Trap #1: Stacking discounts is not addition
A shirt is 20% off, then an extra 20% off at checkout. Many people say "that's 40% off." It is not. The second 20% applies to the already-reduced price, so the combined factor is 0.8 × 0.8 = 0.64 — a 36% discount, not 40%. The gap grows with each layer: three 20% cuts leave you at 0.8³ = 51.2% of the price, a 48.8% total cut, not 60%. The discount calculator applies them in the right order automatically.
Trap #2: Percent increase is not reversible by the same percent
A stock falls 50%, then rises 50%. You are not back to even — you are at 75% of the start. Why? The rise is calculated on the new, lower base. To recover a 50% loss you need a 100% gain, not 50%. General rule: to recover a drop of p%, you need a gain of p/(1−p). This asymmetry quietly destroys portfolios and explains why "flat for the year" after a bad quarter requires a bigger bounce than people expect. The percentage calculator handles "X is what % of Y" both ways so the base is never confused.
Trap #3: Extracting tax from a total
A receipt shows a total of $107 including 7% tax. How much was the tax? Wrong answer many give: $107 × 0.07 = $7.49. Right answer: tax = total × rate / (1 + rate) = 107 × 0.07 / 1.07 ≈ $7.00. The error happens because the 7% was already baked into the $107; multiplying the total by 7% double-counts the tax base. Retailers, accountants, and reimbursement forms all trip on this. The sales tax calculator extracts tax from a total correctly so your books reconcile.
The mental model
Every percentage problem has a base — the number the percent is taken of. Most errors are just using the wrong base: the post-discount price instead of the original, the recovered value instead of the pre-loss value, the tax-included total instead of the pre-tax amount. Name the base explicitly and three-quarters of percentage mistakes disappear.