Some quick math says: ~83h/month = 4.15h/day (conservative approx. - assuming 4 workweeks / month and 5 workdays / week)
I think this rule of thumb works pretty well, factoring in some holidays or illnesses.
The factor of 1000 assumes a 4 hr, 5 day week. The typical way of figuring out your hourly rate (given a fixed salary) is to divide by 2000 = 50 weeks (assuming 2 weeks vacation) * 40hr/week.
That's what the clients will be giving you. Out of that comes insurance and self-employment tax and additional social security (in the USA, as an example).
If you are working backwards from a fixed salary you have to also add in the dollar value of additional taxes and insurance, plus whatever other benefits you might be getting.
$120K salary at a regular job > $120K in paid invoices from clients.
If you're a consultant or contractor or whatever, even if you work 8 hours a day they are not all billable hours. There's the tedious business work to look after (record keeping, business development, etc.)