Physics calculators

Head Loss Calculator

Updated Sep 26, 2026 By Infinity Calculator
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Unit System & Calculation Method
Input Unit System
Switching converts every value already entered.
Calculation Method
Darcy-Weisbach: any fluid, any regime — uses Colebrook-White for the friction factor.
Pipe Geometry (main run)
Positive = outlet above inlet (uphill). Negative = downhill.
Flow Parameters
Driving Input
The other quantity is computed and written back below.
Fluid Properties
Water & sea water auto-fill ρ and μ from temperature.
Pipe Material & Roughness Coefficients
Selecting a material fills all three coefficients below.
Dimensionless — higher C = smoother pipe.
Dimensionless — higher n = rougher pipe.
Pipe Flow Condition (Manning)
Used only when "Partially full" is selected.
Minor Losses — Fittings & Valves
Minor Loss Method
Equivalent length uses Leq = K·D / f and gives the same head loss.
Enter each fitting type and quantity. K values are pre-filled and editable.
Fitting / Valve Qty K value Leq hminor
Subtotal — — — —
Additional Pipe Segments in Series (optional)
Each extra segment carries the same flow rate; its friction loss is added to the main run.
# Length Inner Diameter Material
No additional segments — the pipe above is treated as a single continuous run.
Results
Friction Head Loss (hf)
—
—
Minor Head Loss (hminor)
—
—
Elevation Head (Δz)
—
—
Total Head Loss (htotal)
—
—
Pressure Drop — Friction
—
—
Pressure Drop — Total
—
—
Flow Velocity
—
—
Flow Rate
—
—
Reynolds Number (Re)
—
dimensionless
Darcy Friction Factor (f)
—
dimensionless
Flow Regime
—
—
Hydraulic Gradient (S = hf/L)
—
m/m = ft/ft (dimensionless)
Step-by-Step Solution
Per-Segment Breakdown
Friction loss for each pipe segment in series, at the current flow rate.
Segment Length Diameter Velocity Re f Head Loss
Cumulative friction head loss —
Moody Chart — Operating Point
Head Loss Composition
Sensitivity — What If?
Total head loss (friction + minor + elevation) when diameter or flow rate is changed, all else equal.
Scenario Friction Head Loss Total Head Loss Change vs. Base

Introduction

When water or any fluid moves through a pipe, it rubs against the pipe walls and pushes through bends and valves. That rubbing steals energy. Engineers call this lost energy head loss. This head loss calculator works out how much you lose, in feet or meters of head and in pressure units like psi, kPa, or bar.

You pick a method, type in your pipe and fluid details, and get an answer right away. The tool uses three trusted formulas:

  • Darcy-Weisbach: works for any fluid and any flow speed. It solves the Colebrook-White equation to find the friction factor.
  • Hazen-Williams: a quick method for water in normal water pipes.
  • Manning: for gravity flow, including pipes that are only part full.

The calculator also handles minor losses from elbows, tees, valves, and filters using K-values or equivalent pipe length. You can add extra pipe segments in series, set an elevation change, and switch between US and metric units with one click.

Along with the answer, you get the flow velocity, Reynolds number, Darcy friction factor, and flow regime (laminar, transitional, or turbulent). A step-by-step solution shows every formula with your own numbers plugged in. A Moody chart marks your operating point, a bar chart splits the loss into friction, fittings, and elevation, and a sensitivity table shows what happens if you change the pipe size or flow rate.

This is useful for sizing pumps with a Pump Power Calculator, checking pressure at a fixture, comparing pipe materials, or doing homework in a fluid mechanics class.

How to use our Head Loss Calculator

Enter your pipe size, flow, fluid, and fittings, and this head loss calculator gives you friction head loss, minor loss, total head loss, pressure drop, velocity, Reynolds number, and the Darcy friction factor, plus a step-by-step solution and a Moody chart.

Input Unit System: Pick US Customary or SI. Every value you already typed is converted for you.

Calculation Method: Pick Darcy-Weisbach for any fluid, Hazen-Williams for water in turbulent flow, or Manning for gravity pipe flow.

Pipe Length (L): Type the length of the main pipe run and pick its unit.

Inner Diameter (D): Type the inside diameter of the pipe, not the outside size.

Elevation Change (Δz): Type how far the outlet sits above the inlet. Use a minus sign for downhill.

Driving Input: Choose Flow Rate or Velocity. The calculator works out the other one for you.

Flow Rate (Q): Type the flow moving through the pipe, in GPM, L/s, or another unit.

Flow Velocity (V): Type the speed of the fluid if you chose Velocity as your driving input.

Fluid Type: Pick water, sea water, diesel, SAE 30 oil, or Custom to enter your own numbers.

Fluid Temperature: Type the fluid temperature. Water and sea water fill in density and viscosity from it.

Density (ρ): The weight per volume of the fluid. Change it only if you need custom values.

Dynamic Viscosity (μ): How thick the fluid is. Thicker fluids give more friction loss.

Pipe Material: Pick your pipe type. This fills roughness, C, and n all at once.

Absolute Roughness (ε): The height of the bumps inside the pipe wall. Used by Darcy-Weisbach.

Hazen-Williams C: A smoothness number for water pipes. A higher C means a smoother pipe.

Manning's n: A roughness number for gravity flow. A higher n means a rougher pipe.

Pipe Flow Condition: Choose Full pipe or Partially full for the Manning method.

Depth Ratio (y/D): If the pipe is partly full, type how deep the fluid is compared to the diameter.

Minor Loss Method: Choose K-value or Equivalent length. Both give the same head loss.

Fittings and Valves: Click Add Fitting, pick the elbow or valve, set the quantity, and edit the K value if needed.

Additional Pipe Segments: Click Add Segment to add more pipe in series, then set its length, diameter, and material.

Head, Pressure, Velocity, and Flow Output Units: Pick the units you want your answers shown in.

Click Calculate to see your results, charts, and what-if table. Click Reset to start over.

What Is Head Loss?

When water or any fluid moves through a pipe, it loses energy. The fluid rubs against the pipe wall and against itself, and that rubbing turns some of its pressure into heat. That lost energy is called head loss. We measure it in feet or meters of fluid, and it can also be shown as a pressure drop in psi, kPa, or bar.

Head loss matters because it tells you how strong a pump you need. If you ignore it, the flow at the far end of a pipe can be weak or stop completely.

The Three Parts of Head Loss

  • Friction loss (hf): Energy lost along the straight length of pipe. Longer pipes, smaller pipes, rougher pipes, and faster flow all raise this loss.
  • Minor loss (hminor): Energy lost at elbows, tees, valves, filters, and pipe openings. Each fitting has a K value. Add up the K values and multiply by the velocity head (V²/2g).1 In a pipe with many fittings, these "minor" losses are often not minor at all.
  • Elevation head (Δz): The height the fluid must climb. Going uphill adds head. Going downhill gives head back. This is the same static term you see in the Hydrostatic Pressure Calculator.

Add all three together to get total head loss.

Three Ways to Find Friction Loss

Darcy-Weisbach

The most theoretically correct method.1 It applies to all liquids and to every flow regime.1 The formula is:

hf = f × (L / D) × V² / (2g)

Here f is the Darcy friction factor. It comes from the Colebrook-White equation, which needs the Reynolds number and the pipe's relative roughness (ε/D).3 This is the method to use for oil, hot water, thick fluids, or slow flow.

Hazen-Williams

A simpler formula built just for water in normal turbulent flow.1 It uses a C factor instead of roughness. New plastic pipe has a high C (140 to 150 in the EPA's EPANET manual).1 Old cast iron has a low C (about 100). It is quick and common in water supply and fire sprinkler work, but it is not correct for oil, thick fluids, or very slow flow.

Manning

Made for gravity flow, like sewers and storm drains. It uses Manning's n and the hydraulic radius, so it can handle pipes that are only partly full. Use it for drains, not for pressure pipes.

Reynolds Number and Flow Regime

The Reynolds number (Re) tells you how the fluid is moving. It compares the fluid's push to its stickiness:

Re = ρVD / μ

  • Re below 2300, laminar: Smooth, orderly flow. The friction factor is simply f = 64/Re, and pipe roughness does not matter.
  • Re from 2300 to 4000, transitional: Unsteady and hard to predict. Answers here are estimates only.
  • Re above 4000, turbulent: Mixed and swirling. Most real pipes run here, and roughness now matters a lot.

The Moody chart plots the friction factor against Reynolds number for many roughness values. It is the classic picture of how these two things work together.

Pipe Roughness

Every pipe wall has tiny bumps. Their average height is the absolute roughness, ε. For new pipe, the EPA's EPANET manual lists a roughness of 0.005 thousandths of a foot for plastic, 0.15 for steel and 0.85 for cast iron.1 In millimetres that is about 0.0015, 0.046 and 0.26. Drawn copper is about as smooth as plastic. Concrete and riveted steel are much rougher. Old pipes get rougher over time from rust and scale, so head loss grows as a system ages.

Why Diameter Matters Most

Diameter has the biggest effect of any input. In the Darcy-Weisbach equation, friction loss scales close to 1/D⁵ at a fixed flow rate.1 That means shrinking a pipe by just 20% can more than triple the friction loss. Doubling the flow rate roughly quadruples it, since loss grows with V². If your head loss is too high, going up one pipe size usually helps far more than anything else.

Typical Design Limits

  • Water in supply lines: about 3 to 8 ft/s (1 to 2.4 m/s). Above 10 ft/s you risk noise, erosion, and water hammer.
  • Pump suction lines: keep velocity lower, near 2 to 4 ft/s, to avoid cavitation.
  • Friction gradient: many water mains are designed near 1 to 4 ft of loss per 100 ft of pipe.

Once you know total head loss, you can pick a pump. The pump must supply at least that much head at your design flow rate, plus a safety margin.

Formulas used

Darcy-Weisbach friction head loss 3
h_f = f\,\frac{L}{D_h}\,\frac{V^2}{2g}
Colebrook-White friction factor (turbulent flow) 3
\frac{1}{\sqrt{f}} = -2\log_{10}\!\left(\frac{\varepsilon/D_h}{3.7} + \frac{2.51}{Re\,\sqrt{f}}\right)
Laminar friction factor 2
f = \frac{64}{Re}
Reynolds number
Re = \frac{\rho V D_h}{\mu}
Hazen-Williams friction head loss (SI form)
h_f = \frac{10.67\,L\,Q^{1.852}}{C^{1.852}\,D^{4.87}}
Manning friction slope and head loss 4
h_f = S\,L,\qquad S = \left(\frac{Q\,n}{A\,R_h^{2/3}}\right)^{2},\qquad R_h = \frac{A}{P}
Minor (fitting) head loss and equivalent length 1
h_m = \left(\sum K\right)\frac{V^2}{2g},\qquad L_{eq} = \frac{\sum K \cdot D_h}{f}
Total head loss and pressure drop
h_{total} = h_f + h_m + \Delta z,\qquad \Delta p = \rho\,g\,h_{total}

Frequently asked questions

Why does my head loss change when I switch from Darcy-Weisbach to Hazen-Williams?

The two formulas use different math and different roughness numbers. Darcy-Weisbach uses the Reynolds number and absolute roughness (ε). Hazen-Williams uses only the C factor and ignores temperature and viscosity.

Small gaps of 10 to 20 percent are normal. Big gaps usually mean one of these:

  • Your C value and your ε value do not describe the same pipe condition.
  • Your flow is laminar or transitional, where Hazen-Williams does not apply.
  • Your fluid is not water.

For design work, trust Darcy-Weisbach. It is the physics-based method.

Should I use the outside or inside diameter of my pipe?

Always the inside diameter. Flow only happens inside the pipe, so wall thickness does not count.

This matters a lot for steel and copper pipe, where the nominal size is not the real inside size. For example, 4-inch schedule 40 steel pipe has an inside diameter near 4.026 inches, and 1-inch schedule 80 PVC is closer to 0.957 inches.

Check a pipe dimension table for your exact schedule. Using the wrong diameter is the most common mistake in head loss math, because friction loss changes with roughly 1/D⁵.

My total head loss is negative. Is that an error?

No. A negative total means gravity gives back more energy than friction takes away. This happens on downhill runs.

You typed a negative elevation change, and that drop is bigger than the friction plus minor losses. The fluid can flow on its own with no pump.

Look at the friction head loss card instead. That number is always positive and tells you how much energy the pipe itself eats.

What K values should I use if my fitting is not in the list?

Pick Custom from the fitting list and type your own K value. Most fitting makers publish K values or equivalent length data in their catalogs.

The EPA's EPANET manual lists these values for common fittings:

  • Short-radius elbow: 0.91
  • Long-radius elbow: 0.61
  • 45 degree elbow: 0.41
  • Gate valve, fully open: 0.21
  • Globe valve, fully open: 10.01

A partly closed valve has a much higher K.

K values are approximate. If fittings drive most of your loss, get real data from the maker.

Does the depth ratio work with all three methods?

Not fully. Here is how each method treats it:

  • Manning: Full support. It uses the real wetted area and hydraulic radius. This is the method built for partly full pipes.
  • Darcy-Weisbach: Partial. It applies the hydraulic diameter, which is a fair estimate but not exact for open channels.
  • Hazen-Williams: Ignored. That formula assumes a full bore pipe.

For sewers, storm drains, and culverts, use Manning with the partially full setting.

Why is my Reynolds number so low with oil?

Oil is thick. Dynamic viscosity sits in the bottom of the Reynolds equation, so high viscosity pushes Re down fast.

SAE 30 oil is about 290 times thicker than water at room temperature. The same pipe and the same speed can be turbulent with water and laminar with oil.

In laminar flow, roughness stops mattering and f = 64/Re.2 Head loss then grows straight with velocity instead of with V².2 Always use Darcy-Weisbach for oil.

How do the equivalent length and K-value methods compare?

They give the same head loss. The calculator converts between them with Leq = K·D / f.

Pick the one that fits your workflow:

  • K-value: Cleaner for mixed pipe sizes. K does not change with pipe size or friction factor.
  • Equivalent length: Handy when you want one total pipe length to hand to a pump chart or a spreadsheet.

Note that equivalent length depends on f, so it shifts if your flow rate or pipe roughness changes. K values stay put.

Why did my pipe material reset to Custom?

You edited the roughness, the C value, or Manning's n by hand. When you do that, the material drop-down switches to Custom so it does not overwrite your number.

Your edited value is still used in the math. To go back to the standard preset, just pick your material again from the list and all three coefficients refill.

What friction gradient should I aim for?

A common target for water mains is 1 to 4 feet of loss per 100 feet of pipe, which is a gradient of 0.01 to 0.04.

The Hydraulic Gradient card shows your value directly. Use it to compare pipes of any length on equal footing.

  • Below 0.01: pipe may be oversized and costly.
  • 0.01 to 0.04: usual sweet spot.
  • Above 0.05: expect high pump costs, noise, and wear.

Long transmission lines often run lower to cut pumping bills. Short branch lines can run higher.

Do old pipes need a different roughness value?

Yes. Rust, scale, and slime build up over years, so a 30-year-old pipe is much rougher than a new one.

Rough guides for aging:

  • New steel: ε about 0.046 mm, C about 120.
  • Steel after 20 years: ε 0.5 to 1.5 mm, C 90 to 100.
  • Old cast iron with heavy scale: ε 2 to 4 mm, C 60 to 80.

Plastic pipe barely changes. When you design a system meant to last, use aged values so the pump still works in year 20.

Can I add pipes that split into branches?

No. The extra segments feature only handles pipes in series, one after the other, carrying the same flow rate.

For parallel branches, each path carries a share of the flow, but all paths lose the same head. That needs an iterative network solve.

A workaround: run this calculator once for each branch, guessing the flow split. Adjust your guesses until every branch gives the same head loss.

Why does the pressure drop differ from head loss?

Head loss is a height of fluid. Pressure drop is a force per area. They are linked by Δp = ρgh.

The bridge between them is density. Ten feet of water is about 4.33 psi. Ten feet of mercury is about 59 psi, because mercury is much heavier.

Head loss is handy for pump curves, which are drawn in feet or meters of head. Pressure drop is handy for gauges and pipe pressure ratings.

My velocity looks too high. What should I do?

High velocity brings noise, pipe erosion, and water hammer risk. For water lines, keep it under about 8 ft/s (2.4 m/s), and under 4 ft/s on pump suction lines.

Fixes, best first:

  • Go up one pipe size. Velocity drops with the square of the diameter.
  • Cut the flow rate if the system allows.
  • Split the flow into two parallel pipes.

Bumping a 2-inch pipe to a 3-inch pipe drops velocity by more than half at the same flow.

Does fluid temperature really change the answer?

Yes, mostly through viscosity. Water at 40°F has a viscosity of 1.5452 cP, and at 180°F it is 0.34445 cP.5 That makes cold water about four and a half times as thick.

That changes the Reynolds number, which changes the friction factor. For turbulent water flow, the head loss shift is usually a few percent, so it is small but real.

For oils, temperature is huge. Viscosity can drop tenfold over a 50°F rise, which can flip laminar flow to turbulent. Always enter the true working temperature for oil systems.

Sources

  1. EPANET 2.2 User Manual, Chapter 3: The Network Model. U.S. Environmental Protection Agency. Pipes; Tables 3.1 to 3.3. Accessed September 26, 2026.
  2. EPANET 2.2 User Manual, Chapter 12: Analysis Algorithms. U.S. Environmental Protection Agency. Hydraulics, Pipe Resistance Coefficient. Accessed September 26, 2026.
  3. EM 1110-2-1602: Hydraulic Design of Reservoir Outlet Works. U.S. Army Corps of Engineers. 1980;Paragraph 2-12, Equations 2-6 and 2-10. Accessed September 26, 2026.
  4. Kilgore R, Atayee AT, Herrmann GR. Urban Drainage Design Manual, Hydraulic Engineering Circular No. 22, Fourth Edition (FHWA-HIF-24-006). Federal Highway Administration. 2024;Section 6.1.4, Equation 6.5. Accessed September 26, 2026.
  5. Isobaric Properties for Water (14.696 psia, 40 to 180 °F). NIST Chemistry WebBook, SRD 69. National Institute of Standards and Technology. Accessed September 26, 2026.

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