# Product Manager Math Part 1

### Over the last few years, I have observed a particular insidious kind of math error occur repeatedly in Product Management circles. Let’s…

Over the last few years, I have observed a particular insidious kind of math error occur repeatedly in Product Management circles. Let’s talk about it for a minute, and I’ll give you a bookmark you can use to help ensure you never make it again.

It happens all the time when measuring change and growth. Here’s an example: If your conversion rate is 4%, and you run an experiment that increases the conversion rate to 5%, what will you report was the impact of your experiment?

If you answered that your experiment increased conversion by 1%, you made a very common error. The correct answer is 25%. 4% to 5% is a 25% change (1 is 25% of 4.) This is a very successful experiment!

If you wanted to talk about the amount of change instead of the percentage of change, you could say “Conversion increased by 1 percentage point” but please don’t.

When you say the word *percentage* somebody will assume you’re talking about percent change, since that’s how the word is most often used. Say something like “Conversion is up by a point to 5%, that’s a 25% gain.” You can also use *basis points* which are 100ths of a point. So you could also say “Conversion is up by 500 basis points.”

Here’s the formula for percent change:

( (Value 2 — Value 1) / Value 1 ) * 100 = Percent Change

If conversion went from 5% to 4% it’s going to look like this:

( (4–5) / 4 ) * 100 = Percent Change

( ( -1 ) / 4) * 100 = Percent Change

( ( -.25) * 100 ) = -25%

So here the change from 5% to 4% represents a -25% (that’s negative!) change. You should probably stop the experiment.

If you don’t feel like memorizing the formula, here’s a handy calculator:

I hope that’s helpful. Use it in good health!