebraic rearrangement frees it. Swamee and Jain instead proposed a function of the same shape: a log of (roughness term + Reynolds term), squared and inverted. They then tuned its two free constants to minimise the deviation from Colebrook across the engineering domain.
That is why the equation carries a stated validity range at all. Outside 5,000 ≤ Re ≤ 10⁸ and 10⁻⁶ ≤ ε/D ≤ 5×10⁻², nobody optimised the fit, and the deviation grows without warning. The calculator above flags that rather than quietly handing you a number.
Which method should you actually use?
Use Swamee-Jain for hand calculations, spreadsheets, exams, and anywhere a closed form matters — embedded controllers, or a solver where an inner iteration loop would be awkward. It is one line and it needs no initial guess.
Use Colebrook-White when you are already in software that can iterate cheaply, which today is nearly everything. Iteration converges in three to five steps from a Swamee-Jain starting guess, so the cost of exactness is negligible. The Moody chart calculator does exactly this.
In practice the two disagree by less than the uncertainty in your inputs, so the choice rarely changes a design decision. The longer treatment, including the other explicit approximations, is in Colebrook-White vs Swamee-Jain.
Frequently asked questions
Is Swamee-Jain accurate enough for real engineering?
Yes, for nearly all practical applications. A 3% error in friction factor translates to less than 3% error in pressure drop, well within the uncertainty of most pipe roughness estimates. For water mains and HVAC design, Swamee-Jain is appropriate. Use Colebrook-White for high-stakes, precision-critical work.
What is the Churchill equation, and is it better than Swamee-Jain?
The Churchill (1977) equation is another explicit friction factor approximation, valid across all flow regimes (including laminar and transitional). It's slightly more complex than Swamee-Jain but is more accurate in the transitional zone. For turbulent flow only, Swamee-Jain is simpler and nearly as accurate as Churchill.
Can Swamee-Jain be used for laminar flow?
No. Swamee-Jain is only valid for turbulent flow (Re > 4,000, ideally Re > 5,000). For laminar flow (Re < 2,300), use f = 64/Re. Try our Laminar Flow Friction Factor Calculator.
Related tools
📊 Moody Chart Calculator
Full Colebrook-White solution with interactive Moody diagram visualization.
🌊 Reynolds Number Calculator
Find Re to use as input to this Swamee-Jain calculator.
🔧 Pipe roughness calculator
Look up ε by pipe material and get relative roughness ε/D - the Moody Chart input.
➡️ Laminar Friction Factor
For Re < 2300: use f = 64/Re instead.