It's complicated, and you may want to use a tax calculator web site. You can also make a new test account on Turbotax Online, and try various scenarios.
Briefly, for a single person over 65, the standard deduction for 2023 is $15,700. That means that as long as your taxable income is less than that, you won't actually pay tax. Social security is taxable if half your social security plus all your other income is more than $25,000. Let's assume your SS benefit is $1000 per month, or $24,000 per year.
With these three facts, we can test some examples.
- Suppose you withdraw $10,000. Half your SS plus your IRA is $22,000, so your SS is not taxable and your IRA is less than the standard deduction, so all your income is non-taxable.
- Suppose you withdraw $15,000. Half your SS plus your IRA is $27,000, so $1000 of your SS benefit will be taxable. When you add that taxable amount to the $15,000 IRA, you will be over $15,700 by $300. You will pay 10% tax on $300, or $30 in income tax.
- The more you withdraw from the IRA over $15,000, the more tax you will pay on the IRA withdrawal AND on your SS benefit.
The calculation is similar if you are married filing jointly. If you are married filing separately, 85% of your SS benefit is automatically taxable, plus the IRA withdrawal, so any amount totaling more than $15,700 will be taxable.
