How to calculate what % faster $x$ is than $y$ I recently automated a process at work. The manual process took $16$ hours ($960$ minutes). The automated process only takes $7$ minutes. How do I calculate how many times faster the new process is? I'm hoping for a formula so that I can apply the same math to many similar scenarios.
 A: All you have to do is calculating $\frac{960}{7}$, wich is around $137.14$
So your new process is $137$ times faster (or in percentage: $13714\%$)
A: Let $P_M$ stand for time taken in the manual process and $P_A$ stand for time taken in the automated process. Let us agree to use minutes as the unit of time. Therefore $P_M = 960$ and $P_A= 7$.
To find how many times faster is the automated compared to the manual, write a ratio: $\frac {P_M}{P_A}$. Substitute the values in for $P_M$ and $P_A$.
So:
$$\frac {P_M}{P_A} = \frac {960}7$$
Therefore, $\frac{960}7$ is the the ratio of the manual time and the automated time, and hence the automated time is $\frac{960}7$ times faster, or approximately $137$ times faster.
To express this into a percent, note that $100$% faster means double the speed, $200$% faster means triple the speed, and so on.
So, $137$ times faster will be $13800$% faster.
A: All you have to do is to subtract from the 960 minutes the 7minutes and the divide the result by 7. Finally multiply the outcome by 100.
The formula is (X-Xn)/Xn*100 , where X in the manual time spent and Xn is the improved duration.
In your example it seems that the automated procedure resulted in 13614.29 % faster results.
