Percentage Calculator

What Is a Percentage?

"Percent" literally means "per hundred" (from the Latin per centum). A percentage is a ratio expressed as a fraction of 100. So 25% means 25 out of every 100, or 25/100 = 0.25 as a decimal.

Converting between forms is simple: to go from a percent to a decimal, divide by 100. To go from a decimal to a percent, multiply by 100. To go from a fraction to a percent: divide the numerator by the denominator, then multiply by 100.

Percentages appear everywhere in daily life: sales tax, discounts, interest rates, tips, test scores, investment returns, nutrition labels, and polling data. A solid intuition for percentages is one of the most practically valuable math skills you can have.

The Three Core Percentage Problems

Nearly every percentage question falls into one of three types:

• 1.
  Find the percentage of a number:"What is 20% of $85?" Multiply the number by the decimal form of the percentage: 85 × 0.20 = $17.
• 2.
  Express as a percentage:"30 is what percent of 120?" Divide part by whole, then multiply by 100: (30/120) × 100 = 25%.
• 3.
  Find percentage change:"A $50 item now costs $60 — what's the percent increase?" ((60-50)/50) × 100 = 20% increase.

Percentage Change vs. Percentage Points

One of the most common sources of confusion (and misleading statistics) is the difference between "percentage change" and "percentage points."

Suppose interest rates rise from 2% to 3%. That is an increase of 1 percentage point. But it is also a 50% increase in the rate itself (from 2 to 3 is 1/2 = 50% relative change).

Politicians and advertisers often exploit this distinction. When a tax rate "falls by 5 percentage points," the relative percentage decrease is much larger if the starting rate was low. Always clarify which type of change is being reported.

Mental Math Tips for Percentages

With a few tricks, you can often calculate percentages in your head faster than reaching for a calculator:

• •10% of anything: Move the decimal point one place to the left. 10% of $74 = $7.40.
• •5%: Halve your 10% answer. 5% of $74 = $3.70.
• •15%: Add 10% + 5%. 15% of $74 = $7.40 + $3.70 = $11.10.
• •Reverse the numbers: X% of Y = Y% of X. So 4% of 75 = 75% of 4 = 3. This can make mental math easier.
• •1%: Move the decimal two places left. 1% of $340 = $3.40. Then scale up or down as needed.

Real-World Applications

Understanding percentages helps you make better financial decisions every day:

• •Discounts: A "30% off" item at $120 costs $84. Multiply the original price by (1 - discount rate): 120 × 0.70 = $84.
• •Sales tax: To find the total with 8% tax, multiply by 1.08. A $50 item becomes $54.
• •Investment returns: A $10,000 investment that grows 7% per year becomes $10,700 after one year. After 10 years (compounded), it becomes $19,672 — not $17,000.
• •Pay raises: A 5% raise on a $60,000 salary adds $3,000. To find the new salary: 60,000 × 1.05 = $63,000.

Common Percentage Mistakes

• •Adding percentages sequentially: A 20% discount followed by a 10% discount is NOT a 30% discount. It is 28% off (0.80 × 0.90 = 0.72 = 28% off).
• •Asymmetric reversals: A 50% loss requires a 100% gain to break even. If your $100 drops to $50 (-50%), you need to double it (+100%) to recover.
• •Confusing the base: "20% of what number is 30?" Divide 30 by 0.20 = 150. The base matters.

Avoiding these mistakes can save you significant money — especially when evaluating investment returns, compound interest, and promotional pricing.