How to price your menu so every total is a whole dollar (with the tax math)

If your register never has to make change, the line moves faster, the drawer holds nothing but bills, and nobody counts quarters at close. Getting there is a pricing problem, not a technology problem — and the arithmetic is stranger than it looks.

Written by the owner of Rune Works Comics, Oklahoma, who got tired of coins.

Why bother

Cash isn't the expensive part of taking cash. Coins are. They cost you five to ten seconds on every cash transaction while a line watches, ten to twenty minutes a day counting and rolling at close, a float you have to buy and secure, periodic trips to the bank for change, and the occasional miscount nobody can explain.

Get rid of coins and every one of those goes to zero. And here's the part people miss: you don't have to go cashless to get most of the benefit of cashless. You have to go coinless. Cash customers stay welcome — the unbanked, teenagers, tourists, older regulars, the kid with a five-dollar bill — and the coin tray disappears anyway.

The obvious approach, and why it fails

Say you want an item to ring up at exactly $5.00 with 8.25% sales tax. The instinct is to divide:

Check it: $4.62 × 8.25% = $0.38115, which the register rounds to $0.38. So $4.62 + $0.38 = $5.00 exactly. That worked.

Now try the same formula for a $12.00 target at the same rate:

Also fine. The formula looks reliable — and then it quietly isn't. Because sales tax is rounded to the cent, the relationship between shelf price and out-the-door total isn't smooth. It's a staircase, and the steps aren't all the same height.

The part that surprises everyone: some totals are impossible

This is the discovery that makes the problem interesting.

Because tax is rounded to a whole cent, as you raise the shelf price one cent at a time, the total sometimes jumps by two cents. That means certain out-the-door totals can never occur at all — no shelf price produces them.

Concrete example at a 4.5% tax rate, hunting for $18.00:

The total goes straight from $17.99 to $18.01. $18.00 does not exist at that rate. There is no price you can write on that sticker that makes the register say eighteen dollars even.

This isn't rare or exotic. Roughly 8% of whole-dollar targets are unreachable at any given tax rate — and which ones depends entirely on your specific rate. It's why "just divide by 1 + tax" is not a method, it's a first guess that needs checking.

The method that actually works

Work in whole cents as integers, never in decimals — floating-point math will bite you here. Then:

1. Pick your target out-the-door total, T (say 500 cents for $5.00).
2. Estimate the shelf price: P ≈ round(T ÷ (1 + rate)).
3. Verify, don't assume: does P + round(P × rate) == T?
4. If it misses, test P−1 and P+1, then P−2 and P+2. If nothing within a few cents lands exactly, that target is unreachable — say so instead of fudging it.
5. Only ever move to the adjacent whole dollar. If neither the dollar above nor below is reachable, leave the price as it is.

Done properly at a rate of 8.25%, a few common price points come out like this:

Your rate is almost certainly different, so don't copy this table — run your own numbers.

Price-side vs. register-side: the difference that costs money

There are two ways to make a total come out even, and they are not equivalent.

Price-side (what this article is about)

You set shelf prices so price + tax already lands on a whole number. No discount is ever applied, so it costs you nothing per sale. You simply chose your prices well. It works on every tender, at every register, with no staff training and no button to remember.

Register-side

You ring the sale normally, then knock the odd cents off at the till. It works on any cart, including mixed ones — but it costs you real margin on every single transaction (about 58¢ on average, in our measurements), and someone has to remember to do it.

Use price-side for everything you can, and keep register-side for the stragglers: special orders, mixed baskets, the item you forgot to reprice.

If you're outside the US

In the UK, EU, Australia and New Zealand, displayed prices already include VAT — the sticker price is the total. That makes this whole problem trivial: to have something ring up at £5.00, price it at £5.00. All the difficulty above is a peculiarity of jurisdictions where tax is added at the register.

Practical notes from running it in a real shop

• Your change drawer becomes a stack of $1 bills. Float about $40 in ones; you'll never need a coin again for a sale under $20.
• Round down, not up. Rounding down is a discount in the customer's favour and always defensible. Rounding up charges more than the shelf implies and invites exactly the argument you don't want.
• Tax is still owed. You are absorbing cents, not waiving tax. Every sale still rings through with tax calculated and remitted — that's the difference between a pricing choice and a problem. Your accountant, not a web page, is the authority on your tax posture.
• Watch for drift. Every new product you add arrives at $12.99 and breaks the pattern. If your county changes its tax rate, every price you set needs redoing. Re-check whenever either happens.
• Menu-driven businesses have it easiest. If you run a food truck or coffee cart with fifteen items, this is one afternoon of work and then it's permanently solved.