Background : This is for a $6^{th}$ grade science project. I am doing a project on password cracking and I have created a program to predict how long your password would take to crack and then try to crack it. I have come up with an equation for how to predict how long it would take to crack your password but it always predicts way longer than it actually is. (Passwords can only be lowercase letters and digits, so therefore Total Possible Combination is $36$).
Password length for example will be $8$, and calculations per second will be $\boxed{cps=4\times10^9}$ ($4$ billion calculation per second)
My algorithm is
$\boxed{comb =36^8}\\\boxed{seconds=comb\div cps}$
What is wrong with my math here?
EDIT: I have realized that for where you enter calculations per second I was just using the default, which I had put in a variable to be "$4,000,000,000$" which isn't supported in the language I was using (You have to put "$4000000000$" without the commas)
Combinations = $36^8 \approx 2.8 \times 10^{12}$
Seconds = $2.8 \times 10^{12} / 4 \times 10^9 = 700$ seconds.
If you are getting about $700$ seconds, then there's nothing wrong with your equations. Perhaps you are underestimating in your head how many combinations there are.