How To Calculate The Volume Of A Stone

Calculating the volume of a regular shape, such as a sphere or a square, is just a matter of math. You'd need to make some measurements, fill those into a formula, and crunch some numbers. But how do you find the volume of irregular objects such as rocks?

There's a nifty trick to find the volume of irregular objects: measuring the displacement of water. By watching the water level rise after submerging the object, you can derive the volume of that object:

1. Take a large, measuring beaker and fill it about half-way with water.
2. Read the measurement on the side of the beaker and record this number. This is the current volume of water.
3. Carefully insert the stone into the water. 
4. Read the new measurement of the water level.
5. Subtract the first volume from the second volume to calculate the volume of the stone. For example, if you recorded 40 fluid ounces the first time, and 50 fluid ounces the second time, the stone volume is 10 fluid ounces.

Depending on the measuring beaker you are using, and the unit you are wanting to calculate, you might have to do a conversion. To go from milliliters (ml) to fluid ounces (fl oz) – you might be reading milliliters off your beaker in Europe – multiply your number by 0.034. For example, 100 ml is equal to 3.4 fl oz.

Alternatively, you might want you express your result in cubic inches rather than fluid ounces. 1 fl oz is equal to 1.8 in³. Or in our example from above: 10 fl oz equals 18 in³. Now you know your rock has a volume of 18 in³!

There are plenty of examples of irregular solids that don't have a simple formula to calculate their volume. Think of a potato, a piece of wood or a human body, for example.

In fact, it is reported that Archimedes used this trick to calculate the volume of his own body. By stepping into a bath, he noticed that the water level rose, and he understood that the volume of water that was displaced was equal to the volume of his submerged body. He shouted out: Eureka! (I found it!)

So use this trick to measure the volume of any object, as long as that object is waterproof (maybe don't try this with your phone).

If you don't have a measuring beaker or water available, you can still estimate the volume of the rock. If you assume that the rock is a perfect sphere, you can measure the diameter of the rock and use the formula:

\(V=\frac{4}{3}\pi r^3\)

with ​V​ the volume and ​r​ the radius (or half the diameter) of that sphere. This will give you a rough estimation of the volume of the rock.

This also works for other irregular objects. By approximating the object by a regular shape, or summation of regular shapes, you can get a rough idea of it's volume through basic mathematics equations.