Percentage Calculator

The word percent comes from the Latin per centum, meaning "per hundred." A percentage is a fraction with 100 as the denominator: 25% is the same as 25/100, which equals 0.25. Percentages are useful because they give a unit-free way to compare proportions across different scales — a 10% tip on a $20 bill and a 10% tip on a $200 bill scale the same way.

Almost every percentage problem fits one of three patterns:

• What is X% of Y?   →   (X/100) × Y
  Example: What is 18% of 250? 0.18 × 250 = 45.
• X is what percent of Y?   →   (X/Y) × 100
  Example: 32 is what percent of 80? (32/80) × 100 = 40%.
• X is Y% of what?   →   X / (Y/100)
  Example: 60 is 25% of what? 60 / 0.25 = 240.

To express a change from an old value to a new value:

A positive result is a percent increase, a negative result a percent decrease. Sales going from 200 to 250 is (250 − 200) / 200 × 100 = 25% growth.

A common mistake: the inverse of a 25% increase is not a 25% decrease. To undo a 25% increase you need a 20% decrease, because the larger number is now the base. Always check which value is the denominator.

These are not the same. If interest rates rise from 5% to 7%:

• The increase is 2 percentage points (absolute difference).
• The increase is 40 percent (relative — (7 − 5)/5 × 100).

Headlines sometimes mix these up to dramatize numbers. Reading "rates up 40%" sounds bigger than "rates up 2 points" but they describe the same change.

• 10% — move decimal one place left. 10% of $87 is $8.70.
• 1% — move decimal two places left. 1% of $87 is $0.87.
• 5% — half of 10%.
• 15% — 10% plus half of 10%.
• 20% — double 10%, or divide by 5.
• 25% — divide by 4.
• X% of Y = Y% of X. Sometimes one direction is easier — 8% of 25 is hard; 25% of 8 is just 2.

• Tipping: 18–20% of the pre-tax restaurant bill in the US.
• Sales tax: add the local rate (often 5–10%) to the subtotal.
• Discounts: "30% off" means pay 70% of the original price.
• Markup vs margin: a 50% markup on a $10 cost gives a $15 price; the margin is 33.3% (profit ÷ price).
• Grades: percent of total points possible.
• Statistics: proportions in survey data are almost always reported as percentages.