Pump Pressure Calculator

Pump pressure calculator that finds total dynamic head and required psi from flow, pipe size and lift, converts feet of head to psi or bar, and sizes pump horsepower and running cost.

Head and Pressure: The 2.31 Rule

Pump makers rate pumps in feet of head, but gauges read in psi. The link between them is the weight of the liquid column. One foot of water at about 60°F presses down with 0.433 psi, so it takes 2.31 ft of water to make 1 psi. Every pump pressure calculator is built on that conversion.

$$PSI=\frac{Hea{d}_{ft}\times SG}{2.31}$$

$$Hea{d}_{ft}=\frac{PSI\times 2.31}{SG}$$

SG is specific gravity, the liquid's weight compared with water. For clean water it is 1. The pump pressure calculator uses the unrounded 2.3089 ft per psi, so its answers can differ from hand math in the second decimal place.

The Metric Shortcut Is 10.2, Not 10

$$Bar=\frac{Hea{d}_m\times SG}{10.2}$$

Many guides divide meters of head by 10 to get bar. That shortcut reads about 2% high. One bar actually holds up 10.21 m of water, or 33.49 ft. For quick field checks 10 is fine; for sizing a pump against a tight duty point, use 10.2.

Pressure and Head Conversion Table

These are water values at SG 1, the same figures the pump pressure calculator's Head and Pressure mode returns. They answer most of the "how many feet is…" questions directly.

Pressure	Feet of Water	Meters of Water	Bar	Kilopascals
1 psi	2.31 ft	0.704 m	0.069 bar	6.9 kPa
2 psi	4.62 ft	1.408 m	0.138 bar	13.8 kPa
10 psi	23.09 ft	7.038 m	0.689 bar	68.9 kPa
20 psi	46.18 ft	14.075 m	1.379 bar	137.9 kPa
30 psi	69.27 ft	21.113 m	2.068 bar	206.8 kPa
40 psi	92.36 ft	28.151 m	2.758 bar	275.8 kPa
60 psi	138.54 ft	42.226 m	4.137 bar	413.7 kPa
80 psi	184.72 ft	56.301 m	5.516 bar	551.6 kPa
100 psi	230.89 ft	70.376 m	6.895 bar	689.5 kPa
200 psi	461.79 ft	140.753 m	13.79 bar	1,379 kPa
300 psi	692.68 ft	211.129 m	20.684 bar	2,068.4 kPa

Reading the table the other way: 1 ft of water is 0.433 psi, 20 ft is 8.66 psi, and 200 ft of head is 86.6 psi. In inches, 2 psi equals 55.4 in of water, and 100 in of water is 3.61 psi.

Deep Water and Heavier Liquids

Pressure keeps climbing with depth at the same rate. At 25,000 ft below the surface of fresh water, gauge pressure would be about 10,830 psi. Seawater is heavier, with an SG near 1.025, which pushes that to roughly 11,100 psi.

Lighter liquids work the other way. A diesel pump pressure calculation uses the fuel's SG from its safety data sheet. At SG 0.85, 100 ft of diesel head produces only 36.8 psi, where 100 ft of water gives 43.3 psi. The pump still has to supply the same feet of head; it just takes less pressure to do it.

Total Dynamic Head: What the Pump Has to Overcome

A pump does not just lift water. It also pushes against pipe friction and against any pressure you need at the far end. Add those together and you get total dynamic head, or TDH, which is the first number the pump pressure calculator works out.

$$TDH=H_{static}+H_{friction}+H_{outlet}-H_{suction}$$

• Static head: the height from the source water level to the outlet. If the source sits below the pump, measure from the water surface, not from the pump.
• Friction head: energy lost as water rubs along the pipe. It rises with flow and falls sharply with larger pipe.
• Outlet pressure head: any pressure needed at the end, such as a pressure tank, sprinkler or nozzle, turned into feet.
• Suction head: pressure already in the water at the pump inlet. A pressurized supply subtracts from what the pump must add.

Pump pressure is simply TDH turned back into psi. That is the pressure rise the pump must create at your flow rate.

Friction Loss With Hazen-Williams

$$p_{psi/ft}=\frac{4.52\times Q^{1.85}}{C^{1.85}\times d^{4.87}}$$

Q is flow in GPM and d is the actual inside diameter in inches, not the nominal pipe size. C is the pipe's roughness factor. The pump pressure calculator uses the C values in NFPA 13 Table 28.3.4.8.1: 150 for listed plastic, copper and stainless, 140 for cement-lined iron, 120 for wet steel, and 100 for dry steel and unlined iron.

Hazen-Williams was built for water at normal temperatures. For oils or other thick liquids it underestimates friction, so treat those results as a floor. For a deeper look at the friction side alone, the Hazen Williams Equation Calculator breaks it down by pipe segment.

Worked Example: Filling a Pressure Tank Uphill

A pump moves 30 GPM through 150 ft of plastic pipe with a 1.61 in inside diameter, typical of 1.5 in Schedule 40. The outlet is 25 ft above the source, and the tank there needs 40 psi.

1. Friction = 4.52 × 30^1.85 ÷ (150^1.85 × 1.61^4.87) = 0.0226 psi/ft, so 3.40 psi or 7.84 ft over 150 ft
2. Outlet pressure head = 40 psi × 2.309 = 92.36 ft
3. TDH = 25 + 7.84 + 92.36 = 125.2 ft
4. Pump pressure = 125.2 ft × 0.433 = 54.2 psi
5. Water horsepower = 30 × 125.2 ÷ 3,960 = 0.95 hp; at 60% pump efficiency, the shaft needs 1.58 hp

Notice where the head goes. The lift is only 25 ft, but the tank pressure adds 92 ft. On many home water systems the pressure target, not the height, decides the pump.

Fittings, Valves and the Discharge Gauge

Elbows, tees and valves add friction that straight-pipe formulas leave out. Add their equivalent length, from the fitting maker's table, to the pipe length before you calculate. The pump pressure calculator has a separate fittings field for this, so the pipe length can stay the measured run. Fittings matter most on short runs with many bends.

A discharge gauge reads the suction pressure plus the pump rise. If the pump draws from a supply already at 20 psi and adds 54 psi, the discharge gauge shows about 74 psi.

Longest Pipe Run for a Pump You Already Have

Sometimes the pump is fixed and the question is how far it can reach. Turn the TDH equation around and solve for length.

$$L_{max}=\frac{H_{pump}-H_{static}-H_{outlet}+H_{suction}}{h_f}-L_{fittings}$$

H_pump is the head the pump makes at your flow, read from its curve or a discharge gauge. h_f is the friction head lost per foot of pipe at that flow, in feet per foot.

Say a pump gives 40 psi at 20 GPM. That is 92.4 ft of head. A 10 ft lift leaves 82.4 ft for friction. In plastic pipe with a 1.049 in inside diameter, typical of 1 in Schedule 40, each foot loses 0.199 ft at 20 GPM. That allows about 414 ft of friction length, or 399 ft of straight pipe after 15 ft of fittings. Step up to a 1.61 in inside diameter and the same pump reaches about 3,320 ft.

The pump pressure calculator's Longest Pipe Run mode does this for any pipe size and shows how the reach changes at lower and higher flow.

Fire Pump Discharge Pressure

$$PDP=NP+FL+EL+AL$$

Fire service uses the same idea with its own names. Nozzle pressure is the outlet pressure, friction loss is the hose or pipe friction, elevation loss is the static head in psi, and appliance loss covers wyes and standpipe valves. Elevation still costs 0.433 psi per foot of rise. Hose friction uses its own coefficients rather than Hazen-Williams, so the pipe friction here does not replace a hose friction chart.

To find the flow a building needs before sizing the pump, start with the Fire Flow Calculator.

From Horsepower to Head and Flow

Horsepower links head and flow. For water, one horsepower of hydraulic work moves 3,960 GPM up one foot.

$$WHP=\frac{Q_{gpm}\times H_{ft}\times SG}{3960}$$

$$BHP=\frac{WHP}{\eta }$$

$$Q_{gpm}=\frac{BHP\times \eta \times 3960}{H_{ft}\times SG}$$

WHP is the power that ends up in the water. BHP, or brake horsepower, is what the shaft must supply after pump losses, and η is pump efficiency as a decimal. Efficiency changes with pump size and flow, so read the real figure from the pump curve.

How Much Water a Pump of a Given Horsepower Can Move

The pump pressure calculator's Flow From Horsepower mode runs this math for any motor and any head you enter. This table uses the energy balance above at an assumed 60% pump efficiency. It shows the most each motor size could deliver; a real pump delivers what its own curve says, which is usually less.

Brake Power	At 25 ft of Head	At 50 ft of Head	At 100 ft of Head	At 50 ft, Metric
0.5 hp	47.5 GPM	23.8 GPM	11.9 GPM	90 L/min
1 hp	95 GPM	47.5 GPM	23.8 GPM	180 L/min
1.5 hp	142.6 GPM	71.3 GPM	35.6 GPM	270 L/min
2 hp	190.1 GPM	95 GPM	47.5 GPM	360 L/min
5 hp	475.2 GPM	237.6 GPM	118.8 GPM	899 L/min
20 hp	1,900.8 GPM	950.4 GPM	475.2 GPM	3,598 L/min

So a 1 hp pump could move up to about 48 GPM at 50 ft of head, and a 1/2 hp pump about 24 GPM. A 20 hp centrifugal pump at 100 ft tops out near 475 GPM. A 1.5 hp pump at 50 ft is good for roughly 270 L/min.

What Pressure Does a 1.5 hp Pump Make?

There is no single answer, because pressure falls as flow rises. At 20 GPM and 60% efficiency, a 1.5 hp pump has the energy for about 178 ft of head, which is 77 psi. At 40 GPM the same motor manages only half that. The pump's shutoff head, read from its curve at zero flow, is the highest pressure it can ever make.

How Far Can a 1.5 hp Pump Push Water?

On level ground, distance is limited only by friction. Using that same 178 ft of head at 20 GPM, the friction budget runs out after about 900 ft of 1 in plastic pipe, but after about 7,200 ft of 1.5 in pipe. Pipe size changes the reach far more than motor size does.

Running Cost

Energy per volume pumped depends only on head and efficiency, and the pump pressure calculator's Pump Horsepower mode turns it into a monthly bill. At 100 ft of head and 60% efficiency, each 1,000 gallons costs about 0.52 kWh at the shaft. Motor losses add a little more on the electric bill.

What Water Pressure Is Normal?

For building water systems, codes set the ceiling. The Uniform Plumbing Code, Section 608.2, requires a pressure regulator where static pressure exceeds 80 psi, and the International Plumbing Code says the same in Section 604.8, as local water departments apply it.

• 40 psi: about 92 ft of head. It is well under the 80 psi limit.
• 60 psi: not high. It is under the 80 psi code limit and works well for most homes.
• 100 psi: too high for a house. It is above the 80 psi limit, so the supply needs a pressure-reducing valve.
• 300 psi: industrial territory, equal to about 693 ft of water, far beyond any home plumbing.

To check a home system, enter your well depth and tank pressure in the pump pressure calculator. A water pump's normal pressure is the range its control is set to. Home well pumps run on a pressure switch with a cut-in and cut-out setting, and that pair is the pump's working range. Both settings should stay under the 80 psi code limit.

Pressure Basics Behind Every Pump Calculation

What Is the Formula for Pressure?

$$P=\frac{F}{A}$$

Pressure is force spread over an area. Push 10 lb on a syringe plunger with 0.5 sq in of area and the liquid inside is at 20 psi. Pumps, columns of water and tank gauges are all applications of this one relation.

Units, Standard Pressure and Gauge vs Absolute

• The SI unit of pressure is the pascal, 1 newton per square meter. Pump work uses kilopascals and bar, where 1 bar is 100 kPa.
• 1 psi equals 6.895 kPa, 0.0689 bar, or 27.7 in of water.
• Standard atmospheric pressure is 14.696 psi, or 101.325 kPa.
• Gauges read pressure above the atmosphere, called psig. Absolute pressure, psia, adds the 14.696 psi back in. Suction and NPSH work uses absolute pressure.

Related Pump and Pipe Tools

Measure your actual flow with the Gallons Per Minute Calculator or the Liters per Minute Calculator before you size a pump. Check pipe velocity with the Pipe Flow Calculator, and size a storage or pressure tank with the Tank Volume Calculator.

Every result in the pump pressure calculator can be copied, shared or printed to PDF, which covers the pump head calculation PDF many people look for. For a spreadsheet-style pump sizing sheet, the System Curve table gives head and pressure at five flow rates around your duty point.