Percentage Increase / Decrease Calculator

Multiply the value by (1 + percent ÷ 100). To add 10% to 200: 200 × 1.10 = 220. You can also work out 10% of 200 separately (that is 20) and add it on — same answer, one more step. The single-multiplier version is worth the small effort of learning, because it is what makes repeated changes easy. That number, 1.10, is the factor. Adding 25% is a factor of 1.25; adding 7% sales tax is 1.07; doubling a number is +100%, a factor of 2.00. Once a change is written as a factor, it can be applied, stacked, undone and averaged with plain multiplication and division. Almost every mistake in this topic comes from working in percentages when you should be working in factors.

Multiply by (1 − percent ÷ 100). To take 10% off 200: 200 × 0.90 = 180. A "30% off" tag means the original price times 0.70; a clearance sticker at 65% off means times 0.35. A decrease of 100% is a factor of zero — the value is wiped out — and that is why a decrease can never exceed 100% of the starting amount, while an increase has no ceiling at all. A price can rise 500%; it cannot fall 500%. To undo a decrease you divide by the factor, not add the same percent back. An item marked down 30% now sells for $70, so the original was 70 ÷ 0.70 = $100. Adding 30% to $70 would give $91 — the wrong answer, because that 30% would be calculated against the smaller number.

A store advertising "20% off, then an extra 20% off at checkout" is not offering 40% off. The factors multiply: 0.80 × 0.80 = 0.64, so you pay 64% of the original and the true discount is 36%. The shortfall grows with the size of the discounts. Two 10% discounts give 19% off, not 20%. Two 50% discounts give 75% off, not 100% — which is obvious once stated, since nothing free ever comes out of two half-price cuts. Three 20% discounts give 0.8³ = 0.512, so 48.8% off rather than 60%. The same rule applies in the other direction. Three consecutive annual raises of 10% are not a 30% raise; they are 1.10³ = 1.331, or +33.1%. Increases stacked on increases overshoot the sum, decreases stacked on decreases undershoot it, and in both cases the reason is identical: each step is measured against a base the previous step already changed.

Add 10% and then subtract 10% and you do not come back to the starting value. In factors, 1.10 × 0.90 = 0.99 — you land 1% short, and it makes no difference which change comes first, because multiplication does not care about order. The loss is always there and always in the same direction: applying a rise and an equal fall of p percent leaves you at 1 − (p ÷ 100)² of the original. At 10% that is a 1% shortfall; at 30% it is 9%; at 50% it is a full 25%. This is the arithmetic behind a familiar frustration. An investment that drops 50% has to gain 100% to get back to even, not 50%. In general, recovering from a fall of p percent takes a rise of p ÷ (100 − p) × 100 percent.

The same percentage applied to two different bases produces two different-looking numbers, and pricing is where that bites hardest. Buy an item for $100 and apply a 50% markup and you are computing 50% of the cost: the price becomes $150. The margin, though, is measured against the selling price: the $50 of profit is 50 ÷ 150 = 33.3% of what the customer paid. A 50% markup and a 33.3% margin describe exactly the same transaction. So when someone says "we work on 40%", the number is ambiguous until you know which base it uses. Markup percentages are always the larger figure, and the gap widens fast: a 100% markup is a 50% margin, and a 200% markup is a 66.7% margin. The calculator above applies a percentage to whatever base you type in — deciding which base is correct is the part only you can do.