Percentage Calculator guide
Solve every everyday percentage problem in one place: what is 20% of 150, what percent is 30 of 120, how much did a price change, and what a number becomes after a percent increase or decrease.
The three percentage questions
Almost every percentage problem is one of three questions. What is X percent of Y? Multiply: 20% of 50 = 0.20 × 50 = 10. X is what percent of Y? Divide and multiply by 100: 45 is what percent of 60? 45 ÷ 60 × 100 = 75%. What is the percent change from A to B? (B − A) ÷ A × 100.
This calculator answers all three at once from the same inputs, so you can check your mental math without re-entering numbers.
Percent change is not symmetric
Going from 80 to 100 is a 25 percent increase: (100 − 80) ÷ 80 = 0.25. Going from 100 back to 80 is a 20 percent decrease: (80 − 100) ÷ 100 = −0.20. The base changes, so the percentage changes. This trips up everyone from students to journalists.
It gets worse with repeated changes. A stock that rises 10 percent and then falls 10 percent does not break even. 1.10 × 0.90 = 0.99, a 1 percent loss. A 50 percent drop needs a 100 percent gain to recover.
Worked examples from real life
Discounts: a $120 jacket at 25 percent off costs $120 × 0.75 = $90. Stacked discounts multiply, not add: 20 percent off and then an extra 10 percent off is 0.80 × 0.90 = 0.72, so 28 percent off total, not 30.
Raises: your salary goes from $62,000 to $65,500. (65,500 − 62,000) ÷ 62,000 = 5.6 percent. If inflation that year was 3 percent, your real raise was closer to 2.6 percent.
Test scores: 43 correct out of 50 is 43 ÷ 50 = 86 percent. To hit 90 percent on a 50-question test you need 45 right.
Reverse percentages: if a price after a 15 percent markup is $230, the original was 230 ÷ 1.15 = $200. Do not subtract 15 percent of $230; that gives $195.50, which is wrong.
Percent versus percentage points
If an interest rate moves from 4 percent to 5 percent, it rose by 1 percentage point, but by 25 percent in relative terms. News headlines mix these up constantly. Use points when comparing two percentages directly and percent when describing relative change.
Percentages in money decisions
Credit cards quote an APR, but interest is charged monthly. A 24 percent APR is 2 percent a month. On a $3,000 balance, that is about $60 of interest in one month if you carry it. Savings accounts work in reverse: 4.5 percent APY on $10,000 earns roughly $450 over a year.
Sales tax, tips, discounts, raises, and investment returns are all percentage problems. The most expensive mistake is confusing percent of the original with percent of the new amount. If a stock drops from $100 to $60, it is down 40 percent, and it now needs to rise 67 percent, not 40, to get back to $100.
Percentages in data and statistics
When someone says a risk "doubled", ask about the base rate. A side effect that goes from 1 in 10,000 to 2 in 10,000 has doubled, a 100 percent relative increase, but the absolute increase is 0.01 percentage points. Both numbers are true; only one tells you how worried to be.
Survey results need the same care. "60 percent of respondents" means little without the sample size. Sixty percent of 20 people is 12 people. For comparisons, calculate percentages on the same base, and always say what the percentage is of.
Mental math shortcuts
10 percent: move the decimal one place left. 5 percent: half of that. 20 percent: double 10 percent. 15 percent: 10 percent plus half of it. 1 percent: move the decimal two places.
Percentages are reversible: 8 percent of 25 equals 25 percent of 8, which is 2. When one direction is hard, flip it. Everything here runs locally, so it is fast even offline.
Frequently asked questions
How do I calculate a percentage of a number?
Divide the percent by 100 and multiply by the number. 20% of 150 is 0.20 × 150 = 30.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100. 30 out of 120 is 30 ÷ 120 × 100 = 25%.
What is the difference between percent change and percent difference?
Percent change has a direction and uses the starting value as the base: 80 to 100 is +25%. Percent difference compares two values with no before or after, dividing the gap by their average: |100 − 80| ÷ 90 × 100 = 22.2%.
Why is a 50% drop not undone by a 50% gain?
Because each percent is taken from a different base. $100 down 50% is $50, and $50 up 50% is only $75. You need a 100% gain to get back to $100.
How do I add a percentage to a number?
Multiply by 1 plus the percent as a decimal. 60 increased by 15% is 60 × 1.15 = 69. To subtract 15%, multiply by 0.85 instead: 51.
What is the difference between percent and percentage points?
Percentage points measure the gap between two percentages. A rate going from 4% to 5% is up 1 percentage point, but that is a 25% increase in the rate itself.
Is this client-side?
Everything runs in your browser. Nothing you enter is uploaded to a server or stored by us.
How do I calculate percentage increase?
Subtract the old value from the new value, divide by the old value, then multiply by 100. From 80 to 100 is (100 − 80) ÷ 80 × 100 = 25 percent.
How do I find the original price before a discount?
Divide the sale price by (1 − discount). A $90 item at 25 percent off was originally 90 ÷ 0.75 = $120.