Math
Get original number from percent change: Final / (1 + PctChange)
Back out pre-hike salary, pre-markup cost, or pre-discount list price accurately using division by (1 + Pct) instead of the broken Final * (1 - Pct) shortcut.
Reverse a single percentage change by dividing by its factor
If Final = Original × (1 + Change), recover Original by dividing by (1 + Change). Enter 15% as 0.15 and a 25% reduction as -0.25. Subtracting 15% from the final value uses a different base and does not undo a 15% increase.
This price example requires a nonnegative final amount and a change of at least -100%. At exactly -100%, the original amount cannot be recovered by division: a zero final amount can come from any original, while a nonzero final amount is inconsistent with the assumed model.
Round only the final displayed monetary result to two decimals. A previously rounded sale price may not reveal the exact original price. Sequential changes require multiplying their factors; markup on cost is not margin on selling price. This is percentage arithmetic, not a tax computation rule.
| Scenario | Final Amount (B) | Pct Change (C) | True Original: B / (1 + C) |
|---|---|---|---|
| Post +15% Price Hike | $138.00 | +15% (0.15) | $120.00 (vs wrong $117.30!) |
| Post -25% Clearance Sale | $90.00 | -25% (-0.25) | $120.00 ($90 / 0.75) |
| Implied Dollar Change | Final - Original | 138 - 120 | +$18.00 hike |
| -100% Wipeout Edge Case | $0.00 | -100% (-1.00) | "Undefined (-100%)" (#DIV/0! guard) |
Reverse percentage formula with -100% division-by-zero guard
Validate numeric price and rate inputs before division; -100% reports an undefined original. Changes below -100% are outside this nonnegative price example.
=IF(COUNT(B2:C2)<>2,"Invalid inputs",IF(OR(B2<0,C2<-1),"Invalid inputs",IF(C2 = -1, "Undefined (-100%)", ROUND(B2 / (1 + C2), 2))))Implied dollar change (Final minus Original)
Subtract the unrounded reconstructed original from the final amount, then round the difference. The same -100% guard applies here.
=IF(COUNT(B2:C2)<>2,"Invalid inputs",IF(OR(B2<0,C2<-1),"Invalid inputs",IF(C2=-1,"Undefined (-100%)",ROUND(B2 - (B2 / (1 + C2)), 2))))Try the example
Use the original values or change them to test your understanding.