How to calculate percentages
Percentage calculations are based on percent proportions — the relationship between a part and a whole, expressed as a fraction of 100. There are three fundamental percentage formulas — each corresponds to one tab in the percent calculator above:
1. What is X% of Y?
Result = (X ÷ 100) × Y
Example: 15% of 200 = (15 ÷ 100) × 200 = 30
2. X is what % of Y?
Percentage = (X ÷ Y) × 100
Example: X is what percent of Y? 30 is what % of 200? → (30 ÷ 200) × 100 = 15%
3. Percent change
% Change = ((New − Old) ÷ Old) × 100
Example: 80 → 100 = ((100 − 80) ÷ 80) × 100 = 25% increase
Percentage change formula
Want to know how to find percent change? This percentage change calculator and percentage increase calculator uses a single formula that works for both increases and decreases:
% Change = ((New Value − Old Value) ÷ Old Value) × 100
A positive result means a percent increase. A negative result means a percent decrease. The formula always divides by the original (old) value — this is the reference point.
Percent increase vs. decrease
Percent increase
When the new value is larger than the old. Example: Stock price $40 → $52 = 30% increase. Formula: ((52−40) ÷ 40) × 100.
Percent decrease
When the new value is smaller than the old. Example: Price $100 → $75 = 25% decrease. Formula: ((75−100) ÷ 100) × 100 = −25%.
Key insight: A 50% increase followed by a 50% decrease does not return to the original. $100 + 50% = $150, then $150 − 50% = $75. You'd need a 33.3% decrease to reverse a 50% increase.
Common percentage calculations
Quick reference for tip percentages on common bill amounts:
| Bill | 15% | 18% | 20% | 25% |
|---|---|---|---|---|
| $25 | $3.75 | $4.50 | $5.00 | $6.25 |
| $50 | $7.50 | $9.00 | $10.00 | $12.50 |
| $75 | $11.25 | $13.50 | $15.00 | $18.75 |
| $100 | $15.00 | $18.00 | $20.00 | $25.00 |
| $150 | $22.50 | $27.00 | $30.00 | $37.50 |
| $200 | $30.00 | $36.00 | $40.00 | $50.00 |
Quick fact: 20% of 25 = 5, and 25% of 20 = 5. This isn't a coincidence — X% of Y always equals Y% of X because multiplication is commutative: (X/100) × Y = (Y/100) × X. Use this shortcut when one calculation is easier than the other.
How to calculate percent off (discounts)
Wondering how to calculate percent off a price? Whether you're shopping a sale or calculating a percent discount, the formula is straightforward:
Discount Amount = Original Price × (Percent Off ÷ 100)
Final Price = Original Price − Discount Amount
Example: An $80 item at 25% off — $80 × 0.25 = $20 discount, final price $60. To find out percent off any item, use Mode 1 ("X% of Y") above: enter the discount percentage and the original price to get the discount amount instantly.
| Original Price | 10% Off | 20% Off | 25% Off | 50% Off |
|---|---|---|---|---|
| $25 | $22.50 | $20.00 | $18.75 | $12.50 |
| $50 | $45.00 | $40.00 | $37.50 | $25.00 |
| $80 | $72.00 | $64.00 | $60.00 | $40.00 |
| $100 | $90.00 | $80.00 | $75.00 | $50.00 |
| $200 | $180.00 | $160.00 | $150.00 | $100.00 |
Percentage to decimal conversion
To convert a percentage to a decimal, divide by 100. To go the other way, multiply by 100.
| Percentage | Decimal | Fraction |
|---|---|---|
| 1% | 0.01 | 1/100 |
| 5% | 0.05 | 1/20 |
| 10% | 0.10 | 1/10 |
| 15% | 0.15 | 3/20 |
| 20% | 0.20 | 1/5 |
| 25% | 0.25 | 1/4 |
| 33.3% | 0.333 | 1/3 |
| 50% | 0.50 | 1/2 |
| 75% | 0.75 | 3/4 |
| 100% | 1.00 | 1/1 |
FAQs
How do you calculate a percentage?
To find what percentage one number is of another, divide the part by the whole and multiply by 100. Formula: Percentage = (Part ÷ Whole) × 100. For example, 30 out of 200 = (30 ÷ 200) × 100 = 15%.
What is the percentage change formula?
Percentage change = ((New Value − Old Value) ÷ Old Value) × 100. If the result is positive, it's a percent increase. If negative, it's a percent decrease. For example, going from 80 to 100: ((100 − 80) ÷ 80) × 100 = 25% increase.
What is the difference between percent increase and percent decrease?
Percent increase measures how much a value grew relative to the original (e.g., price went from $80 to $100 = 25% increase). Percent decrease measures how much it shrank (e.g., $100 to $80 = 20% decrease). Note: the percentages are different because the base value changes — a 25% increase followed by a 20% decrease returns to the original.
How do you convert a percentage to a decimal?
Divide the percentage by 100. For example: 25% = 25 ÷ 100 = 0.25. To go the other way (decimal to percentage), multiply by 100: 0.75 × 100 = 75%. This conversion is essential when using percentages in formulas or spreadsheets.
How do you find what percent one number is of another?
Divide the part by the whole, then multiply by 100. Example: What percent is 45 of 180? Answer: (45 ÷ 180) × 100 = 25%. Use the 'X is what % of Y?' tab in the calculator above.
What is 15% of 200?
15% of 200 = (15 ÷ 100) × 200 = 0.15 × 200 = 30. Use the 'What is X% of Y?' tab above for any calculation like this. Quick shortcut: 10% of 200 is 20, half of that (5%) is 10, so 15% = 20 + 10 = 30.
How do you calculate tip percentage?
To calculate a tip: multiply the bill by the tip percentage as a decimal. For a $75 bill at 20%: $75 × 0.20 = $15 tip, total $90. Quick mental math: find 10% (move the decimal point left one place), then double it for 20%, or add half for 15%.
How do you use percentage formulas in Excel?
In Excel or Google Sheets: To find X% of Y, use =X%*Y or =(X/100)*Y. To find what percent A is of B, use =A/B (then format as percentage). For percent change, use =(New-Old)/Old (format as percentage). Excel automatically handles the ×100 when you apply percentage formatting.
What is percent error?
Percent error measures how far an experimental or estimated value is from the true/accepted value. Formula: Percent Error = (|Measured − Actual| ÷ Actual) × 100. It's always expressed as a positive percentage. For example, if you estimated 105 but the actual value is 100, the percent error is 5%.
How do you calculate a discount percentage?
Discount percentage = ((Original Price − Sale Price) ÷ Original Price) × 100. For example, an item marked down from $80 to $60: ((80 − 60) ÷ 80) × 100 = 25% discount. To find the sale price from a discount: Sale Price = Original × (1 − Discount%). A 30% discount on $50 = $50 × 0.70 = $35.
How to calculate body fat percentage?
Body fat percentage = (fat mass ÷ total body weight) × 100. For example, if your fat mass is 30 lbs and you weigh 180 lbs: (30 ÷ 180) × 100 = 16.7% body fat. Common methods to measure fat mass include skinfold calipers, bioelectrical impedance scales, and DEXA scans. For a more detailed health assessment, try our BMI calculator.