Percent Calculator Guide: How to Calculate Percentages (2026)
Quick Answer
- *Percent of a number: multiply by the percentage and divide by 100. (25% of 200 = 50)
- *Percentage change: ((New − Old) ÷ Old) × 100
- *Part as a percentage: (Part ÷ Whole) × 100
- *Reverse percentage: divide by (1 + rate) to find the original value before a markup.
What Does “Percent” Mean?
The word comes from the Latin per centum — “per hundred.” When you say 45%, you mean 45 out of every 100. It's a ratio with 100 as the denominator: 45% = 45/100 = 0.45. Percentages make it easy to compare fractions with different denominators on a common scale.
Three Core Percentage Calculations
1. Find a Percentage of a Number
Formula: Result = (Percentage ÷ 100) × Number
What is 15% of 240? Result = 0.15 × 240 = 36. This is the most common percentage calculation — used for tips, discounts, taxes, and commissions.
2. Find What Percentage One Number Is of Another
Formula: Percentage = (Part ÷ Whole) × 100
What percentage is 18 of 72? Percentage = (18 ÷ 72) × 100 = 25%. Useful for test scores, completion rates, and proportional analysis.
3. Find Percentage Change
Formula: Change = ((New − Old) ÷ Old) × 100
A stock goes from $50 to $65. Change = ((65 − 50) ÷ 50) × 100 = 30% increase.
The Percentage Asymmetry Trap
A 50% drop followed by a 50% gain does not return you to the starting point. If $100 drops 50% to $50, then gains 50%, you have $75 — not $100. Going down 50% requires a 100% gain to recover. This is why large losses are so devastating to investment portfolios.
Reverse Percentages
If a price is $84 after a 20% markup, what was the original? Divide by (1 + rate): $84 ÷ 1.20 = $70. For discounts, divide by (1 − rate): a $60 item after a 25% discount had an original price of $60 ÷ 0.75 = $80.
Percentage vs. Percentage Points
If an interest rate goes from 4% to 5%, that's a 1 percentage point increase but a 25% increase in the rate itself. The distinction matters in finance and statistics. “Inflation rose 2 percentage points” is different from “inflation rose 2%.”
Practical Applications
- Tipping: 20% tip on $85 = $85 × 0.20 = $17
- Sales tax: 8.25% tax on $42 = $42 × 0.0825 = $3.47
- Discounts: 30% off $120 = $120 × 0.70 = $84
- Grade calculation: 43 out of 50 = (43/50) × 100 = 86%
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How do you calculate a percentage of a number?
Multiply the number by the percentage and divide by 100. For example, 25% of 200 = (25 × 200) ÷ 100 = 50. Or convert to a decimal: 0.25 × 200 = 50.
How do you calculate percentage change?
Percentage change = ((New Value − Old Value) ÷ Old Value) × 100. A price going from $80 to $100 is a 25% increase. Note: percentage changes are not symmetric.
What is the difference between percentage and percentile?
A percentage is a fraction of 100. A percentile indicates ranking position — the 90th percentile means you scored higher than 90% of all values. They measure different things.
How do you find what percentage one number is of another?
Divide the part by the whole and multiply by 100. What percentage is 35 of 140? (35 ÷ 140) × 100 = 25%.
How do you calculate a reverse percentage?
Divide by (1 + rate) for markups or (1 − rate) for discounts. A $60 shirt after a 20% discount originally cost $60 ÷ 0.80 = $75.