Percentage Calculator

Multiply the original price by (1 minus the discount percentage divided by 100). For a $120 item at 25% off, the calculation is $120 times 0.75, which equals $90. You can also compute the discount amount first ($120 times 0.25 = $30) and subtract it from the original price. Use the first calculator mode on this page to find the dollar amount of any discount instantly. To verify a store's advertised savings, enter the sale price into the reverse percentage calculator with the discount percentage to confirm the original price matches what the store claims. Stacked discounts work differently: a 20% off plus an additional 10% off does not equal 30% off — it equals 28% total discount because the second discount applies to the already-reduced price.

Use the percentage change formula: ((New Value minus Old Value) divided by Old Value) times 100. If your portfolio grew from $12,000 to $14,400, the change is ((14,400 minus 12,000) / 12,000) times 100 = 20% gain. The critical rule is to always divide by the original (old) value, not the new value. This matters because percentage changes are asymmetric: a 20% gain from $12,000 is $2,400, but a 20% loss from $14,400 is $2,880. This asymmetry is why a 50% gain followed by a 50% loss leaves you at 75% of your starting value, not 100%. The third calculator card on this page automates this calculation with a color-coded badge showing whether the change is positive, negative, or zero.

Use the reverse percentage formula: Original Price = Sale Price divided by (1 minus Discount Percentage / 100). If you paid $67.50 after a 25% discount, the original price was $67.50 / 0.75 = $90. This same technique works for back-calculating pre-tax prices: if a $108 total includes 8% sales tax, the pre-tax amount is $108 / 1.08 = $100. The fourth calculator card handles this automatically. This formula is useful for verifying advertised discounts, filing expense reports with pre-tax amounts, and calculating wholesale costs from marked-up retail prices. Enter the known value and percentage, and the original base number appears instantly.

Because each percentage is calculated on a different base number, and percentages are not additive across different bases. Starting at $100, a 50% increase adds $50 (50% of $100), bringing you to $150. Then a 50% decrease subtracts $75 (50% of $150), leaving you at $75 — a net 25% loss, not breakeven. To return from $150 to $100, you would need a 33.3% decrease. This concept is critical for understanding investment returns: if a stock drops 40%, it needs a 66.7% gain to recover, not 40%. The same principle applies to inflation adjustments, currency conversions, and any scenario involving sequential percentage changes on changing base values.

Multiply the percentages as decimals rather than adding them. If a store offers 20% off and then an additional 10% off the sale price, the total discount is not 30%. Instead, you pay 80% of the original after the first discount, then 90% of that result: 0.80 times 0.90 = 0.72, meaning you pay 72% of the original price — a 28% total discount. On a $200 item, that is $144 instead of the $140 you would get from a flat 30% off. This stacking principle applies to tax-inclusive pricing, commission structures, multi-step markups, and any scenario where percentages apply sequentially. For parallel percentages (like splitting costs), add the percentages directly since they share the same base.