Percentage Calculator

What is X% of Y?

Multiply Y by X ÷ 100. 15% of 200 is 200 × 0.15 = 30. This is the most common percentage calculation — tips, taxes, discounts, and commissions all use this same formula, just with different numbers plugged in.

It works in either order: X% of Y always equals Y% of X. If 8% of 25 is awkward, flip it to 25% of 8, which is 2. For a tip on a restaurant bill, the tip calculator runs this same step, then adds tax and splits the total.

X is what % of Y?

Divide X by Y and multiply by 100. A team that wins 30 out of 120 games has a win percentage of 30 ÷ 120 × 100 = 25%. The same formula works for test scores, survey response rates, or any "part of a whole" question.

Grades work this way too: 42 correct out of 48 questions is 42 ÷ 48 × 100 = 87.5%. When different assignments carry different weights, a plain percentage isn't enough, and the grade calculator handles the weighting.

Percentage increase & decrease

Subtract the starting value from the ending value, divide by the starting value, and multiply by 100 — positive means an increase, negative means a decrease. Weight-loss percentage uses this exact formula: losing weight from 200 lb to 150 lb is a (150 − 200) ÷ 200 × 100 = −25% change, a 25% decrease.

Direction matters, because the starting value is the denominator. Going from 80 to 100 is a 25% increase, but going from 100 back to 80 is a 20% decrease. The gap is 20 both times. Only the base you divide by changes.

Markup percentage

Markup is how much a sale price exceeds cost, as a percentage of cost — mathematically identical to percentage increase, with cost as the "from" value and price as the "to" value. A $10 cost sold at $15 is a (15 − 10) ÷ 10 × 100 = 50% markup. This is different from profit margin, which divides by the sale price instead of the cost.

The same $10 cost and $15 price give a 50% markup but a (15 − 10) ÷ 15 × 100 = 33.3% margin. Margin can never reach 100%, but markup can go far beyond it. Pricing questions that start from a target margin are easier in the margin calculator.

Percent change vs. percent difference

Percent change has a direction: an old value and a new one, with the old value as the base. Percent difference compares two values that are on equal footing, such as the price of the same TV at two stores or two lab measurements. Neither one is the "before", so the formula divides by their average instead: |A − B| ÷ ((A + B) ÷ 2) × 100.

For 40 and 60, the difference is 20 and the average is 50, so the percent difference is 40% whichever way round you enter them. Percent change gives +50% going from 40 to 60 and −33.3% going from 60 to 40. Use the "% Difference" mode when there's no natural starting point, and "% Change" when there is one. Percent error, used in science classes, is a third variant: |measured − true| ÷ true × 100, with the true value as the base.

Percentage points vs. percent

When the values you're comparing are themselves percentages, two different numbers describe the change. If a savings rate rises from 3% to 4%, it went up by 1 percentage point, which is the plain subtraction 4 − 3. It also went up by 33.3 percent, the relative change (4 − 3) ÷ 3 × 100.

Both are correct, but they mean very different things. "Unemployment rose 2 percent" and "unemployment rose 2 percentage points" (say, from 5% to 7%) describe changes that differ by a factor of 20. Loan and interest rates, tax rates, poll results, and test pass rates should usually be compared in points, with the relative change as context.

Reverse percentages: finding the original number

A reverse percentage starts from a result and works back to the number it came from. If 30 is 25% of something, that something is 30 ÷ 0.25 = 120. The same idea undoes an increase or a discount. Turn the change into a multiplier, then divide by it:

• A price of $120 after a 20% rise: $120 ÷ 1.20 = $100 originally.
• A sale price of $68 after 15% off: $68 ÷ 0.85 = $80 originally. The discount calculator does this with stacked discounts too.
• A receipt total of $54 including 8% tax: $54 ÷ 1.08 = $50 before tax.

The trap is to apply the same percentage in the opposite direction. Taking 20% off $120 gives $96, not $100, because 20% of $120 is larger than 20% of $100. Enter the result and the percentage it represents (120 for a 20% rise, 85 for 15% off) in the "Reverse %" mode.

Worked percentage examples

Each row shows which mode to use and the arithmetic behind it:

Common percentage mistakes

• Adding successive percentages. A 10% rise followed by another 10% rise is 1.10 × 1.10 = 1.21, a 21% total increase, not 20%. Stacked discounts shrink the same way: 20% off then 10% off is 28% off.
• Expecting gains and losses to cancel. Down 25% then up 25% leaves you at 0.75 × 1.25 = 0.9375 of where you started, a 6.25% net loss.
• Using the wrong base. "Prices are 20% higher than last year" divides by last year's price. Dividing by this year's price instead understates the rise.
• Mixing up points and percent. A rate moving from 2% to 3% is a 1-point rise but a 50% increase.
• Percent change from zero. Change from 0 is undefined, because there's no base to divide by. Report the absolute change instead. The calculator flags a zero starting value rather than showing a misleading number.
• Averaging percentages directly. 50% of 10 and 90% of 1,000 don't average to 70%. Combine the underlying counts: 5 + 900 out of 1,010 is about 89.6%.