-I have read many articles on FIRE calculators and how FI bloguers did it but while I am saving as much as I can and investing, I do not have a clear idea of when I will be FIRE. Do you just calculate how much you need by year and multiply that by 25?
Yup, that's the general idea: try to understand how much you will need every year (including things that could be invisible to you today as an employee: taxes, healthcare, etc...) once you're retired, multiply that number by 25, and that's your target. Also you'll need to take inflation into account! if you need $1000 a month today, that might mean $1200 a month in 10 years.
Try to see how much you save every year, and make assumption on how much your investments will grow as well. For example, maybe you're saving 25'000 a year, and you already have 100'000, which grow at 7% a year, meaning next year you'll save 25'000 + 7'000 from your investments, meaning your wealth will be 100'000 + 7'000 + 25'000, and so on. There are calculators out there.
It's a lot of approximations as soon as you involve guesses on your investments returns. But many people have said that you should set a date, not necessarily an amount, as your target.
-Since I discovered teh idea of being early retiree by living frugally, I am beating myself up for not realising earlier that I could do it. I mean I like my job but I'd like more doing it out of passion not because I need an income to live on. How do you manage to be patient for 5-10-15 years? I think I'll need between 6 to 10 years. How to stop myself from counting the days?
I think that part is extremely tough. Many people will tell you that if you forget to be happy during these 6-10 years, you're missing the point of financial independence. But honestly, I can't help but check my accounts daily, read as many personal finance blogs as I can... I'm kind of obsessed when I have an idea like that in mind so it's tough for me to think about anything else.
If you're like me, one of your solutions is to really turn this whole thing into your main hobby: create a blog, read other blogs, try to find any possible mean to increase your income and decrease your expenses. In other words, stay completely focused and busy on the Financial independence goal.
Pros: it should accelerate your path to FI
Cons: you'll become even more obsessed and anything that goes against your goal might be even more painful to you
Alternatively, the best option is probably to set everything on autopilot and not worry about it... if you can. 10 years is a long way, so try to not think about it, enjoy life as if you didn't know FI was coming. In my case, easier said than done, but some people seem to be able to do that, somehow...
Note: you mention you're in Paris. If you're French, you might want to check some French forums about Financial independence. France has some pretty different rules, (the "impot sur la fortune" tax on wealth comes to mind) that could make some of the advice on US forums less relevant to you.