Why 'What Price Do I Need?' Is an Algebra Problem on Amazon

The circular part of the problem

"I need $3 profit per unit — what should I charge?" sounds like a subtraction problem, but on Amazon it isn't quite that simple. The referral fee is a percentage of your selling price, and your selling price is exactly the number you're trying to solve for. You can't subtract a fee you don't know yet from a price you haven't picked yet.

The two equations that actually solve it

Rearranging the profit equation so price appears on only one side gives a clean formula for each target type. For a target profit margin: Price = (Cost + Fixed Fees) ÷ (1 − referral% − target margin%). For a flat target dollar profit: Price = (Cost + Fixed Fees + Target Profit) ÷ (1 − referral%). Both isolate price by moving every percentage-of-price term to one denominator.

When the equation has no answer

If your referral fee percentage plus your target margin percentage add up to 100% or more, the denominator hits zero or goes negative — meaning no price, however high, can hit that combination of fee and margin simultaneously. That's not a bug in the math; it's the equation correctly telling you the target itself is impossible as specified.

Skip the algebra

Our Break-Even Selling Price Calculator solves both versions of this equation instantly from your cost, fixed fees, referral rate and target — and flags the impossible-target case explicitly instead of returning a nonsense number.