Contributing $1000 to your 401K will reduce your taxable income by $1000 AND increase your 401K balance by $1000.

Increasing your withholding by $1000 won't reduce your taxable income and won't add anything to your 401K.  All it'll do is put $1000 more in the pot toward your 2016 tax bill.

Hi i was curious how you performed the calculation to know that to save $1K in taxes you need to contribute $4k or more in a 401k.  I'm in a similar situation and wanted to be able to calculate how much to increase my 401k by in order to lower by tax bill by $2700.  Thanks!

Depends what tax bracket you are in.  If you are in the 25% bracket you will save 25% off your tax by reducing your income by Itemized Deductions or pretax contributions.  

So for a 4,000 Contribution you will save 25% or 1,000.

if you increase it to 2,000 you save $500 of Tax.  

To save 2,700 you would need to increase your 401K contribution by 10,800 (10,800 x 25% = 2,700) if you are in the 25% bracket.  Your tax bracket might be different.

Fantastic, thank you so much!  It's exactly what I needed to know.

To decrease tax owed, do I need to do additional tax withholding or increase 401k contributions.

You can do both. Increased contributions will allow you to reduce your taxable income, and additional tax withholding is also a good practice to be sure you don't owe taxes by the end of the tax year.  

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@davidrachelgray1 wrote:

To decrease tax owed, do I need to do additional tax withholding or increase 401k contributions.

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You have to understand the difference between your tax liability and your tax due with your tax return.

Your tax liability is what you owe the government, based on your income, deductions and credits.

You make payments during the year via paycheck withholding, and possibly by making extra payments directly to the IRS.  At the end of the year, your tax return calculates your tax liability.  If your payments are less than your liability, then you owe an additional tax payment to the IRS.  If your payments are more than your liability, you get a tax refund.

Now we consider, if you owe tax for 2020, what can you do?  The only way to lower your tax liability is have less income or more deductions.  It's too late to change your income, and the only deduction you can take now is to make a contribution to an IRA or HSA, if you are eligible.  The money you contribute will reduce your taxable income, and depending on your tax bracket, will reduce your tax by 15%-24% of the amount you contributed (for most people).

To owe less tax for 2021, you can change your liability or your withholding or make additional payments.  But if you change your tax liability (such as by contributing more money to a pre-tax retirement account) that will also reduce your withholding (unless you also adjust your W-4) so you may end up with the same tax payment due at the end of the year.