People use rules-of-thumb and an understanding of passwords to answer this question. Password entropy calculations require understanding the random process used to generate the passwords.
The suggestion these days is to have an 8-10 character password with a mixture of upper case, lower case, and numbers. The characters should be randomly chosen and not include words or the first letters of a phrase. If you are really concerned about security, you might have a 20 character password. If the password contains words, it is vulnerable to a dictionary hack, since words occur with very different probabilities than randomly chosen characters. Even the first letters of a the words in a phrase occur in more predictable patterns than truly random passwords.
Brute-forcing a password requires repeatedly trying the character combinations. Since the question uses the term entropy, I assume this is a familiar concept. An k character password would require 62^k attempts to find an unknown password (where there 56 characters are upper case, lower case, and numbers). Ideally, the password would be a randomly choose password from the total 62^k possible passwords where all the characters appear with equal chance. However, many password generators generate predictable passwords. Please do not use words, the first letters of the words in a phrase, or common variations on predictable themes.
Entropy refers the the unpredictability of a password. In order compute entropy, one must know the password and the distribution by which the characters in the password are generated. The entropy is a straight-forward calculation once that is known. I suggest that you use a password generator that generates characters uniformly at random (i.e. with equal probability) from the set of characters (the 62 characters that include the upper and lower case alphabet and the numbers). This will get you the best entropy.
If on the other hand, you wish to generate your passwords with a distribution that favors the lower-case letter 'a' over all other characters, then your entropy will be drastically lower than if the password is generated with equal probability. This means that passwords consisting only of words have very low entropy and are very predictable.
You might consider instituting a password selection policy that requires passwords to look like they are generated randomly. This will help your password entropy and save you bits in your embedded system.