# lowest tax bracket vs “Tax table” in United States

It is commonly assumed that there are a handful of tax brackets in the United States. For example, when filing as Single, up to a taxable income of 9,700, one is supposedly in the 10% tax bracket. However, reading the instructions for IRS Form 1040 on page 38, it states that if ones income is below 100k, one should use the "Tax Table" provided later on pages 67 onwards. According to this table, the tax owed on a taxable income of 6,000 would be 603 (filing Single), which is more than 10% and not due to rounding. Later in this document on page 79 a tax worksheet is provided which performs the computations one would expect (but it only applies to taxable income >= 100k as per the instructions).

Why is there this disconnect between the lower and higher tax brackets? Again, the 10%, 12%, and 22% tax brackets don't seem to really exist. Instead there seems to be more going in this computation which only approximately results in these percentages. Why isn't everything treated the same way?

The rate is not precise in the tax table because the table covers a range. Taxable income from \$6,000 and \$6,049 results in \$603 for your example, that's marginally above/below 10% depending on where in the range your taxable income falls, but it rounds to 10% in either case:

`603/6000 = 0.1005`
`603/6049 = 0.0996`

I've not seen an official IRS explanation for why they chose to end the tax table where they did, but it looks like they calculate based on the mid-point of each range. A couple good reasons would be that it covers the majority of people by going up to 100k taxable income, it would take tremendous space to have charts that cover every possible income (the instructions still frequently get printed).

We also round all numbers entered on our tax forms to the nearest dollar, which also has minimal impact.

If you look at the 14,000-14,050 row, you will see that Single filer pays 1,493, which is neither 10% nor 12% of any number within this range.

That's true, but that's because the tax brackets are progressive, they'd pay 10% on the first 9,525 plus 12% on the remainder:

`9,525 * 0.1 = 953`
`(14,025 - 9,525) * 0.12 = 540`
`953 + 540 = 1,493`

You only pay the highest rate on the amount of income that falls into that bracket.

• I think the question is not why did they end the tax table at 100k, but rather why is there a tax table. It would be a lot easier to instruct people to take 10% and round up to the next dollar. Also, I still cannot infer what formula generates the tax table. Is there any reference you know of? – NingNing Nov 16 '19 at 1:00
• @NingNing Ah, yeah that gets confusing higher up due to progressive taxation, the higher bracket rate doesn't apply to all your income. See update. – Hart CO Nov 16 '19 at 1:22
• @NingNing "It would be a lot easier to instruct people to take 10% and round up to the next dollar." Math is hard, let's go shopping! – RonJohn Nov 16 '19 at 1:31
• @NingNing, for some people (and for all software), it would be a lot easier to take 10%, etc. But for many people, looking it up in the table is much easier. – prl Nov 16 '19 at 3:23
• @NingNing - Like prl said, a fair number of Americans do not understand percentages well enough to take 12%. – Mattman944 Nov 16 '19 at 8:27