Root mean square

This root mean square thing has come in useful multiple times. In Physics, for example, alternating current circuits have root mean square current, which is very useful because the root mean square current, when treated like direct current, delivers the same power as AC.

Root mean square in Physics pops out of our calculations when we wish to compare one kind of thing with another in energy terms. In another example, this time, in the kinetic theory of gases, the root mean square velocity of the atoms in a gas, when used to calculate the kinetic energy, give the average kinetic energy of any such gas. On the other hand, if we use the average velocity of the atom in the gas and calculate the kinetic energy of a particle having the average velocity, we do not get the average kinetic energy possessed by the gas.

So averages in energy come across as “root mean square” things. Power is simply the rate at which work is done, and work done is equal to change in energy.

The root mean square is self-descriptive. You take the square of the things whose root mean square you want to find. Then you find the mean of these squares. And then you take the square root of that mean.

And in that way, you get what is called the root mean square. It is popularly abbreviated as RMS, and comes in useful in multiple areas of many sciences (including economics).