# Harmonic Series And Niche Search Volume Estimation

Building on my post from last night, I went to work trying to figure out a formula to estimate the total number of searches in a niche based on the number of searches for its most popular term. Applying the rules of power law curves means that I should be able to get a pretty good estimate fairly easily.

In practice, developing this formula was not easy however. As I mentioned yesterday, power laws are generally a series of values that look like this:
100
100/2
100/3
100/4
and so on. This is known as a harmonic series because “the wavelengths of the overtones of a vibrating string are proportional to 1, 1/2, 1/3, 1/4…” (from wikipedia). Math is crazy like that.

If the top term in your list has 100 searches and you want to find the total number of searches in the Wordtracker accessible niche (keywords that have at least 2 searches per day), you’ll need to find the sum of a range of numbers: 100/1, 100/2, 100/3 all the way down to 100/(100/2), a harmonic series. If you graph the sum of the range for every number from 10 to 4000. You get a very slight curve, like this: I’ve plotted it against a linear trend line (in black) to demonstrate that this is in fact a curve, and so there is no simple slope to solve we can use to solve our problem.

I did a little research and it turns out that the sum of a harmonic series increase in very nearly the same way as a log normal curve (the formula is actually ln(n)+.5772156649, which uses Euler’s constant). Using this knowledge I was able to come up a formula.

Where Y is the number of searches for the most popular keyword in the list and X is the total number of searches in the niche:
X=(LN(Y/2)+0.5772156649)*Y

What this means is that if you have a niche where the most popular term has 1200 searches, you should expect to have around 600 total keywords in your list and about 8370 total searches per day.