Fluid Mechanics

Pressure Drop Calculator

Calculate the pressure drop of water, air or another fluid in a pipe from flow rate, diameter, length, roughness, fittings and elevation.

Formula Δp = f (L/D) (ρv²/2) + K (ρv²/2) + ρ g ΔzReviewed Sep 20, 2026

Pressure drop is the pressure a fluid loses as it moves through a pipe, from wall friction, from fittings and valves, and from any rise in height. Knowing it tells you whether a pump can deliver the flow, whether a tap will still have pressure at the end of a long run, and whether a pipe is too small. This pressure drop calculator uses the Darcy-Weisbach equation with the Colebrook-White friction factor. Enter the flow rate and the pipe size, pick the pipe material, add the fittings you have, and it returns the total pressure drop in psi, bar or kPa, split into friction, fittings and elevation, with the velocity and flow regime.

Calculation Bench

Fluid

01Flow Rate

Q · Volume flow through the pipe

Diameter Input

Pipe Type

Nominal Size

Pipe Material Roughness

Schedule pipe comes in PVC and steel. Pick Plastic for PVC and Commercial steel for steel.

02Pipe Length

L · Straight pipe; fittings are added below

03Elevation Rise

Δz · Outlet above inlet; negative if it falls

Fittings and Valves (count each)

Pipe entrance from a tank (sharp edge) (K 0.5)

Pipe exit into a tank (K 1)

90° elbow, regular threaded (K 1.5)

90° elbow, regular flanged (K 0.3)

90° elbow, long radius flanged (K 0.2)

45° elbow, threaded (K 0.4)

Tee, flow through the run (threaded) (K 0.9)

Tee, flow through the branch (threaded) (K 2)

Ball valve, fully open (K 0.05)

Gate valve, fully open (K 0.15)

Globe valve, fully open (K 10)

Swing check valve (K 2)

04Other Losses (total K)

K · Extra K from other fittings or a maker's data

Show Pressure Drop In

Solution

Enter the flow rate, pipe size and length to get the pressure drop.

Δp = f (L/D) (ρv²/2) + K (ρv²/2) + ρ g Δz

Formula Sheet

\Delta p=f\dfrac{L}{D}\dfrac{\rho v^{2}}{2}+K\dfrac{\rho v^{2}}{2}+\rho g\,\Delta z

Re=\dfrac{\rho v D}{\mu}

\dfrac{1}{\sqrt{f}}=-2\log_{10}\left(\dfrac{\varepsilon}{3.7D}+\dfrac{2.51}{Re\sqrt{f}}\right)

ΔpPressure Drop
fDarcy Friction Factor
LPipe Length
DInside Diameter
ρFluid Density
vMean Velocity
KMinor-Loss Coefficient
εAbsolute Roughness
μDynamic Viscosity
ReReynolds Number
ΔzElevation Rise

Variables & Units

Symbol	Variable	Description	Common Units
Δp	Pressure Drop	Total pressure lost between inlet and outlet.	psi, bar, kPa
f	Darcy Friction Factor	Dimensionless wall-friction coefficient from Re and relative roughness.
L	Pipe Length	Length of straight pipe.	ft, m
D	Inside Diameter	Bore of the pipe.	in, mm
ρ	Fluid Density	Mass per unit volume of the fluid.	kg/m³
v	Mean Velocity	Flow rate divided by the bore area.	m/s, ft/s
K	Minor-Loss Coefficient	Loss of a fitting or valve in velocity heads; summed over the run.
ε	Absolute Roughness	Average height of the pipe wall roughness.	mm
μ	Dynamic Viscosity	Fluid resistance to shear.	Pa·s, cP
Re	Reynolds Number	Ratio of inertial to viscous forces; sets the flow regime.
Δz	Elevation Rise	Height of the outlet above the inlet.	ft, m

How to Use This Calculator

01Pick the fluid: water at a set temperature, air, or a custom fluid where you enter the density and viscosity. For air, also enter the line pressure and say whether it is a gauge or an absolute reading.
02Enter the flow rate. For air, use the flow at the line pressure, not free air at atmospheric pressure.
03Pick the pipe diameter: choose a standard size so the calculator uses the real inside diameter, or type the inside diameter directly.
04Pick the pipe material to set the wall roughness, or enter your own roughness.
05Enter the pipe length, and the height the outlet sits above the inlet if the pipe rises (negative if it falls).
06Add the number of each fitting and valve in the line, or enter a total K value. Skip them if you only want straight-pipe friction.
07Read the total pressure drop, the friction, fittings and elevation parts, the velocity and the friction loss per 100 ft.

How the Formula Works

For a full pipe, friction loss follows the Darcy-Weisbach equation: Δp = f (L / D) (ρ v² / 2), where f is the Darcy friction factor, L is the length, D is the inside diameter, ρ is the density and v is the mean velocity from the flow rate divided by the bore area.

The friction factor depends on the Reynolds number Re = ρ v D / μ and the relative roughness ε / D. In laminar flow (Re below 2300), f = 64 / Re and the loss is independent of roughness. In turbulent flow (Re above 4000), f comes from the Colebrook-White equation, solved by iteration. Between the two the flow is unstable, so the calculator blends the two values and flags the result as uncertain.

Fittings and valves add a minor loss of K velocity heads each: Δp = K (ρ v² / 2). Add the K values of every fitting in the run. A pipe rising by Δz also needs ρ g Δz of pressure to lift the fluid, which is added to the total (or subtracted when the pipe falls).

The total is the sum of the three: Δp = f (L/D) ρv²/2 + K ρv²/2 + ρ g Δz. Because velocity is squared, doubling the flow roughly quadruples the loss, and a slightly smaller pipe can raise it sharply.

The equation assumes an incompressible fluid. Liquids qualify. A gas qualifies only while the pressure drop is a small fraction of the absolute pressure, which the calculator checks when you enter the line pressure.

Worked Example 01

20 gpm through 100 ft of 1 in Schedule 40 steel with fittings

Known

Water at 20 °C: 998.2 kg/m³, 1.002 mPa·s
Flow rate: 20 US gpm (1.262 L/s)
Pipe: 1 in Sch 40, bore 26.64 mm, 100 ft (30.48 m), steel 0.045 mm
Fittings: 4 threaded 90° elbows (K 1.5) and 1 ball valve (K 0.05): K = 6.05

Formula

Δp = f (L/D) (ρv²/2) + K (ρv²/2) + ρ g Δz

Substitution

v = 2.263 m/s, Re = 60,070, f = 0.02530; Δp = 0.02530 × (30.48 / 0.02664) × 2556 + 6.05 × 2556 = 73,990 + 15,460 Pa

Result

89.5 kPa = 12.97 psi (friction 10.73 psi, fittings 2.24 psi)

The straight pipe loses 10.7 psi, which is 10.7 psi per 100 ft, and the fittings add another 2.2 psi. The velocity is 7.4 ft/s, within the usual range for water. The 13 psi total is what a pump or the supply has to cover before any pressure is left at the outlet.

Worked Example 02

3 L/s of water through 60 m of 1-1/2 in PVC

Known

Water at 20 °C: 998.2 kg/m³, 1.002 mPa·s
Flow rate: 3 L/s
Pipe: 1-1/2 in Sch 40 PVC, bore 40.89 mm, 60 m, roughness 0.0015 mm

Formula

Δp = f (L/D) (ρv²/2) + K (ρv²/2) + ρ g Δz

Substitution

v = 2.284 m/s, Re = 93,050, f = 0.01845; Δp = 0.01845 × (60 / 0.04089) × 2,604 Pa

Result

70.5 kPa = 0.705 bar = 10.2 psi

Smooth plastic pipe has a low friction factor, so a metric water line like this loses about 0.7 bar in 60 m. Velocity is 2.28 m/s, in the normal range.

Worked Example 03

The same line lifting water 15 m, with fittings

Known

Line: 3 L/s, 60 m of 1-1/2 in PVC (as above)
Fittings: 2 flanged elbows (0.3 each), 1 exit (1.0), 1 ball valve (0.05): K = 1.65
Elevation: outlet 15 m above the inlet

Formula

Δp = f (L/D) (ρv²/2) + K (ρv²/2) + ρ g Δz

Substitution

Δp = 70.5 + 1.65 × 2.604 + 998.2 × 9.80665 × 15 / 1000 = 70.5 + 4.3 + 146.8 kPa

Result

221.6 kPa = 2.22 bar = 32.1 psi

Lifting the water 15 m needs 146.8 kPa on its own, twice the friction loss. Separating the three parts shows that the height, not the pipe, is what a pump has to overcome here.

Worked Example 04

Compressed air at 6.9 bar gauge (8 bar absolute) in 100 m of 50 mm pipe

Known

Air: 20 L/s at line conditions, 8 bar absolute = 6.9 bar gauge (9.51 kg/m³, 0.01825 mPa·s)
Pipe: 50 mm bore, 100 m, smooth (0.0015 mm)

Formula

Δp = f (L/D) (ρv²/2) + K (ρv²/2) + ρ g Δz

Substitution

v = 10.19 m/s, Re = 265,300, f = 0.01509; Δp = 0.01509 × (100 / 0.05) × 493.1 Pa

Result

14.9 kPa = 0.149 bar = 2.16 psi (1.9% of absolute pressure)

The drop is under 10% of the absolute pressure, so the incompressible method is acceptable. If the ratio rose above 10% the calculator would warn that a compressible-flow method is needed.

Applications

01Checking whether a pump or the mains can push enough flow through a long water line
02Sizing a hydronic heating or chilled-water loop by its friction loss per 100 ft
03Estimating the pressure left at the end of an irrigation or transfer line
04Comparing pipe sizes or materials for the same flow
05Rough checks on a compressed-air line, within the incompressible limit

Friction Loss in psi per 100 ft, Schedule 40 Steel, Water at 20 °C

Flow (US gpm)	3/4 in	1 in	1-1/2 in	2 in	3 in	4 in
5	2.68	0.82	0.10	0.03	<0.01	<0.01
10	9.78	2.91	0.35	0.10	0.02	<0.01
20	36.77	10.73	1.25	0.37	0.05	0.01
50	over 16 ft/s	over 16 ft/s	7.02	1.99	0.28	0.07
100	over 16 ft/s	over 16 ft/s	26.69	7.45	1.02	0.26

Absolute Roughness of New Pipe

Pipe material	Roughness (mm)	Roughness (in)
Plastic (PVC, PEX, HDPE) or drawn copper	0.0015	0.00006
Commercial steel	0.045	0.0018
Galvanized iron	0.15	0.006
Cast iron	0.26	0.010

Typical Minor-Loss Coefficients (K)

Fitting or valve	K (velocity heads)
Pipe entrance from a tank (sharp edge)	0.5
Pipe exit into a tank	1.0
90° elbow, regular threaded	1.5
90° elbow, regular flanged	0.3
90° elbow, long radius flanged	0.2
45° elbow, threaded	0.4
Tee, flow through the run (threaded)	0.9
Tee, flow through the branch (threaded)	2.0
Ball valve, fully open	0.05
Gate valve, fully open	0.15
Globe valve, fully open	10
Swing check valve	2.0

Water Properties Used by the Calculator

Temperature	Density (kg/m³)	Viscosity (mPa·s)
10 °C	999.7	1.307
20 °C	998.2	1.002
40 °C	992.2	0.653
60 °C	983.2	0.467
80 °C	971.8	0.355

Assumptions

01The pipe is full, round, straight, and of constant diameter, and the flow is steady.
02The fluid is Newtonian and incompressible. Liquids qualify. A gas is treated as incompressible only while the drop stays under about 10% of the absolute pressure.
03Fresh-water density and viscosity come from standard tables at the chosen temperature; air uses ideal-gas density at 20 °C and a constant viscosity.
04Roughness is the value for new pipe. Old, scaled or corroded pipe is rougher and loses more pressure.
05Fitting K values are typical figures for the stated type and vary by maker and size.

Where This Model Stops

01Does not model compressible flow. For a gas with a large drop, or for choked flow, use a compressible-flow method instead.
02Does not handle two-phase flow, slurries, or non-Newtonian fluids such as heavy oils, pastes and polymer solutions.
03Does not include pumps, heat exchangers, filters, meters, or control valves. Add their pressure drop from the maker's data as a separate line.
04Transitional flow (Reynolds number 2300 to 4000) is unstable and the friction factor there is an estimate.
05Flow rate for air must be at the line pressure. Free air (SCFM or normal m³/h) has to be converted first.
06Does not check water hammer, cavitation, noise, or the pressure rating of the pipe.

References

[1]
Flow of Fluids Through Valves, Fittings, and Pipe, Technical Paper 410
Crane Co.
Source of the classic pipe roughness values and fitting resistance coefficients used here.
[2]
Colebrook, C. F. (1939): Turbulent flow in pipes, with particular reference to the transition region between the smooth and rough pipe laws
Journal of the Institution of Civil Engineers
The Colebrook-White equation used for the turbulent friction factor.
[3]
Fundamentals of Fluid Mechanics, Chapter 8: Viscous flow in pipes
Munson, Young, Okiishi (Wiley)
Darcy-Weisbach equation, the Moody chart, and the minor-loss coefficients for common fittings.
[4]
Water - Dynamic and Kinematic Viscosity at Various Temperatures
Engineering ToolBox
Reference for the water viscosity values used at each temperature.

Frequently Asked Questions

How do you calculate pressure drop in a pipe?

Use the Darcy-Weisbach equation: pressure drop = f × (L / D) × (ρ v² / 2), where f is the friction factor, L the length, D the inside diameter, ρ the density and v the velocity. Add K × ρv²/2 for each fitting and ρ g Δz for any rise in height. This calculator does all of that from the flow rate and pipe size.

How much pressure drop per 100 ft is acceptable?

It depends on the system, and there is no single code limit. As a rule of thumb, hydronic and building water systems are often designed for around 1 to 4 psi of friction per 100 ft (2 to 9 kPa per 10 m), with velocity kept under about 5 to 8 ft/s. The calculator reports the friction loss per 100 ft and the velocity so you can compare them with your own limit. The reference table on this page lists the loss per 100 ft for common sizes.

Why is nominal pipe size not the diameter to use?

The flow area is set by the inside diameter, which depends on the wall thickness. A 1 in Schedule 40 pipe has a 1.049 in bore. Because the loss varies roughly with the fifth power of the diameter for a fixed flow, using the nominal size can be badly wrong. Choose a standard size in the calculator to use the real bore.

What roughness should I use?

Use 0.0015 mm for plastic (PVC, PEX, HDPE) and drawn copper, 0.045 mm for new commercial steel, 0.15 mm for galvanized iron and 0.26 mm for cast iron. These are new-pipe values. Old pipe with scale or corrosion can be several times rougher, so allow a margin.

Can I use it for compressed air?

Yes, within limits. Enter the flow at line conditions (actual volume at the line pressure) and the line pressure, choosing gauge or absolute. The calculator scales air density with pressure and warns if the pressure drop is more than 10% of the absolute pressure, where the incompressible assumption stops holding. Convert free-air SCFM to actual flow first by multiplying by 14.7 / (line pressure in psia), at the same temperature.

How do I include a valve rated by Cv?

Work out its drop separately and add it to the total. For a liquid, the pressure drop in psi is the specific gravity times (flow in US gpm divided by Cv) squared; water has a specific gravity of 1. A valve with Cv 20 passing 20 gpm of water drops 1 psi.

What are the K values and where do they come from?

K is the loss of a fitting in velocity heads. The calculator uses typical published values: 1.5 for a regular threaded 90° elbow, 0.3 for a flanged one, 0.05 for an open ball valve, 10 for an open globe valve and so on. Real values vary by size and maker, so use the manufacturer's K or Cv when you have it.

How is this different from the Pipe Size and Pump Hydraulic Power calculators?

The Pipe Size Calculator chooses a diameter from a flow rate and target velocity, and the Pump Hydraulic Power Calculator finds the power for a given head and flow. This one finds the pressure a fluid loses in a pipe you already have. Its result is the head a pump has to add.

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