How To Calculate The Weight Of Water

Calculating the weight of water might be important in real life if you're working with a recipe that uses an unusual method of measurement for liquids, but it's most likely that you'll encounter a problem like this in science class.

The challenge of calculating the weight of water really comes down to exactly what it means to find the weight of water, and whether the use of the term is for a specific reason or is simply a colloquial way of asking for the mass of water. In any case, you can easily find the result using the general formula for density and the value of the density of water.

The most important thing to understand before you try to calculate the weight of water is the difference between mass and weight. The mass of a substance is a measure of how much matter is present, and it's measured in kilograms or pounds. Most of the time, this is the most useful measure when you want to see how much of a substance is present.

The weight of a substance or an object is the force that gravity exerts on it due to its mass. For this reason, weight is technically measured in newtons or pounds-force. When most people say "weight" in real life, they are actually referring to the mass of the substance, because in colloquial language the words are basically interchangeable. However, in physics they have very specific meanings, and as such, you have to be careful to ensure you're using the right words and calculating the right quantities.

The metric system has a lot of advantages when it comes to converting between masses and volumes of water. This really comes down to the convenient value for the density of water, but if you just want to calculate the weight or mass of water without going into much detail, this is the simplest approach to use.

In short, 1 mL (milliliter) of water has a mass of 1 g, so 1 liter has a mass of 1 kg. You can use this fact to work out the mass of water from any volume: for example, 450 mL is 450 g, and 1.35 liters is 1.35 kg.

You should learn the general formula for density to convert the mass of anything to the volume, or vice-versa, and of course you can also use this for water. Density ρ is defined as the mass m divided by the volume V, or (equivalently) the mass per unit volume of a substance. The formula is:

\(ρ = \frac{m}{V}\)

However, if you're looking to calculate the mass or weight of water (or another substance) you can re-arrange the formula to:

\(m = ρV\)

Then all you need to find is the volume of water you're trying to measure and the density of water. Make sure that the units match before making the calculation. For example, if you have the density of water in kg/m³, you need to measure the volume in m³, and if you've measured the volume in ft³, you'll need the density in lb/ft³. The density of water in kg/m³ is 1,000 kg/m³, and in lb/ft³ it is 62.4 lb/ft³.

So if you have 0.01 m³ of water, this is:

\(\begin{aligned}\)
\(m &= ρV \
&= 1000 \text{ kg/m}^3 × 0.01 \text{ m}^3 \
&= 10 \text{ kg}
\end{aligned}\)

Finally, you can convert between mass and weight (if you really do need the weight rather than the mass) using the formula:

\(W = mg\)

Where W is the weight, m is the mass and g = 9.81 m/s² = 32.17 ft/s², the acceleration due to gravity. So continuing from the previous example gives:

\(\begin{aligned}\)
\(W &= mg\)
\(&= 10 \text{ kg} × 9.81 \text{ m/s}^2\)
\(&= 98.1 \text{ N}\)
\(\end{aligned}\)

Again, you need to make sure the units match up, so if you have the mass in lb, you'll need the acceleration due to gravity in ft/s² to ensure the answer makes sense.