Is there a way to calculate how much an IRA contribution will lower my taxes?

An IRA contribution is a deduction in calculating taxable income, it is not a tax credit.  The tax savings is the amount of your contribution X your tax rate.

Use the Turbo Tax software to do the analysis.

To see what an IRA contribution may do for your tax situation, enter a contribution in Turbo Tax. Before you enter the information note what your refund or amount due is. Then, compare the amount to what the program calculates after you enter a contribution to an IRA.

If you are not happy with the results, you can delete the contribution.

Contributions to an IRA are handled in Deductions and Credits:
• Select Federal Taxes
• Select Deductions and Credits
• Select Show More at Retirement and Investment
• Select Start at Traditional and Roth IRA contributions

To delete the contribution:
• Select Federal Taxes
• Select Deductions and Credits
• Select Show More at Retirement and Investment
• Select Revisit at Traditional and Roth IRA contributions
• Deselect the Traditional IRA contribution
• Select Yes to Remove the IRA Contribution

You can open and make contributions to a traditional IRA if you (or, if you file a joint return, your spouse) received taxable compensation during the year, and you were not age 70½ by the end of the year.

The maximum contribution to a Traditional IRA is $5,500 ($6,500 if over age 50).  If filing a married filing jointly tax return these amounts are per person.  

If you are covered by a retirement plan through work, your deduction may be limited (see Chart below).