How much does a fluid ounce of water weigh

Update 2009-08-07: Now the slightly lower density of water at room temperature is taken into account, improving the answer by 0.3%.

Is this a silly question? Not at all, if you're using either American or Imperial measurements.

I just ran across two web pages that say one cup of water weighs 8 ounces (oz). To protect the guilty, I won't mention the sites except to say that one is from a physicist and the other from a cooking magazine, both of whom should know better—though from different perspectives—than to publish this incorrect information. Let's do the math:

By definition, 1 liter (L) holds 1000 cubic cm (cm3, or cc) of volume, thus 1 milliliter (mL) is the same as 1 cc in volume. The weight of water was also initially defined as being 1 kilogram (kg) per liter, but that definition has been discarded since the density of water changes with temperature and atmospheric pressure (if you're curious, this PDF outlines some factors to consider when measuring water in a lab). Taking this into account, the following calculations are based on data at room temperature (25 °C/77 °F) and 1 atmosphere (basically, air pressure at sea level). Tap water is slightly denser than pure water, but the difference is negligible at room temperature. Under these conditions, water has a density of 997.13 kg/m3. For the calculations, we'll also need a few conversion factors:

1 m = 100 cm
1 kg = 1000 g
1 L = 1.0567 US quarts (qt)
1 qt = 4 cups
1 lb = 16 oz = 453.59 g

(997.13 kg/m3) × (1000 g/kg) × (1 m/100 cm)3 × (1000 cm3/L) = 997.13 g/L

(997.13 g/L) × (1 lb/453.59 g) × (1 L/1.0567 qt) = 2.0803 lb/qt

(2.0803 lb/qt) × (16 oz/lb) × (1 qt/4 cups) = 8.3214 oz/cup (US)

In the US customary measurement system, then, one cup of water, which is 8 fluid ounces (fl. oz) in volume, is actually 8.3214 oz in weight. Is it close enough? I don't think so. If you were measuring water on a digital scale that displays 1/8-oz increments, the nearest reading would be 8-3/8 oz. For scales with 1/4-oz resolution, the nearest reading would be 8-1/4 oz.

Based on the above, we can make some handy tables for various volumes. Let's start with metric figures first: Weight of water at 25 °C (77 °F) at sea level.

In US units: * Based on these defined (i.e., exact) figures: 1 US liquid gallon = 231 in3 and 1 inch = 2.54 cm. See the Wikipedia links below for source data.

Let's pause for a moment and think about terminology a bit. It seems that some people have trouble distinguishing between how weight and volume are defined. What's the difference? Simply,

Weight = how heavy
Volume = how big

Speaking of fluid ounces, what do you think happens when the name of a unit normally associated with weight (oz) gets included in a unit for measuring volume (fl. oz)? Constant confusion, that's what. The nomenclature makes for a huge mess, but it's what we're stuck with.

It also doesn't help matters that the US measures are colloquially called "English" or "British" units, even though the official US and Imperial systems differ significantly when it comes to measuring volume. As it happens, 1 Imperial fl. oz equals 0.96076 US fl. oz, so 8 Imperial fl. oz of water is equivalent to 7.9948 oz by weight, which I believe is actually close enough to 8 oz for cooking-measurement purposes.

Further, not only do the measurements differ between US customary and Imperial units, so do the multipliers. An Imperial pint, for example, is 20 Imperial fl oz, whereas a US pint is 16 US fl oz. So a pint of water weighs either 16.643 oz (US) or 19.987 oz (Imperial). Not quite "a pint's a pound the world around," there. At any rate, we can also calculate a table for Imperial units: * Based on these defined (i.e., exact) figures: 1 Imperial gallon = 4.54609 L & 1 Imp. tbsp = 5/8 Imp. fl. oz. See the Wikipedia links below for source data.

Notice how close an Imperial gallon of water comes to weighing 10 lbs. That's because, similar to the original kg/L equivalence, the Imperial gallon was defined as the volume occupied by 10 lbs of distilled water, but at a lower temperature and slightly higher pressure than what I used here (specifically, 62 °F and 30 inches of mercury, which is about 1.0025 atm).

Conversely, we can also figure volumes based on a starting weight, again under the condition of 25 °C (77 °F) at sea level:

You know, this post started as a rant but turned into a bunch of conversion tables. How did that happen? I think I'll stop here before I get all worked up over the distinction within the US system itself of liquid quarts vs. dry quarts or how the customary measures used in cooking differ from the FDA-regulated measures used for food nutrition labeling. Makes me wish all of our recipes would be published in metric, but I know I'll never see the day.

Oh, if you've read this far (thank you, really), you may now be wondering why I haven't yet provided a conversion table between US and Imperial volumes or between cubed lengths and volumes. The reason is because this post is about the weight of water, expressed in multiple units, and not about converting a volume from one unit to another. Besides, the existing tables already contain enough information, in the form of metric volumes or weights, for you to derive these conversions yourself—or, for a more direct route, you can use any of the calculators available online. You can also check with Wikipedia for conversion tables and unit definitions:

• Comparison of US & Imperial Units
• Conversion of Units
• US Customary Units
• Fluid Ounce

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