Several cents difference in the actual and calculated "Withholding Tax" values

Question

I have decided to check/calculate my salary in a spreadsheet. All the numbers align correctly, except the federal Withholding Tax.

I have tried to use the Schedule 15, and Schedule 15A (Tax year 2013) to calculate the Withholding Tax. For the Schedule 15 I used the Percentage Method Tables for Income Tax Withholding (Page 45), and for Schedule 15A I used the Wage Bracket Percentage Method Tables for Computing Income Tax Withholding From Gross Wages (Page 34), and Formula Tables for Percentage Method Withholding (for Automated Payroll Systems) (Page 25). Each one of these calculations, gave me a result that is within several cents from the actual Withholding Tax showing on my salary's breakdown/pay-stub.

When I asked my Payroll office, they said its due to "Rounding Error". Can this be true? Can someone explain this to me?

Can it be due to something else? Any ideas? solutions? answers? theories?

The calculations for MA Tax, Social Security, and Medicare deductions are all accurate per the published ways to calculate:

• Social Security: Taxable Wages * 0.124 / 2 (12.4% divided between me and employer)
• Medicare: Taxable Wages * 0.029 / 2 (2.9% divided between me and employer)
• MA State Tax: If combined Social Security and Medicare is under $2000, then they are deducted from the Taxable Wages, once its over $2000, they are not sheltered anymore, and its 5.25%.

Answer 1

From the Publication 15-A (Year 2013) that you cite, at the top-right corner of Page 25, it says the following:

Other methods. You may use other methods and tables for withholding taxes, as long as the amount of tax withheld is consistently about the same as it would be as discussed under Percentage Method in Publication 15 (Circular E). If you develop an alternative method or table, you should test the full range of wage and allowance situations to be sure that they meet the tolerances contained in Regulations section 31.3402(h)(4)-1 as shown in the chart below.

If the tax required to be          The annual tax
withheld under the annual          withheld under your
percentage                         method may not differ
is—                                by more than—

Less than $10.00                   $9.99

$10 or more but under $100         $10 plus 10% of the
                                   excess over $10
$100 or more but under $1,000      $19 plus 3% of the
                                   excess over $100
$1,000 or more                     $46 plus 1% of the
                                   excess over $1,000

Identical wording is in the bottom-right corner of Page 25 in the PDF version 2017 edition of Publication 15-A (or under "Other Methods" in the HTML version.)

Essentially, the people writing your payroll system implemented their own system for calculating your tax withholding, which likely does rounding or other calculations slightly differently from the official tables you referenced. If it's within several cents, it sounds to be like it's well within the tolerance that the regulations provide for. Even being off as much as $0.19 per week is well within the limits given by the table regardless of the amount of tax, and it sounds like the discrepancies you found are less than that. Especially as tax withholding is just an "estimate" collected throughout the year that is reconciled at the end of the year via one's tax return, the regulations only care that the withheld amount is "consistently about the same" as the table.