How Percentages Work
A percentage expresses a quantity as a fraction of 100. The word “percent” literally means “per hundred.” For example, 25% represents 25 out of every 100, which is the same as 0.25 or one quarter.
Finding a Percentage of a Number
Convert the percentage to a decimal by dividing by 100, then multiply by the number. For example, 15% of 200 is 0.15 × 200 = 30.
Finding What Percent One Number Is of Another
Divide the first number by the second and multiply by 100. If 45 out of 180 items meet a condition, 45 ÷ 180 × 100 = 25%.
Calculating Percentage Change
Subtract the original value from the new value, divide that difference by the absolute value of the original, then multiply by 100. A positive result represents an increase and a negative result represents a decrease. Percentage change is undefined when the original value is zero.
Working Backward from a Percentage Change
If a $120 price is 20% higher than its original price, divide $120 by 1.20 to get $100. If a value is 20% lower than the original, divide the final value by 0.80 instead.
Everyday Percentage Examples
| Situation | Calculation | Result |
|---|
| 20% of $75 | 0.20 × 75 | $15 |
| $30 is what percent of $120? | 30 ÷ 120 × 100 | 25% |
| Price rises from $50 to $60 | (60 − 50) ÷ 50 × 100 | 20% increase |
| $80 after a 20% discount: original? | 80 ÷ 0.80 | $100 |
Percentage Points vs. Percent Change
These terms are different. If a rate rises from 10% to 12%, it increased by 2 percentage points. Relative to the original 10% rate, however, the increase is 20%.
Percentages Above 100%
Percentages can exceed 100%. For example, 150% of 40 equals 60. A 100% increase means the original amount has doubled; a 200% increase means it has tripled.
Frequently Asked Questions
How do I calculate 10% quickly?
Move the decimal point one place to the left. Ten percent of 250 is 25.
How do I calculate a discount?
Multiply the original price by the discount percentage to find the discount amount, then subtract it from the original price.
How do I add a percentage to a number?
Multiply the original number by 1 plus the percentage written as a decimal. To add 8%, multiply by 1.08.
How do I subtract a percentage from a number?
Multiply the original number by 1 minus the percentage written as a decimal. To reduce a number by 15%, multiply it by 0.85.
Why can’t percentage change use zero as the original value?
The standard percentage-change formula divides by the original value. Division by zero is undefined, so a conventional percentage change cannot be calculated from an original value of zero.
Are the calculator results rounded?
CalcPct displays practical rounded results while calculations use JavaScript numeric precision. For financial, tax, legal, or other consequential decisions, verify the required rounding rules for your situation.
About CalcPct
CalcPct is a free educational utility for common percentage calculations. The goal is to show both the answer and the underlying method so users can understand how each result is produced.