I will try to answer this as best I can, but don't hold me to these numbers because it's been a while since I did manual payroll run!
When calculating payroll, you need to pay taxes, FICA, and unemployment.
State and Federal taxes are withdrawn from the hourly rate, so you don't really 'pay' it as much as you divert a portion of the employees pay to the government. So this effectively costs you nothing.
FICA/Social security is essentially a split - you pay half and the employee pays half. This is a big expense - you pay 6.2% of the employees income and they have 6.2% deducted from their pay.
Then there is FUTA / SUTA which is harder to predict, but basically the employer pays up to 6.2% for federal (FUTA) but that is offset/credited by the amount of unemployment that you pay to the state (SUTA) and that varies by state, so it can be as little as .8% (on the first 7k) to the Fed and the rest to the state. Also, this tax is only paid on the first 7k (I think) of income so it really get's tricky. In Kentucky I think it's around 2.7% for new businesses on the first $8000 of income, which would be around $220 + the remaining FUTA of <$100. (info unverified!) This changes with your history - a new business will pay more than an established on with a perfect record.
So where does that leave you? If you paid an employee around 10k a year, then for each dollar you paid to them it would break out (on your side) something like this:
Gross Pay = $1.00
Social Security = employer pays 6.2 cents extra
Medicare = employer pays about 1.5 cents extra
FUTA/SUTA = employer pays about 3 cents extra
So you are paying about 10% extra. These are WILD numbers that I mostly pulled from the cobwebs in my head but maybe that will give you an idea.
Note that it's not the hourly rate that effects things, it's the annual income. If you paid an employee $150,000/year then the percent that you have to pay in taxes would be much because there are caps on these things.
You also need to consider workers comp insurance, which isn't exactly payroll taxes but you will probably have to pay it. That varies wildly, but I've paid anywhere from $400 to $2100 per year per employee.
Hmm.. what a blather. I hope that's helpful.