My tax refund this year will be $2,043 from the federal government, and $957 from New York State. That comes out to exactly $3000. I figure the chances of that happening are pretty low.

Is there some law I'm running into that is capping my tax return (and I guess thereby making me lose money on my taxes)?

The reason why I believe $3000 is special and has a higher chance of being special than any other random number is that if there was a cap it would likely be at a nice even number, like $3000.

  • 75
    The chances of getting a refund of exactly $2,043 from the federal government are pretty low, too. It's just that our brains like round numbers, so they tend to stand out. Feb 16 '18 at 12:40
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    Actually, the chances of that happening are pretty high, given how many people there are in the US Feb 16 '18 at 13:51
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    @PeteBecker But arguably it's more likely that the amount would be capped at a round number, if there were a cap Feb 16 '18 at 17:02
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    @phyrfox I think you've misunderstood. Refundable credits are credits that will pay out to you even if it effectively makes your total taxes negative. However, regardless of whether a credit is refundable or not, you're always able to (potentially, i.e. if you have zero tax liability) get all the money back that you had withheld.
    – stannius
    Feb 16 '18 at 17:16
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    @BenAaronson, but neither of his refunds were round numbers. He received two refunds that happen to add up to a round number. If OP had filed somewhere other than New York, it likely would have added up to some other random number.
    – Seth R
    Feb 16 '18 at 18:40

One can overpay their state and federal taxes by tens or hundreds of thousands of dollars. Tax time is when it gets reconciled, a payment due or a refund. No cap either way, your $3000 is just coincidence that it’s a round number.

  • 5
    In fact, it happens to roughly 1/1000 people * 323.1 million people in usa = ~323,000 people every year. Feb 16 '18 at 23:37
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    152M tax returns filed. No idea if the owed/overpaid numbers are clustered, e.g. a high number between +/- $900, or if there’s a wider random spread. Still, a large number will end in 000 Feb 17 '18 at 0:55
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    I had a particularly complex US return one year, and was due a $1 refund. I didn't cash the check; I kept it as a souvenir. Next year the IRS credited me for the check I didn't cash! Feb 17 '18 at 3:09
  • @MarkStewart Nicely done. I guess you've set up your tax withholding about as precisely as it can be done.
    – Daniel
    Feb 19 '18 at 18:48
  • With the potential for Roth recharactrization after year end, it was easy to get the tax return to show nothing owed, no refund. Feb 19 '18 at 20:11

Is there some law I'm running into that is capping my tax return

You're filing two returns, not one. Thus, the premise of your question is flawed.

Just as importantly, the two tax returns don't ask each other what the other's current year refund is.

  • 4
    Line 10, Form 1040 does in fact ask what the state refund was for the prior year? There may not be a cap, but the number definitely is an input into the calculation of tax.
    – user662852
    Feb 16 '18 at 15:05
  • But only if you itemized deductions the prior year. Feb 16 '18 at 15:18
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    @user662852 Sure but it asks what your state refund was for the prior year. If the question had been "I got $957 back from the state last year and $2043 from the IRS this year," it would still be a coincidence, but at least there would be a connection.
    – stannius
    Feb 16 '18 at 16:54
  • Since many of the inputs to the state and federal tax returns are the same, it's theoretically possible that one of them could calculate the refund for the other, and then take that into account when determining its refund.
    – Barmar
    Feb 16 '18 at 22:03
  • I disagree that my premise is flawed. New York State can easily have a law that says something like 'your total tax return from NY and the feds is capped at $3000' Feb 19 '18 at 2:54

Roughly, about one in a thousand people will have a tax return in multiples of a thousand. If 100 million people/families file, there could be around 100,000 with a return that’s a multiple of 1,000.

Most deductions are limited to the total amount of taxes you owe, some are not. Therefore, your return is mostly limited by how much taxes you already paid - but not always. Otherwise, there is no cut-off (I once got over 20k$ back).

I think it was pure coincidence that yours was 3,000.

  • 30
    The distribution of digits is not uniform... a result of Benford's Law
    – user71659
    Feb 16 '18 at 3:52
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    I appreciate your point is that with a large enough group of people you can expect 'nice' numbers to appear relatively commonly, but your maths is well off the mark here...
    – Phill
    Feb 16 '18 at 4:54
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    This is so poor mathematically that it will actively hurt understanding the principles. Without an explanation of the probability this response does nothing except say "it's a coincidence". Please fix the maths or delete the answer, and avoid harming future maths knowledge.
    – Nij
    Feb 16 '18 at 6:40
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    Aside from Benford's Law, there are other biases to take into account. For example, a tax refund of $0 is probably a lot more common than any other given amount.
    – BenM
    Feb 16 '18 at 6:43
  • 29
    The Benfords' Law applies for the first digit of a number. Here we are dealing with the last digits, which should be more or less uniformly distributed (of course, other biases not withstanding...). Feb 16 '18 at 9:26

The size of your refund is calculated by a simple formula:

Refund = (amount withheld) + (amount of refundable credits) - (taxes owed)

(This could come out to a negative number, in which case you will have to pay in more money instead of getting a refund, but that's a digression.)

None of those inputs have any influence on each other.** Your refund is just the disparity between the amount you have already given to the IRS (or state agency) for the year, and the amount it turns out you actually owe after going through the complicated steps of the 1040 form.

So, supposed you go through the tax form and find out your tax liability is $8,437 (let's leave credits out of this), and it you actually paid in $11,437 through withholding, your refund will be $3,000. If you had withheld more, your refund would be higher. If you had withheld less, your refund would be lower. Bt your withholding and actual tax liability have nothing to do with each other.

In your case, you actually have 2 refunds which happen to add up to a round number. But these, too, are independent calculations. The federal government doesn't care how much you pay into your state (other than the fact that your state withholding is deductible if you are itemizing, provided you count your state refund as income in the following year), and the state doesn't care what you paid the feds. They each have their own rules for calculating what you owe. The fact that your two refunds combined add to a nice round number is coincidence.

** If you have regular employment, you could argue that the taxes owed influences the amount withheld, as your withholding is supposed to be a projection of what the IRS thinks you will owe according to a calculation using the size of your paycheck and the number of exemptions you claim. It is entirely up to you to declare your exemptions, though, and the actual tax calculation is much more complex than the one used to determine withholding, so it is rare for those numbers to match exactly. But it is to your benefit to get these two numbers as close as possible.


There is no "maximum refund amount". I presume the round number is a coincidence.

How did you calculate your refunds? If you filled out the forms by hand, presumably you know exactly what calculations you did, and you'd know whether you applied some rule about a maximum. I suppose if you used some tax software package you might not know how they calculated your refunds. In that case, you could print out the forms and follow through each step to see where the numbers come from.

If you studied the calculations, it's possible that the number is not strictly a "coincidence", that you come up with a round number because other numbers going into the calculation are round numbers or some such.

Note that while the probability that your tax refund will be an exact multiple of $1000 is, presumably, about 1 in 1000, it is a classical fallacy to make much of this. If either the fed tax alone or the state tax alone had been a round number, you would likely have been equally impressed. Or if either tax, or the total of the taxes, or the total withheld, etc. Just in your taxes there are probably dozens of "interesting" numbers. Then consider your credit card balance, your bank account balance, etc. The probability that one specific number will come out to a round number is small. But the probability that ANY number that you might encounter in your personal finances will turn out to be a round number is not that small.

This is how psychics work. I saw on the news once that a psychic was asked to assist the police in solving a murder. He said things like, "The letter 'R' will be important." And then it turned out that the first name of the man who found the body started with an "R". Amazing prediction! Not really. He would surely also have claimed a hit if "R" had been the first letter of the man's last name, or of the street where the body was found, or the town, or a nearby store, or a river or a hill, or the model car someone involved drove. He never said it would be related to finding the body, so he could claim success if there was an "R" in the name of a witness, if the person was found tied with "rope", etc etc.

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