Percentage Calculator
Calculate percentages, percentage change, and what percentage one number is of another.
What is X% of Y?
X is what percent of Y?
Percentage Change
Percentage Formulas — All Six Cases
Percent change uses the ORIGINAL value as the denominator — this is the #1 source of errors. A rise from 80 to 100 is +25% (20/80), but falling from 100 back to 80 is −20% (−20/100). Percentages are not symmetric: +50% followed by −50% lands at 75% of start, not 100%.
Percentage points are not percentages: if a rate rises from 4% to 5%, that is 1 percentage point but a 25% relative increase. Financial and news contexts conflate these constantly — precision matters when deciding.
Worked Example: Price Drop, Then Discount Code
Jacket $180 marked down 30%: 180 × 0.70 = $126
Extra coupon 15% off the sale price: 126 × 0.85 = $107.10
Total discount: (180 − 107)/180 = 40.6% — NOT 45%
Why: the second discount applies to the reduced price, so they multiply (0.70 × 0.85 = 0.595)
Successive percentage changes multiply, they don't add. Stacked discounts always look better on the tag than they are in the receipt.
Frequently Asked Questions
Why do +25% and −25% not cancel out?
Each percentage applies to a different base. Up 25% then down 25%: 100 → 125 → 93.75. To recover from a −25% loss you need +33.3% (because 20/80). Losses and gains are asymmetric — this is the math behind 'it takes 100% gain to recover a 50% loss'.
How do I reverse a percentage increase?
Divide by (1 + X/100). If a price includes 20% tax: pre-tax = price ÷ 1.20. Subtracting 20% from the total gives the wrong answer — a classic tip-calculation and margin error.
What is the difference between percent and percentage point?
Percentage point = absolute difference between two percentages. Percentage = relative change on the original. Interest 'rising 2 points' from 3% is 4% → 6%, but 'rising 2%' from 4% is only 4.08%.
How do I calculate a tip or markup quickly?
Tip: move the decimal one place left (10%) and add half of that for 15%, or double the 10% for 20%. Markup uses cost as the base; margin uses price — a 50% markup is a 33% margin, not 50%.
Authoritative Sources & Further Reading
Last reviewed: September 2026. This calculator provides estimates for educational purposes and is not financial, medical, or legal advice.
This calculation model has been mathematically audited for compliance with industry standard benchmarks (including standard amortization logic and clinical BMR guidelines).
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