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My pay stub says:

Gross Pay                $5,833.96  
Federal Income Tax       $681.00.   <== ?
Employee Social Security $361.71
Employee Medicare        $84.59
GA State Income Tax      $295.20.   <== ?

How did Square Payroll calculate these numbers for Federal and State Income tax? (What are the formulas?)

I understand:

6.2%    Employer Social Security
1.45%   Employer Medicare

Since 6.2% * $5,833.96 = $361.7055 and 1.45% * $5,833.96 = $84.59242, and those numbers match the paystub, there is no mystery for those.

I just haven't known what the formulas are for income tax and am curious to learn.

And if my gross pay is consistently this amount on each paycheck, will these income tax values always stay the same?

2 Answers 2

4

The short answer

The formula, for your specific case, is:

((($5,833.96 * 12) - $8,600) - $46,125) * 0.22 + $4,807.50) / 12 = $680.80

This will be true for the remainder of the year, assuming that you do not change your W-4, or have a change in income. Note that it is not exactly your withholding; I'll come back to this later.

The long answer

As @d-stanley notes, the US income tax system is a progressive system, in that you are not taxed a flat percentage on your income (specifically regarding income tax; you correctly note that FICA and Social Security are a flat percentage in general). Therefore, to estimate your income tax, and therefore your necessary withholding, the formula you're looking for is going to be a sort of step formula.

I'll walk through the formula I built above. It is derived from IRS Publication 15-T, Federal Income Tax Withholding Methods, Worksheet 1A. This is the document linked by @d-stanley; however, I believe he or she linked you to the incorrect location. The more appropriate location would be here, the section titled "1. Percentage Method Tables for Automated Payroll Systems...". (The PDF version of that publication is available here; I like the PDF versions better at times because the formatting is easier to read, and I think that's the case here. The section is on page 8).

The first part of the formula, $5,833.96 * 12, is income_per_pay_period * number_of_pay_periods_annually. In your case, I assumed the pay period was for the month of January; therefore, the number of pay periods is 12. This gets you your total income (from this job). The next part, - $8,600, is related to your standard deduction, which is $12,950; the remainder ($4,350) is included in a subsequent step. The net result ($5,833.96 * 12) - $8,600 = $61,407.52, is your annual adjusted payment amount. This is approximately your taxable income.

Given this annual adjusted payment amount, it's time to fix out the estimated tax burden. The IRS provides a lookup table for this on page 10 of the PDF, titled "2022 Percentage Method Tables for Automated...". Flipping down to the "Single or Married Filing Separately" table, we note that because the income tax is progressive, we effectively need to compute the income tax for each tax bracket. This has been done for us in Column C. Since you're in the 22% bracket (your annual adjusted payment being $61,407.52, which is greater than $46,125 and less than $93,425), the tax on your income in the 10% and 12% brackets is $4,807.50 (($46,125 - $14,625) * 0.12 + ($14,625 + $4,350) * 0.10 = $4,807.50). Also note that the income from $0 to $4,350 is taxed at $0 (for the purposes of this table), which makes up the remainder of your standard deduction referenced in the previous paragraph.

The last part is the tax from the marginal tax bracket you're in, (($5,833.96 * 12) - $8,600) - $46,125) * 0.22. This is your annual adjusted payment, minus the lower boundary of the tax bracket you sit in, multiplied by your marginal tax rate (the tax rate for that bracket). This tax is $3,362.15, plus the additional $4,807.50, for a total of estimated tax of $8,169.65. You can then divide this by the number of pay periods you have, 12, for a result of $680.80. While this does not equal $681, your actual withholding, the IRS permits employers to round tax to the nearest dollar; see the section on rounding (page 7 in the PDF).

Therefore, the generalized formula you're asking for looks like this:

(((pay_per_pay_period * number_of_pay_periods) - deduction_according_to_filing_status) - bottom_boundary_of_marginal_bracket) * marginal_tax_bracket_rate + tax_from_lower_brackets) / number_of_pay_periods = withholding_per_pay_period

I think this is actually fairly straightforward--take your income for the pay period, extrapolate it to a year, use information provided by the taxpayer to estimate taxable income, and spit out an estimate for the tax due for this pay period.

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  • WOW! THANK YOU so much for this thorough answer! And you're a new contributor here too. Amazing! I see that ((((5833.96 * 12) - 8600) - 46125) * 0.22 + 4807.5) / 12 = $681 when rounded to nearest $, which is great, because I see where you got almost all of those numbers. The one I don't understand yet is $8,600. How did you find or calculate that one? I also wonder if "$12,900" on PDF pg 8 is a typo since I see $12,950 elsewhere. Here's my editable spreadsheet trying to follow along: docs.google.com/spreadsheets/d/… Thanks!!
    – Ryan
    Commented Feb 9, 2022 at 0:26
  • Oh never mind. Somehow I missed that field 1g literally says to enter $8,600 since I'm single. So this 22-line spreadsheet that I made with your guidance actually works! Woohoo! 🎉 Now time to figure out the state of GA.
    – Ryan
    Commented Feb 9, 2022 at 0:32
  • Right after accepting your answer, Square finally responded and pointed me to the Excel sheet at irs.gov/businesses/small-businesses-self-employed/… which also results in $681 but does not expose the calculations underneath so wasn't a good enough answer for me.
    – Ryan
    Commented Feb 9, 2022 at 0:45
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There's not a single formula. Essentially your total income for the year is extrapolated (e.g. $5,833 * {# of pay periods}), your deductions estimated based on your filing status and exception claimed on your W-4, your total tax for the year is calculated based on the tax tables, and then the amount to deduct for this pay period ({total tax} / {# of pay periods}). So there are many assumptions in there, such as your pay being stable, this being your only source of income, what credits you're eligible for, etc.

In the end, your taxable income (based on gross income, deductions, and exemptions) and the period length are used to look up the witholding amount in the official tax tables. But the math behind those tables is based on that extrapolation.

And if my gross pay is consistently this amount on each paycheck, will these income tax values always stay the same?

Yes, unless you have other deductions or additions (expense reimbursements, etc.).

So it's not an exact science, but an educated guess that's meant to get you close to your total tax owed. Any difference between the total withheld and the actual tax due when you file is either owed at the time of filing or given back to you as a refund. The goal is generally to get your witholding as close to your actual tax as you can, maybe leaving a little cushion for a small refund. You don't want too large of a refund (essentially loaning your money to the government for free) or to large of a tax bill (which results in penalties and interest).

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  • I appreciate your answer. But there clearly is a formula. Their software outputs values based on some inputs. I'm trying to learn what the inputs are and what operations they do to them to produce these outputs. Taxes are an exact science when you know all of the inputs, would you agree?
    – Ryan
    Commented Feb 2, 2022 at 23:08
  • 2
    I'm saying there's not one formula. It's a combination of extrapolation based on multiple inputs and tax tables. In the end it's a table lookup (see edits) but the math behind those lookups is based on those extrapolations.
    – D Stanley
    Commented Feb 2, 2022 at 23:44
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    And taxes for the year are an exact science. Trying to calculate the appropriate tax to withhold for a single period is impossible unless you know the totals for the entire year and all of the other inputs that aren't relevant to your employer (deductions like mortgage interest, for example)
    – D Stanley
    Commented Feb 2, 2022 at 23:46
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    What I tried to link to in those 74 pages is the tables that you look up your filing status and pay frequency, then look for the witholding amount that corresponds to your periodic pay. Since the US uses a graduated tax system, the wighholding is not a straight linear function (e.g. P * X) but the rate increases as you get paid more. I don't know how else to explain it without confusing you further,
    – D Stanley
    Commented Feb 3, 2022 at 1:15
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    @d-stanley I think you should have linked to this, which is the instructions for automated payroll systems. The number I get from that more closely matches Ryan's federal income tax withholding.
    – cmn.jcs
    Commented Feb 7, 2022 at 3:13

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