As volatility has a great influence on option prices, you'd like to sell options in high volatility environments and purchase options in moments of low volatility. But what is high/low volatility? Implied volatility rank (IVR) and implied volatility percentile (IVP) tell you this.

The implied volatility rank is given by $$IVR=\frac{IV-52Low}{52High-52Low},$$ where we refer to the 52 week maximum/minimum of implied volatility.

The implied volatility percentile is given by $$IVP=\frac{\#Days \; with\; lower \; IV \; than \;today}{\#Trading \; Days \; in \; a \; year}.$$

So, $IVR$ compares the current $IV$ to its historical maximum and minimum whereas $IVP$ tells you how many days in the last year had a lower $IV$ than today.

Clearly, both $IVR$ and $IVP$ take numbers between $0$ and $1$ (whereas $IV$ may take any positive number). Normally, $IVR