Flow regime
Reynolds number calculator
Give it a speed, a bore and a kinematic viscosity and it returns the Reynolds number, which band the flow is in, and which friction-factor correlations that band permits. Free, no signup, and it computes in the browser. It also does the part most calculators leave out: it converts Re 2000 and Re 4000 back into the actual gpm at which your fluid changes behavior, for every size in the pipe family at once.
- 100% free
- No signup
- Bands with the boundary flows
- 4 friction correlations
- cSt or cP input
Three quantities, no density
A speed, a bore and a kinematic viscosity. Nothing else enters the group — which is why the same Re means the same thing in a water main, an oil line and a wind tunnel.
The D in the group is the bore the fluid actually sees, so this list uses the schedule diameter and never the size on the label.
Prefilled at 60 °F. Water thins fast with heat: 1.12 cSt at 60 °F against 0.29 cSt at boiling, which nearly quadruples Re at the same flow.
REYNOLDS NUMBER
32,223
Dimensionless — no unit, in any system.
REGIME
Turbulent
Laminar below 2,000, turbulent above 4,000.
| Velocity v | 4.455 ft/s · 1.358 m/s |
|---|---|
| Bore D | 1.0490 in · 26.64 mm (Steel, Schedule 40 1 in) |
| Kinematic viscosity ν | 1.1227 cSt · 1.123e-6 m²/s · 1.209e-5 ft²/s |
| Flow at this velocity | 12 gpm · 0.757 L/s |
| Relative roughness ε/D | 1.715e-3 |
What turbulent means here. Above Re 4000 the friction factor depends on the Reynolds number and on the relative roughness together, which is what the Colebrook equation expresses and the Moody chart draws. Far enough to the right the Reynolds dependence disappears and only roughness is left — that is the fully rough zone, and it is where Crane's fitting factors are defined.
Where the bands sit, in numbers you can set
Same bore, same fluid. These are the two speeds at which this pipe changes behavior.
LAMINAR BELOW RE 2,000
0.2765 ft/s
0.7448 gpm
TURBULENT ABOVE RE 4,000
0.553 ft/s
1.4896 gpm
Crane Technical Paper 410: flow in a pipe is laminar below Re 2000. Academic texts more often quote a critical Reynolds number of 2300 from Reynolds' own experiments; the difference has no practical effect because nothing is designed to run in this band. Crane Technical Paper 410: flow is fully turbulent above Re 4000. Between 2000 and 4000 is the critical zone, where the friction factor is genuinely unpredictable and no correlation is reliable.
What this Re does to the friction factor
The band decides which correlation is allowed, not merely which is convenient. Only the rows marked as applying are answers for your flow.
Moody's figure for this wall is 0.0457 mm and it reaches 0.1219 mm in service.
| Correlation | f | At Re 32,223 |
|---|---|---|
| 64 / Re | 0.00199 | N/AExact in laminar flow and has no roughness term — the wall could be sandpaper and the answer would not move. |
| Colebrook-White | 0.02725 | APPLIESThe implicit equation the Moody chart is drawn from, solved by iteration. The reference for turbulent flow. |
| Swamee-Jain | 0.02751 | APPLIESAn explicit fit to Colebrook, within about 1% over 5000 ≤ Re ≤ 10⁸ and 10⁻⁶ ≤ ε/D ≤ 10⁻². Outside that window it drifts quietly. |
| Fully rough f_T | 0.02249 | APPLIESColebrook with the Reynolds term deleted — the right-hand end of the chart, where only roughness is left. This is the factor Crane's valve and fitting resistances are defined against, at every Re. |
Where water at 60 °F turns turbulent, size by size
Steel, Schedule 40. Below the left column the flow is laminar and the roughness of the pipe stops mattering; above the right column every friction correlation on this site is on firm ground. The gap between them is the band nobody can predict.
| Nominal | Bore, in | Laminar below, gpm | Laminar below, ft/s | Turbulent above, gpm | Turbulent above, ft/s |
|---|---|---|---|---|---|
| 1/8 in | 0.269 | 0.191 | 1.0782 | 0.382 | 2.1564 |
| 1/4 in | 0.364 | 0.258 | 0.7968 | 0.517 | 1.5936 |
| 3/8 in | 0.493 | 0.35 | 0.5883 | 0.7 | 1.1766 |
| 1/2 in | 0.622 | 0.442 | 0.4663 | 0.883 | 0.9326 |
| 3/4 in | 0.824 | 0.585 | 0.352 | 1.17 | 0.704 |
| 1 in | 1.049 | 0.745 | 0.2765 | 1.49 | 0.553 |
| 1-1/4 in | 1.380 | 0.98 | 0.2102 | 1.96 | 0.4204 |
| 1-1/2 in | 1.610 | 1.143 | 0.1802 | 2.286 | 0.3603 |
| 2 in | 2.067 | 1.468 | 0.1403 | 2.935 | 0.2806 |
| 2-1/2 in | 2.469 | 1.753 | 0.1175 | 3.506 | 0.2349 |
| 3 in | 3.068 | 2.178 | 0.0945 | 4.357 | 0.1891 |
| 3-1/2 in | 3.548 | 2.519 | 0.0817 | 5.038 | 0.1635 |
| 4 in | 4.026 | 2.859 | 0.072 | 5.717 | 0.1441 |
| 5 in | 5.047 | 3.583 | 0.0575 | 7.167 | 0.1149 |
| 6 in | 6.065 | 4.306 | 0.0478 | 8.613 | 0.0956 |
| 8 in | 7.981 | 5.667 | 0.0363 | 11.333 | 0.0727 |
| 10 in | 10.020 | 7.114 | 0.0289 | 14.229 | 0.0579 |
| 12 in | 11.938 | 8.476 | 0.0243 | 16.952 | 0.0486 |
| 14 in | 13.126 | 9.32 | 0.0221 | 18.639 | 0.0442 |
| 16 in | 15.000 | 10.65 | 0.0193 | 21.301 | 0.0387 |
| 18 in | 16.876 | 11.982 | 0.0172 | 23.965 | 0.0344 |
| 20 in | 18.814 | 13.358 | 0.0154 | 26.717 | 0.0308 |
| 24 in | 22.626 | 16.065 | 0.0128 | 32.13 | 0.0256 |
The group itself. Re = v D / ν, with D the bore in feet. The shorthand Re = 7742 v d / ν in cSt is this same expression with the unit conversions folded in, and is derived rather than quoted. Once you have the regime, the loss over a real run is worked on the pipe pressure loss calculator. Reference tables and arithmetic; the local code and a licensed engineer decide what gets built.
How to tell whether a line is laminar or turbulent
Three quantities go in. Only one of them is usually wrong, and it is not the one people check.
Enter the speed, as flow or as velocity
If you have a pump curve or a design flow, give it the gpm and the page derives the velocity from the bore. If you have an anemometer or a meter reading in ft/s, give it that instead and the page derives the flow. The two are the same input reached from opposite directions, so nothing is assumed either way.
Use the bore, not the size on the box
The characteristic length in the group is the diameter the fluid actually occupies, so a 1 in Schedule 40 line contributes 1.049 in and not 1 in. Pick the pipe from the schedule list and it is handled; type a measured bore and it is used as given. For a rectangular duct or an annulus the length is the hydraulic diameter, 4A/P, which is not the width and not the diagonal.
Get the viscosity at the running temperature
This is the input that goes wrong. Water is 1.12 cSt at 60 °F and 0.29 cSt at boiling, so a heating loop and a chilled loop with identical geometry sit almost four times apart on Re. Oils move further still. If your data sheet is written in centipoise, switch the unit select — a density field appears solely to divide it, because dynamic viscosity is a different quantity from the kinematic one the group needs.
Technical specifications
| Group | Re = v D / ν, dimensionless in every unit system, computed with D in feet and ν in ft²/s |
|---|---|
| Band boundaries | Laminar below Re 2000, turbulent above Re 4000, critical zone in between — Crane TP-410's split, not the textbook 2300 |
| Correlations reported | 64/Re for laminar, Colebrook-White solved by iteration, Swamee-Jain explicit, and the fully rough f_T that Crane's fitting resistances are defined against |
| Viscosity input | Centistokes direct, or centipoise with a density to divide by; water 32–212 °F comes from the interpolated table instead |
| Water at the two ends | 1.12 cSt at 60 °F, 0.66 cSt at 104 °F, 0.36 cSt at 180 °F, 0.29 cSt at 212 °F — a factor of 3.8 across the liquid range |
| Boundary chart | Every nominal size of the selected family with the flow in gpm and the velocity in ft/s at both Re 2000 and Re 4000 |
| Worked example | 1 in Schedule 40 steel on 60 °F water is laminar below 0.74 gpm and turbulent above 1.49 gpm — which is why a building water system is never laminar |
| Privacy | Nothing is sent anywhere; the iteration and the chart are built in the page |
Frequently asked questions
Why does the Reynolds number not need a density?
Because the density is already inside the kinematic viscosity. The group can be written two ways — ρvD/μ with the dynamic viscosity, or vD/ν with the kinematic one — and ν is defined as μ/ρ, so the density cancels. Asking for it separately would be asking for the same information twice and would let a user enter an inconsistent pair. The only reason a density field appears on this page is to convert a centipoise figure off a data sheet into centistokes.
Is the critical Reynolds number 2000, 2300 or 4000?
All three are in print and the disagreement does not matter, because nothing is designed to operate there. Reynolds' own experiments give a critical value near 2300 for the transition from laminar flow; Crane TP-410, which this page follows, puts the laminar limit at 2000 and the fully turbulent threshold at 4000 and calls the gap the critical zone. What is common to every version is the message: inside that band the friction factor is not predictable, and a design point that lands in it should be moved.
My building water system reads Re 30,000 — is that unusually high?
No, that is ordinary, and the interesting thing is how hard it is to get a water system to be anything else. One foot per second in a 1/2 in Schedule 40 pipe is already Re 4,300, and 1 in Schedule 40 at 60 °F water goes turbulent above 1.5 gpm. Laminar water in a building is a symptom, not a design: it usually means a dead leg, a closed balancing valve, or a flow figure entered in the wrong unit. Laminar flow is normal in oil, syrup and lubrication lines, where the viscosity is one to four orders of magnitude higher.
What is the characteristic length for a rectangular duct?
The hydraulic diameter, four times the cross-sectional area divided by the wetted perimeter — so a 12 in by 8 in duct gives 4(96)/(40) = 9.6 in, not 12, not 8, and not the 14.4 in diagonal. For a round pipe running full that definition reduces to the bore, which is why it never gets mentioned. For a pipe running partly full, as a gravity drain does, the wetted perimeter changes with depth and the whole open-channel treatment applies instead.
Why is the fully rough friction factor shown even when my flow is laminar?
Because it is not a property of your flow — it is a property of your pipe, and it is the number Crane's valve and fitting resistances are defined against at any Reynolds number. Every L/D in a fitting table is converted to a resistance coefficient by multiplying it by f_T, so the value is needed to price an elbow whether the pipe is laminar or turbulent. It is Colebrook with the Reynolds term deleted, which is the far right of the Moody chart where the curves go flat.
Does surface roughness change the Reynolds number?
No, and confusing the two is the most common misreading of the Moody chart. Roughness has no place in the group at all — Re is only inertia against viscosity, and a glass tube and a rusted steel tube of the same bore at the same velocity have identical Reynolds numbers. Roughness enters afterwards, as the second axis of the chart, and decides what friction factor that Reynolds number maps to. Below Re 2000 it does not even do that: laminar friction is 64/Re regardless of the wall.
Can I use this for air or another gas?
For the Reynolds number itself, yes — the group is fluid-agnostic and takes any kinematic viscosity you can supply, which is why this page asks for a viscosity rather than for the name of a fluid. This site does not carry air or gas viscosities, so take yours from a gas-property table at your own temperature and pressure rather than from anything here; air's kinematic viscosity is an order of magnitude above water's, so a duct velocity that sounds fast sits at a far lower Reynolds number than the same velocity in a pipe. What does not carry over at all is the pressure loss afterwards: a gas is compressible, and the incompressible loss equations hold only while the total drop stays small against the absolute inlet pressure.
About the Reynolds number and what each band does
Osborne Reynolds dyed a filament of water in a glass tube in 1883 and watched it either hold a straight line or burst into eddies, and the ratio he extracted from that experiment is still the only thing that decides which equations a pipe obeys. It is inertia against viscosity, it has no units, and its whole usefulness is that it is transferable: the same value means the same behavior in a capillary and in a transmission main, which is what allows a model tested in a tank to say anything about a ship. On these pages it does one job — it says which friction correlation is permitted — and getting it wrong silently invalidates whatever is calculated next.
The three bands are qualitatively different, not three shades of one thing. Below Re 2000 the fluid moves in parallel layers, the friction factor is exactly 64/Re, and the pipe wall might as well be glass — roughness has no effect whatsoever, which is counterintuitive enough that it is worth checking on the correlation table above. Above Re 4000 the factor depends on Reynolds number and relative roughness together, which is the two-axis structure of the Moody chart and what the pipe pressure loss calculator solves for. Between the two nothing is reliable, and no honest correlation exists: two identical pipes carrying identical flow can differ by a factor of two on friction factor, because what decides it is upstream disturbance that no equation can see.
The reason this page prints the boundaries as flows rather than leaving them as numbers is that the abstraction hides how lopsided the bands are in practice. Water in building pipe is turbulent at almost any flow worth having — a 1 in line is over the threshold past 1.5 gpm — so the laminar branch is nearly dead there, and the empirical shortcut the pipe friction loss calculator uses can get away with assuming turbulence. In oil and hydraulic work the position is reversed and the laminar branch is the normal case, which is why a machine tool coolant line and a domestic riser are not the same problem even at the same size. It is also why the fluid pages here ask for viscosity rather than which trade you are in — and why duct sizing for air uses friction rate charts built on their own fluid entirely.
Where the numbers stay
Every number on this page is worked out by JavaScript running in the tab you are reading it in. Nothing you type — loads, lengths, nameplate ratings, the rates your utility charges you — is uploaded, logged or kept, which is also why the calculators carry on working in a mechanical room with no signal.