Calculating employment taxes

I am the sole owner and sole employee of a S-Corp. Rather than using Quickbooks Payroll or TimeTrex, which cost money, can't I calculate them myself by multiplying my gross income for the pay period (minus 401k contributions) by the current rates for social security (0.124) and Medicare (0.029) and my federal income tax (20% in my case)? Other than state and federal unemployment taxes, am I missing anything or mistaken? I'm in Florida so I don't have to pay state income tax.