This could almost be an English question as much as mathematics. I pondered the idea (initiated by conversation about an answer I'm posting on Stack Overflow, comparing run-times for two similar coding methods), and the more I looked into it, the more confused I became - between questions on various Stack sites, Wikipedia, online "faster than" calculators, and other forums like Quora. There are many a few different answers depending on who you ask, and the context.
The basis of the calculation comes down to one rule:
Something can't be more than 100% faster than something else.
The way I figure it, the calculation for FasterThan %
is:
$$\frac{({\color{Red} S}lower-{\color{Green} F}aster)}{{\color{Red} S}lower}=\%Faster Than$$
Alternatively, the calculation for SlowerThan %
is:
$$\left |\frac{({\color{Green} F}aster)-{\color{Red} S}lower}{{\color{Green} F}aster} \right |=\%Slower Than$$
Example Result Pairs:
A (Slower) B (Faster)
--------------- --------------- -------------------------- -------------------------------
100 seconds 90 seconds B is 10% faster than A A is 11.1% slower than B
2 seconds 1 second B is 50% faster than A A is 100% slower than B
1.348 seconds 0.605 seconds B is 55.1% faster than A A is 122.6% slower than B
5.106 seconds 0.851 seconds B is 83.3% faster than A A is 500% slower than B
1 0 B is 100% faster than A A is infinitely slower than B
€ 100.00 € 90.00 B costs 10% less than A A costs 11.1% more than B