The provincial and federal tax rates are both calculated on your gross income, after certain allowed deductions.
But, don't waste your time trying to calculate your take-home pay that way — it's a lot of work, as you're discovering. Even if you succeed in figuring the federal and provincial income tax rates for your salary, you'll still need to factor in deductions for Employment Insurance (EI) and Canada Pension Plan (CPP), and the rate at which tax is withheld from your pay may ultimately differ from the tax you owe when you file.
Rather, you should know that the Canada Revenue Agency (CRA) offers a definitive Payroll Deductions Online Calculator. This is the same tool that a small employer could use to determine exactly how much in payroll taxes to withhold from your paycheck:
The Payroll Deductions Online Calculator (PDOC) calculates federal and
provincial payroll deductions for all provinces (except for Quebec),
and territories based on the information you provide.
Using the tool and inputting the correct information, you should be able to figure out, to the penny, what your take-home pay will be for each pay period.
Note 1: While the PDOC will calculate an employee's payroll deductions, some of the amounts reported by the tool will be employer-paid amounts that aren't deducted from your salary, such as the employer's portion of your Canada Pension Plan and EI contributions. This should be evident in the tool, but I wanted to point it out since the tool is geared more towards employers, rather than employees.
Note 2: Your first paycheck of the year and your last paycheck of the year may not necessarily be the same amount, even if your salary remained constant. Both EI and CPP deductions are front-loaded. That is: your take-home pay may go up at the point where you max out each of your EI and CPP contributions for the year.
Also, bear in mind that the tax you pay through payroll deduction isn't exactly the amount of tax you might end up owing to the government. Payroll deductions are a deposit against your actual tax liability, which will get figured when you file an income tax return after the year is over. Once your income tax return is filed, you may owe more (if your payroll deductions weren't sufficient, e.g. if you had another income source), or get a refund (if too much had been withheld, e.g. if you had tax credits or deductions to claim.)
Bear in mind that your employer may have other deductions from your pay (e.g. supplemental health insurance, long term disability insurance, life insurance, etc.) so the CRA's tool may not exactly match your take-home pay. Check with your company's HR department to learn what other deductions might be taken from your pay.
(p.s. we don't call them "slabs", we say "tax brackets.")