Percentage Calculator
Calculate percentages instantly. Find X% of a number, figure out what percent one number is of another, or calculate percentage change.
All calculations are exact to the precision shown. Use this calculator for everyday math, homework, finance, and shopping.
How the Percentage Calculator Works
This calculator handles the three most common percentage calculations. Choose a mode and enter the required values.
Mode 1: What is X% of Y?
Use this when you need to find a portion of a number. Example: "What is 15% tip on a $60 bill?"
Formula: Result = Y × X ÷ 100
- 15% of $60 = 60 × 15 ÷ 100 = $9.00
- 20% of $85 = 85 × 20 ÷ 100 = $17.00
Mode 2: X is what percent of Y?
Use this when you know two numbers and want to find the percentage. Example: "I scored 42 out of 60 on a test — what's my percentage?"
Formula: Percentage = X ÷ Y × 100
- 42 out of 60 = 42 ÷ 60 × 100 = 70%
- $15 tip on a $60 bill = 15 ÷ 60 × 100 = 25%
Mode 3: Percentage change from X to Y
Use this to find the percentage increase or decrease between two values. Example: "My salary went from $50K to $58K — what's the raise?"
Formula: % Change = (Y − X) ÷ X × 100
- $50K → $58K = (58000 − 50000) ÷ 50000 × 100 = +16% increase
- $120 → $90 = (90 − 120) ÷ 120 × 100 = −25% decrease
Percentage Basics
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." Percentages are used everywhere — from grades and sales tax to interest rates and nutritional labels.
Quick mental math tricks
- 10% — move the decimal one place left. 10% of $250 = $25.
- 5% — find 10%, then halve it. 5% of $250 = $12.50.
- 1% — move the decimal two places left. 1% of $250 = $2.50.
- 20% — find 10%, then double it. 20% of $250 = $50.
- 25% — divide by 4. 25% of $200 = $50.
- 50% — divide by 2. 50% of $80 = $40.
Combine these building blocks for any percentage. Need 18%? Take 20% and subtract 2% (which is 1% doubled). Need 35%? Take 25% and add 10%.
Common fraction-to-percentage conversions
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333 | 33.3% |
| 1/4 | 0.25 | 25% |
| 1/5 | 0.2 | 20% |
| 1/8 | 0.125 | 12.5% |
| 2/3 | 0.667 | 66.7% |
| 3/4 | 0.75 | 75% |
| 3/8 | 0.375 | 37.5% |
| 5/8 | 0.625 | 62.5% |
Worked Examples
Example 1: Calculating a restaurant tip
Your dinner bill is $73.50 and you want to leave a 20% tip. How much is the tip?
- Using Mode 1: What is 20% of $73.50?
- $73.50 × 20 ÷ 100 = $14.70
- Total with tip: $73.50 + $14.70 = $88.20
Example 2: Test score percentage
You got 37 questions right out of 45 on a biology exam. What's your score?
- Using Mode 2: 37 is what % of 45?
- 37 ÷ 45 × 100 = 82.2%
- That's a solid B grade.
Example 3: Salary increase
Your salary went from $62,000 to $71,300. What's the percentage raise?
- Using Mode 3: % change from 62000 to 71300
- (71300 − 62000) ÷ 62000 × 100 = 9300 ÷ 62000 × 100 = +15% increase
Example 4: Sale price comparison
A jacket was $145 last month and is now $87. What's the discount?
- Using Mode 3: % change from 145 to 87
- (87 − 145) ÷ 145 × 100 = −58 ÷ 145 × 100 = −40% (40% off)
Common Percentage Mistakes
- Adding percentages that apply to different bases. If rent goes up 10% and food goes up 10%, your total expenses don't go up 10% — they go up by different amounts depending on how much you spend on each.
- Thinking a 50% increase + 50% decrease = back to start. It doesn't. $100 + 50% = $150. $150 − 50% = $75. You've lost $25 because the decrease is taken from a larger number.
- Confusing "percentage points" with "percent." If interest rates go from 4% to 6%, that's a 2 percentage point increase — but a 50% increase (2 ÷ 4 = 0.50). Journalists often mix these up.
- Rounding too early. When chaining percentage calculations, keep full precision until the final answer. Rounding at each step introduces cumulative errors.
Real-World Percentage Applications
Percentages appear everywhere in daily life. Here's how to handle the most common situations:
Sales tax and VAT
If your local sales tax is 8.25% and you buy something for $45.99:
- Tax amount: $45.99 × 8.25 ÷ 100 = $3.80
- Total with tax: $45.99 + $3.80 = $49.79
Quick shortcut: multiply the price by (1 + tax rate). $45.99 × 1.0825 = $49.79 in one step.
Restaurant tips
For a 20% tip on a $67 bill:
- Find 10% first: $6.70
- Double it for 20%: $13.40
- Total with tip: $67 + $13.40 = $80.40
Split between 3 people: $80.40 ÷ 3 = $26.80 each.
Discounts and sale prices
A $89 shirt is marked 35% off:
- Discount: $89 × 35 ÷ 100 = $31.15
- Sale price: $89 − $31.15 = $57.85
- Shortcut: $89 × 0.65 = $57.85 (multiply by the complement)
Interest rates and returns
You invest $5,000 at a 4.5% annual interest rate:
- Annual return: $5,000 × 4.5 ÷ 100 = $225
- After 1 year: $5,000 + $225 = $5,225
- After 3 years (simple interest): $5,000 + ($225 × 3) = $5,675
With compound interest, each year's interest earns interest too — use our compound interest calculator for that.
Percentage error and accuracy
You predicted 150 attendees but 132 showed up. What's the error?
- Absolute error: |150 − 132| = 18
- Percentage error: (18 ÷ 150) × 100 = 12% off
This is useful for evaluating estimates, measurements, and predictions.
Percentage Quick Reference
Common percentages with their decimal equivalents and quick calculation methods:
| Percentage | As Decimal | Multiply by | Mental Trick |
|---|---|---|---|
| 5% | 0.05 | × 0.05 | 10% then halve it |
| 10% | 0.10 | × 0.10 | Move decimal one place left |
| 12.5% | 0.125 | × 0.125 | Divide by 8 |
| 15% | 0.15 | × 0.15 | 10% + half of 10% |
| 20% | 0.20 | × 0.20 | Double 10% |
| 25% | 0.25 | × 0.25 | Divide by 4 |
| 30% | 0.30 | × 0.30 | Triple 10% |
| 33.3% | 0.333 | × 0.333 | Divide by 3 |
| 40% | 0.40 | × 0.40 | Double 20% |
| 50% | 0.50 | × 0.50 | Divide by 2 |
| 75% | 0.75 | × 0.75 | Subtract 25% (÷4) |
| 90% | 0.90 | × 0.90 | Subtract 10% |
The "Multiply by" column gives you the fastest path: just multiply any number by that decimal. For mental math, use the tricks in the right column — they're faster than any calculator.
Frequently Asked Questions
To find X% of Y: multiply Y by X ÷ 100. Example: 20% of 150 = 150 × 0.20 = 30. To find what % X is of Y: divide X by Y × 100. Example: 30/150 × 100 = 20%.
((New − Old) ÷ Old) × 100. Price from $80 to $100: (100−80)÷80×100 = +25%. Price from $120 to $90: (90−120)÷120×100 = −25%.
Multiply by (1 + X/100). Add 15% to $80: $80 × 1.15 = $92. To subtract: multiply by (1 − X/100). Subtract 20% from $50: $50 × 0.80 = $40.
Move the decimal one place left. 10% of $250 = $25. Then build from there: 20% = double, 5% = half, 15% = 10% + 5%. This works for any number.
Divide numerator by denominator, multiply by 100. 3/8 = 0.375 × 100 = 37.5%. Common ones: 1/4=25%, 1/3=33.3%, 1/2=50%, 2/3=66.7%, 3/4=75%.
Because the second percentage applies to a different base. $100 + 50% = $150. Then 50% of $150 = $75, not $100. The decrease is taken from the larger number, so it's bigger in absolute terms.
If a rate goes from 4% to 6%, that's a 2 percentage point change. But in percent terms, it's a 50% increase (2÷4=0.50). "Percentage points" describe absolute differences; "percent" describes relative change.
Same formula as percentage change: ((Old − New) ÷ Old) × 100 gives a positive decrease. $120 item now $90: (120−90)÷120×100 = 25% decrease. Or use Mode 3 on this calculator.