# Who gets fractional sales tax?

A 7% sales tax on an item costing \$10.00 would be 70¢. On \$9.99, it would come to 69.93¢, but the customer still pays 70¢. Where does that 0.07 of a cent go?

Put another way, a hundred \$10 transactions (totaling \$1,000) would have \$70 sales tax (100 × 70¢). The total tax on a hundred \$9.99 transactions (\$999) would also come to \$70 collectively paid by the customers, but 7% of \$999 is \$69.93. Does the business pocket that 7¢, or does the government get it?

Edit: I did some math. Assuming each transaction only includes a few items (as low as 4 in the highest-taxed region of California), and each item is priced at a penny under any dollar amount, the tax collected is always rounded up.

For instance, a local coffee shop averaging a modest 200 cups per day at *.99 would overcollect annually by a rounding error of `tax rate × 1¢ × 200 × 365`, or an extra \$29.20 with 4% tax, \$51.10 with 7% tax, etc.—it would never “balance out” even if people bought them seven at a time. Who keeps that extra amount?

Editing to more clearly lay out the math:

I’m using a 7% sales tax since that’s what I live with, and I’ll use x (e.g., x.99) as a wildcard to stand in where the dollar amount makes no difference.

Assuming the tax is rounded to the nearest cent, there is a roughly fourteen cent range of prices for which the sales tax comes out identical. For instance:

• x.93–x.07
• 7% of 12.93 = 0.9051, rounds to 0.91
• 7% of 13.07 = 0.9149, rounds to 0.91
• x.50–x.64
• 7% of 12.50 = 0.875, rounds to 0.88
• 7% of 12.64 = 0.8848, rounds to 0.88

These rounding errors can never amount to more than half a penny, by definition. The exact amount is dependent only on the value after the decimal point:

• 99¢, \$2.99, and \$199.99 are all off by \$0.0007 or 0.07¢
• 98¢, \$1.98, and \$555.98 are all off by 0.14¢

This means that for two items priced at x.99—whether taxing them separately as individual transactions, or putting them both on one receipt and then taxing it—the rounding error comes out to 0.14 of a cent. Similarly, seven x.99 charges (totaling x.93) are taxed with a rounding error of 0.07¢ × 7 = 0.49¢, regardless of whether the rounding is done individually or on a subtotal.

I’ll emphasize that: a single purchase of seven x.99 items is taxed exactly the same, and has the same rounding error, as the seven products purchased individually. Ten people each buying seven 99¢ widgets total precisely the same as seventy people buying one each.

In other words, if a business sells seven or fewer taxable items at a time, every line item sold brings in an extra seven-hundredths of a cent. Sell thousands, and that’s an extra couple dollars.

Starting at 8 × x.99, or x.92, the tax is rounded down rather than up, with rounding errors of 0.44, 0.37, and so on. Assuming all prices are x.99, it would take 0.49 / 0.44 ≈ 1.14 eight-item transactions for every seven items sold in any combination of lower quantities. Perhaps unintuitively, it would take larger amounts of higher-count transactions to balance out: about 1.3 nine-item charges, 1.63 ten-counts, etc., per any permutation of seven.

Thus, any trend toward a low item count per transaction means the business is invariably collecting more taxes than the actual tax rate.

The math works out much the same for other tax rates: at 6%, the tipping point is around 8¢ from the dollar (or 8 × 99¢); at 4%, around 12¢; etc.

• It's rounded off to cents. Rounded down. iIRC, so there is no extra; the government just loses a fraction of a cent of tax on that sale. Commented Mar 31 at 5:20
• @keshlam Sales tax isn’t rounded down, but rounded to the nearest cent; 7% tax on \$9.99 (or anything down to \$9.93) would be 7¢, not 6. So a repeat customer in the example would lose out to that rounding error. Who benefits? Commented Mar 31 at 6:11
• Ah. Correction appreciated. But as others have said, I think that makes the average error zero unless people are deliberately setting prices to skew it. I'm also thinking that this is not actually a personal finance question, which means it may get closed. Commented Mar 31 at 12:38
• It is indeed not a personal finance question, but it is a money question. Is there a better SE for it? Commented Mar 31 at 12:52
• Huh, the logo looks more like they’re two separate things: personal finance, and also money in general. But I’m surprised there’s not an SE devoted to taxes. Commented Apr 1 at 14:34

In my experience, back when I had to look up the sales tax at the pizza place I worked at, the tax was rounded up. Back then the sales tax was 5% so it was possible to also calculate it in your head.

For example if the total was \$1.00 the tax at 5% was \$0.05. But if the total was \$1.01 the tax was \$0.06.

In my experience the tax was only calculated on the end of the entire transaction, not on each individual line.

It is possible that some jurisdictions do it differently, but I just checked and the state I worked retail still rounds up.

The decision is based on the taxing authority for the applicable jurisdiction. It can get complex because the tax rate in a place like a grocery store can have multiple tax rates. It is also possible that the store has to send money to both a state and a local government.

In the end the store will send all the tax money collected as a tax to some government agency. At the end of the day the manual cash register we used decades ago would tell us how much money in the drawer was tax. These totals were recorded by the manager as part of the end of day duties.

The tax is usually calculated per receipt, and rounded to the nearest cent. The business remits all the taxes collected.

Rounding up and down averages out over multiple purchases, so in the long term no one is harmed.

For example, if an item is priced at 0.99 and the tax rate is 7% - a tax for a purchase of a single item would be 0.0693, i.e.: 0.07.

But if you buy 10 of these 0.99 items in a single transaction, you've spent 9.90, and the calculated tax would be 0.693, i.e.: 0.69.

In the first example 0.0017 was added, in the second: 0.003 was removed. That's how these average out in the end.

In reality, rounding rules may differ between jurisdictions. Tax rates may differ as well, so the overall math may be even more complex if you're trying to chase fractionals between transactions.

In the comments the OP stated that "The question was about the amount of sales tax collected vs the amount remitted". The answer to that is simple - all the tax collected is remitted. Rounding has nothing to do with that.

• If all prices end in `.99`, and all transactions include only a few items, then it certainly would not average out; the tax collected includes an extra fraction of a cent per item. After hundreds of sales per day, at the end of the year the total tax collected would be tens of dollars over the rate. For instance, a coffee shop selling 300 cups of coffee per day, even selling up to 7 cups per transaction, at any price ending with `.99` , would overcollect a 7% sales tax by an extra \$76.65 annually. So what happens to that \$70+ rounding error? Commented Mar 31 at 13:49
• @Frungi It just means the effective rate doesn't exactly match the stated tax rate, the actual collected goes to the government. Whether prices ending in .99 results in rounding up or down on sales tax will depend on the tax rate. There are certain situations where a store might have a larger disparity between effective and stated sales tax rates due to a large percentage of their transactions being at a certain price, but for the people paying the sales tax (consumers), the rounding averages out. Commented Mar 31 at 14:03
• @HartCO That seems like a pretty definitive answer. Thanks! Commented Mar 31 at 14:13
• @Frungi tax is calculated per receipt, not per item Commented Mar 31 at 19:20
• Sales tax is not charged on "total sales", sales tax is charged on each sale. Sales tax is a tax on the buyer, not the seller. Commented Apr 7 at 8:11