In the simple case, the real cost of the item is the cost you pay minus the taxes you save. The taxes you save are equal to the cost of the item times your marginal tax rate, T. So then the cost would be
COST = PRICE * (1 - T)
You can get a guess of your marginal tax rate by looking up your taxable income (after exemptions and deductions) somewhere the tax brackets are posted.
Of course, there are lots of cases where this won't be exactly right, such as if you are on the edge of a marginal tax bracket or when reducing your taxable income will entitle you to special tax breaks (like the child tax credit). Also it is possible, if you desire, to spread the deduction over several years using depreciation instead of expensing it in the year in which you actually spent the money.
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TTT makes a good point. Your marginal tax rate actually includes the effects of all applicable taxes: federal, state, local, and possible FICA taxes. For simplicity you can add these tax rates together to get a good approximation. T = Ta + Tb + Tc where Ta, Tb, and Tc are the various taxes you must pay on your income.
Technically any taxes that deduct the cost of other taxes should be multiplied (for example, you often can deduct state taxes from your federal income tax). In that case the math would be
COST = PRICE * (1 - Ta) * (1 - Tb) * (1 - Tc)
But that's getting very specific. Adding the tax rates together is a good approximation.