What is a percentage?
A percentage is a way of expressing a number as a fraction of 100. The word comes from the Latin per centum, meaning “by the hundred.” When you say 45%, you mean 45 out of every 100 — or 0.45 as a decimal.
Percentages appear in almost every area of daily life: interest rates, discounts, test scores, nutrition labels, tax rates, polling results, and financial reports. The math behind all of them comes down to three formulas.
The key conversion
To convert a percentage to a decimal, divide by 100. To convert a decimal back to a percentage, multiply by 100.
45% = 45 ÷ 100 = 0.45
0.08 = 0.08 × 100 = 8%
The three percentage formulas
Formula 1
Find a percentage of a number
Result = (Percentage ÷ 100) × Number
What is 20% of 85?
- →Convert the percentage to a decimal: 20 ÷ 100 = 0.20
- →Multiply by the number: 0.20 × 85 = 17
- →Answer: 20% of 85 is 17
Formula 2
Find what percent one number is of another
Percentage = (Part ÷ Whole) × 100
What percent is 34 of 200?
- →Divide the part by the whole: 34 ÷ 200 = 0.17
- →Multiply by 100: 0.17 × 100 = 17
- →Answer: 34 is 17% of 200
Formula 3
Calculate percentage change
Change % = ((New − Old) ÷ Old) × 100
A price went from $80 to $92. What is the percentage increase?
- →Subtract old from new: 92 − 80 = 12
- →Divide by the old value: 12 ÷ 80 = 0.15
- →Multiply by 100: 0.15 × 100 = 15
- →Answer: a 15% increase
How to handle percentage decrease
Formula 3 works for decreases too — the result will just be a negative number. A negative percentage change means the value went down.
Example: A product price dropped from $200 to $170.
Step 1: 170 − 200 = −30
Step 2: −30 ÷ 200 = −0.15
Step 3: −0.15 × 100 = −15%
Answer: a 15% decrease
The sign tells you the direction. Positive means increase, negative means decrease. When reporting, drop the negative sign and say “decreased by 15%” — the word decrease already carries the direction.
Percentage vs percentage points
These two terms are often confused, and the difference matters in financial and statistical contexts.
Percentage change
A relative change. If an interest rate rises from 4% to 5%, that is a 25% increase (1 ÷ 4 × 100).
Percentage points
An absolute difference. If an interest rate rises from 4% to 5%, that is a 1 percentage point increase.
Politicians and financial commentators sometimes exploit this distinction. A rate going from 2% to 3% sounds small (“just one percentage point”) but is actually a 50% increase in relative terms. Pay attention to which unit is being used.
Real-world examples
Discount at checkout
An item costs $120 and is 25% off. Use Formula 1: 25% of $120 = $30 off → you pay $90.
Test scores
You got 43 out of 50 questions right. Use Formula 2: (43 ÷ 50) × 100 = 86%.
Salary increase
Your salary went from $52,000 to $57,200. Use Formula 3: ((57200 − 52000) ÷ 52000) × 100 = 10% raise.
Sales tax
A product is $45 before 8% tax. Use Formula 1: 8% of $45 = $3.60 → total $48.60.
Body weight change
You went from 185 lbs to 172 lbs. Use Formula 3: ((172 − 185) ÷ 185) × 100 = −7.0% (a 7% decrease).
Campaign conversion rate
340 people clicked and 17 converted. Use Formula 2: (17 ÷ 340) × 100 = 5% conversion rate.
Common percentage mistakes
Adding percentages directly
If a price rises 50% and then falls 50%, you do not end up where you started. A $100 item rises to $150, then 50% of $150 = $75. The base changes each time. Always apply percentages to the current value, not the original.
Confusing percent of and percent more than
"30% of $200" is $60. "30% more than $200" is $260 ($200 + $60). These are different calculations — one finds a portion, the other adds a portion.
Using the wrong base in Formula 3
Percentage change always divides by the original (old) value, not the new value. Dividing by the new value gives a different result and is a common error in financial analysis.
Rounding before the final step
Round only the final answer, not intermediate steps. Early rounding compounds errors, especially in multi-step calculations.
Quick reference
| What you want to find | Formula |
|---|---|
| X% of a number | (X ÷ 100) × Number |
| What % is Part of Whole | (Part ÷ Whole) × 100 |
| % change from Old to New | ((New − Old) ÷ Old) × 100 |
| Value after X% increase | Number × (1 + X ÷ 100) |
| Value after X% decrease | Number × (1 − X ÷ 100) |