The Water Constants 7.48, 8.34 and 231

Why this matters

Four numbers do most of the water math in the trades: 7.48 gallons in a cubic foot, 8.34 pounds in a gallon, 62.4 pounds in a cubic foot and 231 cubic inches in a gallon. Every tank volume, every fill estimate, every "will the floor hold it" question and every per-gallon chemical dose runs through at least one of them. Most techs know two or three by heart and half-remember the rest, which is how a tank gets sized with 8.34 where 7.48 belonged.

The fix is to see them as one chain, not four facts. Each one can be derived from the others in a line, so if you remember the chain you can rebuild any number you forget and check any number you are unsure of. This card lays out the chain, works conversions in both directions, and says where the numbers stop being true: they are values for cold fresh water, and hot water, brine and glycol mixes do not weigh the same.

The chain

THE FOUR WATER CONSTANTS, ONE CHAIN
(cold fresh water, about 60 F)
----------------------------------------------------
 1 cu ft  = 12 x 12 x 12 in  = 1728 cu in
 1 gal    = 231 cu in             (US gallon, exact)
 1 cu ft  = 1728 / 231      = 7.48 gal
 1 gal    = 8.34 lb               (weight of water)
 1 cu ft  = 7.48 gal x 8.34 = 62.4 lb
----------------------------------------------------
 reverse  1 gal  = 0.1337 cu ft
          1 lb   = 0.120 gal  = 27.7 cu in
          1 cu ft of water = 62.4 lb
----------------------------------------------------
 two are definitions:  1728 and 231
 two are measured:     8.34 and 62.4 (vary w/ temp)

Two of these are definitions and two are measurements. 1,728 is geometry (12 cubed), and 231 cubic inches is the legal definition of the US gallon (as published in NIST Handbook 44). So 7.48 is exact arithmetic: 1,728 / 231 = 7.4805. Those three never change.

8.34 and 62.4 are the measured weight of water, and they change with temperature and with what is dissolved in the water. That is the whole reason this card has a section on where the numbers stop working.

Rebuilding a number you forgot. If you remember 231 and 1,728, you have 7.48. If you remember 7.48 and 62.4, you have 8.34 (62.4 / 7.48 = 8.34). If you remember 8.34 and 7.48, you have 62.4. Any two of the measured or derived values give you the third, and the multiplication is the check.

A note on the imperial gallon. These are US gallons. An imperial gallon is larger (about 1.2 US gallons) and weighs about 10 lb. Equipment literature from outside the US sometimes uses it; a volume that looks about 20 percent off is the tell.

Worked conversions, forward

A rectangular tank, from dimensions to gallons to pounds. A rectangular holding tank measures 4 ft by 3 ft inside, and the water stands 2.5 ft deep.

1. Volume = 4 ft x 3 ft x 2.5 ft = 30 cu ft.
2. Gallons = 30 cu ft x 7.48 gal/cu ft = 224.4 gal.
3. Weight = 224.4 gal x 8.34 lb/gal = 1,871 lb.
4. Check by the other route: 30 cu ft x 62.4 lb/cu ft = 1,872 lb. The one-pound difference is rounding in the constants. The two routes agreeing is the confirmation that nothing slipped.

A small reservoir, from cubic inches. A reservoir is 12 in by 12 in by 16 in inside.

1. Volume = 12 in x 12 in x 16 in = 2,304 cu in.
2. Gallons = 2,304 cu in / 231 cu in per gal = 9.97 gal.
3. Weight = 9.97 gal x 8.34 = 83.2 lb.
4. Check: 2,304 cu in / 1,728 = 1.333 cu ft, and 1.333 x 62.4 = 83.2 lb.

When the dimensions are in inches, 231 takes you straight to gallons without passing through cubic feet. Dividing cubic inches by 1,728 first and then multiplying by 7.48 gets the same answer with one more step and one more chance to slip.

Worked conversions, backward

From a rated capacity to space and weight. A spec sheet gives a tank as 1,000 gal. How big is the water, and what does it weigh?

1. Cubic feet = 1,000 gal / 7.48 gal per cu ft = 133.7 cu ft.
2. Weight = 1,000 gal x 8.34 = 8,340 lb of water, before the tank itself.
3. Check: 133.7 cu ft x 62.4 = 8,343 lb. Agrees within rounding.

That 8,340 lb is the number that matters for anything set on a floor, a slab, a roof or a trailer. The tank's empty weight and its stand go on top. See related: How to Tally the Load of a Filled Tub or Tank on a Floor.

From a scale reading to volume. A drum on a scale reads 400 lb more full than empty. How much water is in it?

1. Gallons = 400 lb / 8.34 lb per gal = 47.96 gal, about 48 gal.
2. Cubic feet = 47.96 / 7.48 = 6.41 cu ft.
3. Check: 6.41 x 62.4 = 400 lb.

Weighing is often the most accurate way to measure water in an irregular container, because the scale does not care about the shape.

The two slips the chain catches

Using 8.34 where 7.48 belongs. Both are "the water number," and both sit between gallons and something. Multiply 30 cu ft by 8.34 and you get 250 "gallons," about 11 percent high. The units catch it: 8.34 is pounds per gallon, so cubic feet times pounds per gallon leaves cu ft x lb / gal, which is not gallons. See related: Units Carried Through Every Line of a Calculation.

Dividing where you should multiply. 30 cu ft / 7.48 = 4.0 "gallons," which is absurd for a tank you can see is bigger than a bucket. The rough check is physical: a cubic foot is a box about the size of a milk crate, and it holds about seven and a half gallons, about one and a half 5-gallon buckets. A volume in gallons should always be a larger number than the same volume in cubic feet.

The 8.34 inside every parts-per-million dose

Concentrations in water treatment are usually written in parts per million (ppm), which for dilute solutions in water is the same as milligrams per liter. Because a gallon of water weighs 8.34 lb, a million gallons weighs 8.34 million lb, and one part per million of it is 8.34 lb. That gives the dosing formula used across water treatment:

Pounds of active chemical = target ppm x millions of gallons x 8.34.

A 500 gal storage tank brought to 50 ppm of available chlorine: 50 x (500 / 1,000,000) x 8.34 = 50 x 0.0005 x 8.34 = 0.2085 lb of active chlorine, about 3.3 oz.

Check it from the weight of the water instead: 500 gal x 8.34 = 4,170 lb of water, and 50 parts per million of 4,170 lb is 4,170 x 50 / 1,000,000 = 0.2085 lb. Same answer.

Two things the formula does not give you. It gives pounds of the ACTIVE ingredient, so a product that is only partly active (a liquid sold at some percent strength) takes the active pounds divided by that fraction, with the strength and density read off the product label. And the target concentration and contact time come from the procedure your health authority, the equipment manufacturer or the governing standard specifies, not from this card.

Where the numbers stop being true

The weight values (8.34 lb/gal, 62.4 lb/cu ft) describe cold fresh water, around 60 F. The volume values (7.48, 231) are geometry and hold for any liquid. So when the liquid changes, gallons still convert exactly, and pounds do not.

Hot water is lighter. Water expands as it warms, so a gallon of hot water weighs less than a gallon of cold:

For a load on a floor, the cold figure is the conservative one and is the right one to use. For anything where the mass of water matters precisely (a heat calculation, a weighed dose), use the value at the actual temperature. The same table shows the expansion: water that is 60 F at fill takes up about 3 percent more volume at 180 F (62.4 / 60.6 = 1.03), which is the volume an expansion tank on a closed loop has to absorb.

Salt water and brine are heavier. Seawater runs about 64 lb/cu ft, roughly 8.55 lb per gallon. A softener brine tank or a saltwater pool sits somewhere between fresh water and that, depending on how much salt is dissolved, and a saturated brine is heavier still.

Glycol mixes differ. Propylene and ethylene glycol solutions used in hydronic and chilled loops weigh a few percent more than water per gallon, depending on the glycol and the concentration, and they also expand more than water when heated. Take the density and the expansion figure from the fluid's data sheet for the mix you are using, not from this card.

Water with air in it is lighter. Aerated water, foam or a slurry is not water, and none of these constants apply to it. A sump full of sludge weighs more than the same volume of water; a frothy pool return weighs less.

Where the constants go next

These four numbers are the inputs, not the answers. They feed pressure and head (one foot of water column exerts 0.433 psi, which comes from 62.4 lb spread over 144 square inches), heat (1 BTU raises 1 lb of water 1 F, so 8.34 lb per gallon turns gallons into BTUs per degree), and every floor-load and fill-time calculation. Those relationships each have their own card; this one is the foundation they share.

See related: Pressure and Head: The 2.31 and 0.433 Pair, The Sensible Heat Formulas for Air and Water, and What Standing Water Weighs on a Ceiling or Floor.

References

• National Institute of Standards and Technology Handbook 44 and related weights-and-measures publications, for the definition of the US gallon as 231 cubic inches
• Engineering tables of water density versus temperature (for the 140 F and 180 F values), and the fluid manufacturer's data sheet for glycol mixes
• See related: Units Carried Through Every Line of a Calculation
• See related: Pressure and Head: The 2.31 and 0.433 Pair
• See related: How to Tally the Load of a Filled Tub or Tank on a Floor