Pressure and Head: The 2.31 and 0.433 Pair

Why this matters

Every trade that moves a fluid lives on two numbers: 1 psi of pressure holds up about 2.31 feet of water, and 1 foot of water presses down with about 0.433 psi. Get them backwards and a third-floor bath "needs" 69 psi to reach it, a boiler gets filled to the point its relief valve weeps, or a gas reading of 7 inches of water column gets written up as 3 psi. Those are not exotic mistakes. They are the same pair of constants used upside down or in the wrong unit, and they happen on site with a pencil, which is exactly where this card is meant to live.

Where the two numbers come from

Head is the height of a column of liquid. Pressure is force per unit of area. The bridge between them is the weight of the liquid.

Water near room temperature weighs about 62.4 lb per cubic foot. Stand that cubic foot on its 1 ft by 1 ft base and it presses 62.4 lb onto 144 square inches, which is 62.4 / 144 = 0.433 psi for every foot of height. Turn it over: one psi supports 144 / 62.4 = 2.31 ft of water. The two numbers are reciprocals of each other, so 2.31 x 0.433 = 1.00, and that product is the fastest check you have that you wrote the right one down.

Two conditions sit inside those numbers, and they travel with them:

• They are for water. Any other liquid scales by its specific gravity (its weight compared to water). A glycol mix is a few percent heavier than water, so the same foot of height makes a little more pressure; take its specific gravity from the fluid's data sheet and multiply 0.433 by it.
• They are for water near 60 F. Hot water is lighter. At 180 F water weighs about 60.6 lb per cubic foot, which makes 1 psi worth about 144 / 60.6 = 2.38 ft, roughly 3 percent more height than the cold figure. That matters for a pump calculation on a hot loop and almost never for a fill pressure.

The conversion card

WATER, about 60 F

1 psi            = 2.31 ft of water
1 ft of water    = 0.433 psi
1 psi            = 27.7 in of water column (in WC)
1 in WC          = 0.036 psi
1 in of mercury  = about 13.6 in WC
1 in of mercury  = about 0.49 psi

CHECKS
2.31 x 0.433     = 1.00
27.7 / 12        = 2.31   (inches to feet, same number)
13.6 x 0.036     = 0.49

WORKED
30 ft rise   x 0.433 psi/ft = 13.0 psi lost
13.0 psi     x 2.31 ft/psi  = 30.0 ft    (check)
7 in WC      x 0.036 psi/in = 0.25 psi
7 in WC      / 27.7 in/psi  = 0.25 psi   (check)

The 27.7 is not a new constant. It is 2.31 ft multiplied by 12 in per foot, so inches of water column are just feet of head written in a smaller unit. Mercury is 13.6 times as heavy as water, which is why one inch of it does the work of 13.6 inches of water and why vacuum and barometric gauges read in inches of mercury: the numbers stay small.

Worked example: what a 30 ft rise costs a fixture

A three-story building takes its water at a meter in the basement. A gauge on the main reads 62 psi with nothing flowing. The highest fixture, a shower on the top floor, sits 30 ft above that gauge.

Static pressure falls with height at 0.433 psi per foot:

• 30 ft x 0.433 psi/ft = 12.99 psi, call it 13 psi.
• 62 psi at the gauge minus 13 psi = 49 psi at the top shower with nothing flowing.

Check it from the other direction: 13 psi x 2.31 ft/psi = 30.0 ft. The units cancel to feet, which is what the rise was measured in. Rough estimate: a story is about 10 ft, and 10 ft of water is a bit over 4 psi, so three stories lose a bit over 12 psi. The answers agree.

What the 49 psi does not include is flow. Open the shower and friction in the pipe, the meter, any softener or filter, and the valve itself takes its own share. Elevation loss is the part you can compute exactly with a tape; friction loss depends on flow and pipe size and belongs to a different card. So a top-floor complaint of weak flow with 49 psi of static available points at the piping or a restriction, not at the height. If the static reading at the top had been 30 psi, the height would not explain it either: the basement figure would have to be wrong, or something between the gauge and the shower is closed down.

The common slip here is dividing where you should multiply: 30 ft / 0.433 = 69 "psi". The sanity check catches it instantly, because nobody's top floor needs more pressure than the city delivers to the curb, and because 69 x 2.31 = 160 ft is not the height of a three-story building.

Worked example: a boiler fill pressure

A closed hydronic loop has to be filled to more than the height of water above the fill valve, or the highest radiator runs with air in it and no pressure to push the air out. A common field approach, which the boiler's own manual overrides wherever they differ, is static height in psi plus a few psi of margin at the top.

Say the highest point of the loop is 21 ft above the boiler gauge:

• 21 ft x 0.433 psi/ft = 9.09 psi just to hold water at the top.
• Add a margin of 4 psi so the top of the system stays positive: 9.09 + 4 = 13.1 psi, set cold at about 13 psi.

Check: 13 psi x 2.31 = 30 ft of head available, which is 21 ft to lift the water plus about 9 ft, or 4 psi, left over at the top. That closes.

Two things change the answer. A relief valve on a residential boiler is commonly rated at 30 psi; the fill pressure plus the rise from heating has to stay well under it, which is what the expansion tank is sized for, and a fill set high enough to crowd the relief is a callback that soaks the floor. And on a glycol loop the 0.433 rises by the mix's specific gravity, so 21 ft of a mix with a specific gravity of 1.04 needs 21 x 0.433 x 1.04 = 9.46 psi to hold the column, about 0.4 psi more than water. Small, but the kind of thing that decides whether the top air vent gurgles.

Water column on the gas side

Fuel gas is delivered and measured in inches of water column because the pressures are tiny. A typical natural gas appliance in a house is fed somewhere around 7 in WC, and propane commonly around 11 in WC, but those are typical values only: the appliance's rating plate and installation manual give its own inlet and manifold ranges, and the supplier sets the delivery.

Convert 7 in WC to psi:

• 7 in WC x 0.036 psi/in WC = 0.25 psi.
• Check: 7 / 27.7 = 0.253 psi.

So the whole gas supply to a furnace is about a quarter of one psi. That is why a manometer, not a water-pressure gauge, reads it, and why a 1 in WC drop in supply when the burner lights is a meaningful number rather than noise. It is also why the unit matters so much on a work order: "7 psi" on a gas line written by someone who meant 7 in WC is 28 times the real pressure, and a reader who believes it is reading a different system entirely.

Measuring gas supply and manifold pressure means opening a test port on a live gas train. That is work for a gas-qualified technician holding whatever license your jurisdiction requires. If you are not that person, recognize the reading on a report and call the person who is. Anyone who smells gas at a port or fitting leaves the area with everyone else, touches no switches, and calls the gas utility from outside.

Head on a pump curve

Pump curves are drawn in feet of head rather than psi for a reason worth knowing: a pump lifts every liquid to the same height at a given flow, and only the pressure that height produces changes with the liquid's weight. A curve in feet is good for water, glycol or anything else the pump is rated for. To turn a pump's head into the psi a gauge will show, multiply by 0.433 and by the specific gravity.

A circulator rated at 18 ft at the flow you need will show about 18 x 0.433 = 7.8 psi of difference between gauges on its suction and discharge, on water. If the gauges show 3 psi, the pump is not making its rated head at that flow, the impeller is worn or bound, or one gauge is lying. Before blaming the pump, put both readings on the same gauge (move one gauge between the two ports) so a calibration offset between two instruments drops out of the difference.

Gauge pressure, absolute pressure, and vacuum

Most field gauges read psig: pressure above the atmosphere, zero when open to air. Psia adds the atmosphere back, about 14.7 psi at sea level and less at altitude. Head calculations between two points in the same building work in either, because the atmosphere cancels in the difference.

Vacuum is pressure below atmosphere, commonly read in inches of mercury. The atmosphere at sea level supports about 29.9 in of mercury, which in water terms is 29.9 x 13.6 = 407 in WC, or about 34 ft. That is the hard ceiling on suction lift: no pump can pull water up more than about 34 ft at sea level, and in practice friction, vapor pressure and the pump's own needs take a good share of it. A shallow well jet pump is limited for exactly this reason.

Sanity checks that catch the usual slips

• Multiply or divide? Feet times 0.433 gives psi. Psi times 2.31 gives feet. If you divide by either, you have the other unit's answer inflated by a factor of about five.
• A story is about 4 psi. Ten feet of water is 4.33 psi. Any answer that disagrees with that by more than you can explain is wrong.
• Inches or feet of water column? Gas and duct pressures are in inches. A drain or well depth is in feet. Writing one as the other is a factor of 12.
• Mercury or water? A vacuum gauge in inches of mercury read as inches of water is off by 13.6 times.
• Which liquid, at what temperature? On anything but cold water, the 0.433 picks up the fluid's specific gravity, and the sentence that states the answer says which fluid it was.

References

• Fluid property data for water density by temperature (engineering handbook or fluid-property tables)
• Appliance rating plates and installation manuals for gas inlet and manifold pressure ranges
• Boiler and expansion tank manufacturer documentation for fill pressure and relief valve ratings
• See related: Common Unit Conversions + Math Formulas; How to Figure the Force on a Test Plug or Cap; Write the Calculation Down: The Field Math Habit