Percentage Calculator
How do I work out a percentage quickly?
Three everyday percentage problems, solved instantly. A percentage is simply a fraction of 100. Every percentage problem is one of three questions. "What is X% of Y?": multiply: Y × X ÷ 100. This is the math behind tips, taxes, discounts, and commissions. "X is what percent of Y?": divide the part by the whole: X ÷ Y × 100. If you got 45 out of 60 on a test, that's 45 ÷ 60 × 100 = 75%.
Three everyday percentage problems, solved instantly.
Last updated: October 2026
What is X% of Y?
Answer: 30
X is what percent of Y?
Answer: 75%
Percentage change (increase / decrease)
Answer: 25% increase
How percentage calculations work
A percentage is simply a fraction of 100. Every percentage problem is one of three questions. "What is X% of Y?": multiply: Y × X ÷ 100. So 20% of $150 is $150 × 20 ÷ 100 = $30. This is the math behind tips, taxes, discounts, and commissions.
"X is what percent of Y?": divide the part by the whole: X ÷ Y × 100. If you got 45 out of 60 on a test, that's 45 ÷ 60 × 100 = 75%. This is the formula behind grades, completion rates, and body-fat-style ratios.
"What is the percentage change?": take the difference, divide by the starting value: (New − Old) ÷ Old × 100. A stock moving from $40 to $50 rose 25%. Note the direction matters: going from $50 back to $40 is a 20% decrease, not 25%, the base changed. That asymmetry trips people up constantly with discounts and markups.
Percentage points vs. percent: a common trap
When a value that is already a percentage changes, two different numbers describe the move. If an interest rate rises from 5% to 7%, that is a 2 percentage point increase, but a 40% increase relative to where it started (2 ÷ 5 × 100). Headlines and salespeople often choose whichever sounds better: "rates up 40%" sounds scarier than "up 2 points," and a raise "from 2% to 3%" can be spun as a "50% increase."
The defense is simple: always ask "percent of what?" If someone quotes a percent change on a percent, convert it to percentage points to see the real size of the move.
Compounding percentages
Percentages applied in sequence do not add, they multiply. A 20% discount followed by another 20% discount is not 40% off: the second 20% applies to the already-reduced price, so you pay 80% × 80% = 64% of the original, a 36% total discount. The same math governs investment returns: +10% then −10% does not break even, $100 becomes $110, then $99.
This is why "stacking" discounts is less generous than it sounds, and why volatile investments need higher average returns just to stay flat. Whenever percentages chain together, multiply the remaining fractions instead of adding the percentages.
Percentages in everyday money math
Percentages quietly run most household money decisions. A mortgage rate, a credit card APR, a 401(k) contribution rate, a sales tax, a raise, all percentages. The skill that pays is translating them into dollars: 1% of a $60,000 salary is $600 a year, or $50 a month. When a number is quoted as a percent, multiply it out. "Just" 2% in extra fees on a $300,000 retirement account is $6,000 a year, percentages feel small until you attach them to big bases.
Tips for percentage problems
Convert to decimals for chained math. "30% off" is × 0.70; "8% tax" is × 1.08. Multiplying $120 × 0.70 × 1.08 = $90.72 gets you the jacket answer in one line.
Sanity-check the direction. A discount must lower the number; a markup must raise it. If your answer moves the wrong way, you multiplied when you should have divided.
Watch the base. "20% more than $50" is $60, but "20% less than $60" is $48, the base changed. Most percentage errors come from applying the percent to the wrong starting number.
Worked example: the three calculations everyone confuses
"45 is what percent of 180?" Divide the part by the whole: 45 / 180 = 0.25, which is 25%. This is the "what percent" question, and the answer always comes from part divided by whole.
"A price rises from $80 to $100. What is the percent increase?" Divide the change by the starting value: ($100 - $80) / $80 = 20 / 80 = 0.25, a 25% increase. The starting value is the denominator, which is why going from $100 back down to $80 is a 20% decrease, not 25%.
"What is $200 increased by 15%?" Multiply by one plus the rate: $200 x 1.15 = $230. For a decrease, multiply by one minus the rate instead: $200 reduced by 15% is $200 x 0.85 = $170.
Three percentage calculations, untangled
Most percentage confusion comes from mixing up three different questions. Percent of ("what is 15% of $200?") multiplies: 0.15 x 200 = $30. What percent ("$45 is what percent of $180?") divides part by whole: 25%. Percent change ("$80 to $100") divides the difference by the starting value: 25%.
The classic trap is treating a change symmetrically: a 25% rise followed by a 25% fall does not return to the start. $80 up 25% is $100, but $100 down 25% is $75, because the second percentage applies to a bigger base. Whenever a percentage surprises you, write down which number is the base, and the confusion usually dissolves.
Percentage FAQs
How do you calculate X percent of Y?
Multiply Y by X and divide by 100. Example: 20% of 150 = 150 × 20 ÷ 100 = 30. For chained math, convert to a decimal instead: 30% off means multiply by 0.70.
How do you find what percent one number is of another?
Divide the part by the whole and multiply by 100. Example: 45 ÷ 60 × 100 = 75%. This is the same formula behind grades, completion rates, and similar ratios.
How do you calculate percentage increase?
(New − Old) ÷ Old × 100. A price rising from $40 to $50 is a 25% increase. Remember the reverse trip uses a different base: $50 back to $40 is a 20% decrease, not 25%.
What is the difference between percent and percentage points?
Percentage points measure the absolute change between two percentages; percent change measures it relative to the starting value. A rate rising from 5% to 7% is up 2 percentage points but up 40% relative to 5%. Always ask 'percent of what?' when someone quotes a change on a percent.
Why isn't a 20% discount followed by another 20% off equal to 40% off?
Because the second discount applies to the already-reduced price. You pay 80% × 80% = 64% of the original, a 36% total discount, not 40%. Sequential percentages multiply; they never add.
How do you apply a discount and sales tax in one calculation?
Convert each to a multiplier and chain them: a 30% discount is × 0.70 and 8% tax is × 1.08, so $120 × 0.70 × 1.08 = $90.72. Order does not matter, multiplication commutes.
How do I find the original price before a sale?
Divide the sale price by one minus the discount rate. A $68 item after 15% off started at $68 / 0.85 = $80.00. The common mistake is adding 15% to $68, which gives $78.20, because the discount was taken off the original price, not the sale price.
How do I add a percentage to a number?
Multiply by one plus the decimal rate: $200 increased by 15% is $200 x 1.15 = $230. For decreases use one minus the rate: $200 decreased by 15% is $200 x 0.85 = $170. This single pattern handles tips, taxes, markups, and raises.
What does a one percentage point rate change mean?
If a rate moves from 5% to 6%, that is a one percentage point increase, but a 20% relative increase (1 divided by 5). Lenders and headlines sometimes blur the two, so always check which one is meant: one percentage point on a mortgage rate is a big deal, while a large relative rise on a small base may be less dramatic than it sounds.
How do I calculate the percent I saved?
Divide the amount saved by the original price. An item marked down from $120 to $90 saved you $30, and $30 / $120 = 25% off. Use the original price as the base, not the sale price: dividing by $90 would wrongly give 33%.