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A percentage is just a fraction of 100 — "20%" means 20 out of every 100. The boxes above cover the situations that come up most often, but they all reduce to the same core relationship: part = percent × whole.
To find X% of Y, convert the percent to a decimal (divide by 100) and multiply: 20% of 150 is 0.20 × 150 = 30. To go the other way — figuring out what percent one number is of another — divide the part by the whole and multiply by 100: 30 ÷ 150 × 100 = 20%. And if you know a part and its percentage but need the total population or group size, divide the part by the percentage as a decimal: 30 ÷ 0.20 = 150.
Percentage change (the "% change" tab) is different from a simple percentage — it measures how much a number moved relative to where it started: (new − old) ÷ old × 100. This is why going from 100 to 150 is a 50% increase, but going back from 150 to 100 is only a 33.3% decrease — the base number changed.
Percentages are one of the few math concepts almost everyone uses weekly without necessarily thinking of it as "math." Sales tax is a percentage of a purchase. A tip is a percentage of a bill. Grade weighting in school ("homework is 20% of your grade, the final is 40%") is percentages. Interest on a savings account or credit card balance is a percentage. Population growth, inflation rates, and election polling are all reported as percentages. Even a "50% more free" label on a shampoo bottle is a percentage claim worth being able to check.
Because percentages appear in so many different contexts, the same four calculations on this page cover a surprising range of real situations. A student figuring out what score they need on a final exam to get an 85% in a class, a shopper deciding if a "40% off, plus an extra 20% off" sale is actually a good deal, and an investor checking how much their portfolio grew this year are all, mathematically, doing the same kind of arithmetic.
Averaging percentages incorrectly. If a shop had a 10% conversion rate in a month with 100 visitors and a 30% conversion rate in a month with 1,000 visitors, the overall conversion rate isn't 20% (the simple average) — it depends on the total number of visitors and sales across both months. Averaging percentages only works cleanly when the underlying group sizes are equal.
Confusing "percentage of" with "percentage points." If a survey shows support for something rising from 40% to 50%, that's a 10 percentage point increase, but a 25% relative increase (10 ÷ 40 × 100). News headlines sometimes blur this distinction in ways that make a change sound bigger or smaller than it actually is.
Applying a percentage to the wrong base. A classic error: if a price increases by 10% and then decreases by 10%, people often assume it returns to the original price. It doesn't — the second 10% is calculated on the new, higher number, so the final price ends up slightly lower than the original.
A percentage point is a raw difference between two percentages. If interest rates go from 5% to 7%, that's a 2 percentage point increase — but a 40% increase in relative terms (2 ÷ 5 × 100). Financial news often uses these interchangeably, which causes confusion.
Because each percentage is calculated from a different base. $100 increased by 50% is $150. But $150 decreased by 50% is $75, not $100 — the second calculation is 50% of a bigger number. This is the most common source of percentage confusion.
Use the "X is what % of Y" logic in reverse: if a discounted price of $80 reflects a 20% markdown, the discounted price is 80% of the original. Divide $80 by 0.80 to get the original price of $100.
Yes. A percentage over 100% just means the part is larger than the whole (200% of 10 is 20). A negative percentage change means a decrease — this calculator's "% change" tab shows a minus sign automatically when a value has gone down.
Both work the same way as "X% of Y" — a 15% tip on a $40 bill is 0.15 × 40 = $6. For sales tax, add the result to the original amount: $40 + $6 = $46 total. If you're specifically calculating a tip, the dedicated Tip Calculator also splits the bill between people.
Only if the underlying group sizes are equal. If 10 out of 20 people (50%) prefer option A in one survey, and 60 out of 100 people (60%) prefer it in another, the true combined rate is 70 out of 120 (about 58%) — not the simple average of 55%. Always go back to the raw counts when combining percentages from different-sized groups.
Because the second percentage is calculated on a different, changed base number. A $50 item increased by 10% becomes $55; that same $55 decreased by 10% becomes $49.50, not back to $50. The gap grows the larger the percentage — this is why marketing claims like "50% off, then an extra 50% off everything" sound more dramatic than the real combined discount actually is.