How to Calculate Percentages: 3 Useful Formulas
Learn the three percentage formulas that cover most everyday questions, with examples for discounts, ratios, increases, and decreases.
Most percentage questions are variations of three calculations. Once you know which number is the base, the arithmetic is usually simple. The examples below show the formulas, why they work, and the mistakes that most often produce the wrong answer.
1. Find a percentage of a number
Use this when the question is “What is 15% of 80?” Convert the percentage to a decimal and multiply:
15 ÷ 100 = 0.15
80 × 0.15 = 12
So 15% of 80 is 12. The same method works for tips, commissions, tax estimates, discounts, and any “X percent of Y” question.
Shortcut for adding a percentage
To add 15% to a value, multiply by 1.15. To subtract 15%, multiply by 0.85.
2. Find what percentage one number is of another
Use this when you know a part and a total. The formula is:
part ÷ whole × 100
If 18 people out of 72 completed a task, 18 ÷ 72 × 100 = 25%.
The order matters. Dividing 72 by 18 answers a different question.
3. Calculate percentage change
Use the original value as the denominator:
(new − old) ÷ old × 100
If revenue moves from $80,000 to $100,000, the change is 20,000 ÷ 80,000 × 100 = 25%.
Why a 25% increase and 25% decrease do not cancel out
Start at 100. A 25% increase gives 125. A 25% decrease from 125 removes 31.25, leaving 93.75. The percentage is being applied to a different base the second time.
Reverse a percentage correctly
If a price already includes a 20% increase, do not subtract 20% to recover the original. Divide by 1.20. For example, 120 ÷ 1.20 = 100.
Percentage points vs percent change
If a rate moves from 20% to 25%, it increased by 5 percentage points. Relative to the original 20%, that is a 25% increase. Both statements can be correct, but they describe different things.
Quick checklist
- Identify the original or whole value.
- Decide whether you need a portion, a ratio, or a change.
- Convert percentages to decimals before multiplying.
- Keep enough decimal places during the calculation and round at the end.
Frequently asked questions
How do I calculate a percentage without a calculator?
Break the percentage into easy parts. Ten percent is one tenth, 5% is half of 10%, and 1% is one hundredth. For 15% of 80, 10% is 8 and 5% is 4, giving 12.
What if the starting value is zero?
The standard percentage-change formula divides by the original value, so a change from zero does not have a finite percentage increase under that formula.