# Is this the correct math for estimating federal taxes using marginal tax brackets?

(I updated this because I think I wasnt making myself clear in the first part of the question and I clarified what I'm trying to do. I'm just looking to use marginal tax brackets to derive a good estimate of how much federal income tax I'll owe from each paycheck, assuming no deductions. The math I do seems to mostly match what the IRS withholding calculator gives me so I think its right, but I want to check)

I want to estimate the federal income taxes that I owe on each paycheck (my gross salary is 50900 and I live in Illinois) using marginal tax brackets. Just to get a feel for the numbers I'm assuming no deductions (except the standard deduction and 1 personal exemption because I'm single).

I first used a paycheck calculator and ran the numbers. I put 0 W4 allowances and no deductions. That calculator gives me:

``````Semi-monthly Gross Pay \$2,120.83
Federal Withholding \$334.11
Social Security \$131.49
Medicare \$30.75
Illinois \$106.04
``````

Gross pay is 50900/24, SS is 6.2% of 50900, Medicare is 1.45% of 50900, so I get all of that. Illinois income tax is 5% so I understand that too. Federal withholding is just an estimate from the IRS, and the number that calculator gives me matches what I get from the IRS table. The IRS table says that if the paycheck is between 1631 and 3817, I should do 211.65 plus 25% of the excess over 1631, so

``````211.65 + 0.25 * (2120.83 - 1631) = 334.11
``````

so that matches the calculator too.

When I use marginal tax brackets to calculate the actual amount of federal income tax I'll owe on each paycheck, I use these brackets:

``````0     - 9075  ==> 10%
9075  - 36900 ==> 15%
36900 - 89350 ==> 25%
``````

so I calculate my total federal income tax would be

``````0.10 * 9075 + 0.15 * (36900 - 9075) + 0.25 * (50900 - 6200 - 3950 - 36900) = 6043.75
``````

because I'm single so my standard deduction is 6200 and my personal exemption is 3950.

I don't itemize deductions and for this calculation Im not including any pre tax deductions, so healthcare insurance and all that isnt included. On last year's tax return, I had all my usual deductions, so just using the tax I paid last year isn't good enough, and I want to do this using tax brackets.

So based on the 6043.75 I calculate from marginal tax brackets, I'll owe around 6043.75 / 24 = 251.83 in federal income taxes each pay period right?

This question popped up so I went to the IRS withholding calculator, put in 50900 as my gross income and 0 for everything (so once again, no deductions except standard and personal exempt). That tells me that my federal income tax is 6050, which is really close to the number I calculated up above, so I think thats a good estimate, assuming no deductions.

Is this a good, rough estimate of the federal income taxes I'll owe for each paycheck, assuming no deductions and not having to use anything from last year (because my financial situation has changed, tax brackets have changed etc)?

• There are a lot of things that would affect your final taxes. For instance, sometimes you are taxed on things your employer provides: my job gives me extra money to cover health premiums. Or you might have deductions before taxes are taken, like a 401k contribution. I have found the best way to estimate your taxes is to take your effective tax rate from last year and calculate this years from what you know. May 2, 2014 at 18:00
• Not sure if this will make your numbers come out exactly right, but note that there is also a personal exemption in addition to the standard deduction. May 2, 2014 at 18:13
• @mlathe I ignored all deductions (except standard) and all other income when I put the numbers into the payroll calculator, the IRS witholding calculator, and when I calculated tax by hand. I know plenty of other things affect this but that's why I said in the question that I'm ignoring all other deductions. If I ignore them in every calculation that shouldnt make a difference. May 2, 2014 at 18:16
• @BrenBarn So the personal exemption for singles is 3950 so I would just subtract that off my salary when I calculate tax like I do for the standard deduction? Wouldnt that just lower the fed withholding that I calculate myself even more? It seems like my hand calc is already underestimating it. May 2, 2014 at 18:19
• @BenK, well then you can't really expect them to come up with the same answer. Each calculation you did is giving you a different "thing". The W4 is supposed to give you a rough final number (ie including normal deductions people would have), ideally a bit high. Using tax brackets is going to give you the "gross taxes", but your numbers are flawed since you don't get taxed an your gross earnings (59k). etc May 2, 2014 at 18:22

An IRS withholding calculator should give you the exact amount that your employer will withhold. I presume the formula they send to employers is the same one they put on the web site. (Okay, I haven't verified that, but I've worked with the formula they give employers, it's not all that complicated, I don't see why they couldn't easily reproduce it on a web site.)

BUT ... the amount your employer withholds is not guaranteed or expected to exactly equal your tax liability for the year. It's just supposed to be close, with a bias to being somewhat high. Neither your employer nor the IRS have any idea what deductions you will have for the year. Odds are most people don't know themselves until they pull their records together to prepare their taxes. So the IRS just works some statistical averages into the formula. As long as it's at least generally in the ball park, it doesn't matter, as it will all get straightened out next April 15. The IRS tries to guess high because, (a) they'd rather get the interest-free loan from you for the year and have to pay it back than have to wait to get their money, and (b) most people prefer to get a refund than to owe money. If you get a refund, you can surely find things to spend it on. If you owe money, you may have to struggle to come up with the cash.

Oh, and the discrepancy between your calculated \$6,043 and the IRS's \$6,050 is probably -- I haven't checked on this, but this could easily explain it -- because the IRS doesn't actually apply the formula to your income to calculate your tax. You're supposed to use the tax tables that come with the instructions for your tax return. To keep the size of the tax tables within reason, they group incomes into ranges and calculate one tax for all income in that range. This can give you a discrepancy of a few dollars from what you'd get if you applied the formula to your exact income.

• Thanks! That makes a lot of sense. My employer is actually really good about breaking down the details on my paychecks, so when I want to estimate this with deductions and other things, pretty much all of the ones that I use (transportation, health/dental etc) are already taken out pretax. May 2, 2014 at 21:16

If your question is "is the estimator on the IRS website a reasonable way to estimate my withholding", the answer is obviously yes. That's why the IRS puts it on the website. That doesn't mean it's infallible, but it's definitely legitimate.

If you're worried about withholding too little because your income/tax situation has changed substantially from last year, just err on the side of caution and set your withholding to the high range of whatever estimates you get. Note that you won't be penalized for not being exactly right, as described here:

If you did not pay enough tax throughout the year, either through withholding or by making estimated tax payments, you may have to pay a penalty for underpayment of estimated tax. Generally, most taxpayers will avoid this penalty if they owe less than \$1,000 in tax after subtracting their withholdings and credits, or if they paid at least 90% of the tax for the current year, or 100% of the tax shown on the return for the prior year, whichever is smaller.

That said, if your income/tax situation changed drastically, it is wise to err on the side of caution. Better to withhold too much and get a refund than withhold far too little and risk a penalty. Yes, you will be "losing money" on an interest-free loan to the government, but you need only do this for one year. Next year you will have a more accurate estimate of your taxes (based on this year's results) and can adjust withholding if need be.

• +1 Is my calculation using marginal tax brackets pretty accurate then? Its not just coincidence that its close to the IRS calculator? That's my question. May 2, 2014 at 20:40
• +1 for the link to Tax Topic 306. I had not seen that in writing anywhere previously.
– dg99
May 2, 2014 at 22:10

The W4 calculators don't estimate your tax liability. I think that's the fundamental flaw in your reasoning. W4 calculators estimate withholding based on the data you supply. They will give you different numbers depending on the marital status/allowances you put in the calculation, but it is not what you owe for taxes - that is what the employer will withhold.

Using the correct numbers to feed the W4 calculator will help getting closer to the actual taxes to be owed. So if you're single, living alone, only have a standard deduction and no other income than the salary in question - you should enter Single + 2 allowances (not 0 that you entered) to get to the number close to your actual tax liability (you'll get to \$251.82 withholding when the actual liability you estimated to be \$251.83 per period). Each allowance changes the amount of taxes withheld by hundreds of dollars, so you can't expect the calculation to be precise.

As to how I came up with the 2 allowances... Reading the W4 instructions of course.

Enter “1” for yourself if no one else can claim you as a dependent.

Enter “1” if:

• You are single and have only one job; or
• You are married, have only one job, and your spouse does not work; or ...
• Your wages from a second job or your spouse’s wages (or the total of both) are \$1,500 or less.

Totals to 2 allowances.