How to Calculate Percentages: Formulas and Examples
Updated: March 2026 · Category: Math & Education
Percentages are one of the most practical math concepts you will use in everyday life. From calculating a tip at a restaurant to figuring out how much you save during a sale, understanding percentages is an essential skill. This guide covers all the key formulas with step-by-step examples you can follow.
What Is a Percentage?
The word “percent” comes from the Latin per centum, meaning “by the hundred.” A percentage is simply a way of expressing a number as a fraction of 100. For example, 45% means 45 out of 100, or 45/100, which equals 0.45 as a decimal.
Percentage = (Part ÷ Whole) × 100
Formula 1: Finding X% of a Number
Result = Number × (Percentage ÷ 100)
Example: What is 15% of 200?
- Convert the percentage to a decimal: 15 ÷ 100 = 0.15
- Multiply: 200 × 0.15 = 30
So, 15% of 200 is 30.
Formula 2: What Percentage Is X of Y?
Percentage = (X ÷ Y) × 100
Example: What percentage is 35 of 140?
- Divide the part by the whole: 35 ÷ 140 = 0.25
- Multiply by 100: 0.25 × 100 = 25%
So, 35 is 25% of 140.
Formula 3: Percentage Increase
% Increase = ((New Value − Old Value) ÷ Old Value) × 100
Example: A product’s price went from $80 to $100. What is the percentage increase?
- Find the difference: 100 − 80 = 20
- Divide by the original value: 20 ÷ 80 = 0.25
- Multiply by 100: 0.25 × 100 = 25%
The price increased by 25%.
Formula 4: Percentage Decrease
% Decrease = ((Old Value − New Value) ÷ Old Value) × 100
Example: A shirt was $60 and is now on sale for $45. What is the percentage discount?
- Find the difference: 60 − 45 = 15
- Divide by the original value: 15 ÷ 60 = 0.25
- Multiply by 100: 0.25 × 100 = 25%
The shirt is discounted by 25%.
Quick-Reference Table
| Task | Formula | Example | Result |
|---|---|---|---|
| Find X% of N | N × (X/100) | 20% of 150 | 30 |
| X is what % of Y | (X/Y) × 100 | 45 of 180 | 25% |
| % Increase | ((New−Old)/Old) × 100 | 50 → 65 | 30% |
| % Decrease | ((Old−New)/Old) × 100 | 80 → 60 | 25% |
Real-World Applications
Calculating a Tip
At a restaurant, you want to leave a 20% tip on a $65 bill:
65 × 0.20 = $13.00 tip. Total: $65 + $13 = $78.00.
Calculating Sales Tax
You are buying a laptop for $899 in a state with 8.25% sales tax:
899 × 0.0825 = $74.17 in tax. Total: $899 + $74.17 = $973.17.
Finding a Sale Price
A $120 jacket is marked 30% off:
Discount: 120 × 0.30 = $36. Sale price: 120 − 36 = $84.00.
Grade Calculations
You scored 42 out of 50 on a test. What is your grade?
(42 ÷ 50) × 100 = 84%.
Common Mistakes to Avoid
- Confusing percentage increase with percentage points. Going from 20% to 25% is a 5 percentage-point increase, but a 25% relative increase.
- Applying percentage decrease then increase (or vice versa) and expecting the same number. A 20% decrease followed by a 20% increase does not return you to the original value.
- Dividing by the wrong base. For percentage increase, always divide by the original (old) value, not the new value.
Calculate Percentages Instantly
Use our free Percentage Calculator to solve any percentage problem instantly. Whether you need to find a percentage of a number, calculate a percentage change, or work out a tip, our tool does the math for you in one click.