Percentage Calculator
Select the operation below: calculate percentage value, share percentage or change percentage. Enter numbers and the result updates immediately.
How much is X% of Y?
15% of 200 is
What % of Y is X?
Share of the whole
By what percentage did the value change?
Change
Change in numbers
What Does Percentage Mean?
Percentage (%) literally means "per hundred" (Latin: per centum). It is one of the most fundamental mathematical concepts used in everyday life — from shopping discounts and tax rates to exam scores and investment returns. Understanding how to calculate percentages quickly can save you time and money in dozens of daily situations.
- 100% = the whole amount
- 50% = half
- 25% = one quarter
- 10% = one tenth
- 1% = one hundredth
Three Functions of the Percentage Calculator
1. What is X% of Y?
Use this when you know the percentage and the total amount and need the concrete value.
Formula: result = (percentage ÷ 100) × value
Example: 15% tip on a $85 dinner bill: 15 ÷ 100 × 85 = $12.75
2. What percentage is X of Y?
Use this when you need to express a part as a share of the whole.
Formula: percentage = (part ÷ whole) × 100
Example: You scored 42 out of 50 on a test: 42 ÷ 50 × 100 = 84%
3. Percentage change (increase or decrease)
Use this to measure how much a value has grown or shrunk relative to its starting point.
Formula: change% = ((new value − old value) ÷ |old value|) × 100
Example: Rent went from $1,400 to $1,540: (140 ÷ 1,400) × 100 = +10%
Common Percentage Calculations — Quick-Reference Table
| Situation | Formula | Example |
|---|---|---|
| Discounted price | price × (1 − discount% ÷ 100) | $80 item at 25% off = $60 |
| Price after markup | price × (1 + markup% ÷ 100) | $50 + 20% markup = $60 |
| Sales tax | price × (1 + tax%) | $100 + 8.25% tax = $108.25 |
| Pre-tax price | total ÷ (1 + tax%) | $108.25 ÷ 1.0825 = $100 |
| Percentage change | ((new − old) ÷ old) × 100 | $50 → $65 = +30% |
| Grade percentage | (points earned ÷ total points) × 100 | 88 / 100 = 88% |
Mental Math Tricks for Percentages
Calculating percentages in your head is easier than you think:
- 10% — Divide by 10. Example: 10% of $65 = $6.50
- 5% — Half of 10%. Example: 5% of $65 = $3.25
- 20% — Double 10%. Example: 20% of $65 = $13.00
- 15% — Add 10% + 5%. Example: 15% of $65 = $6.50 + $3.25 = $9.75
- 25% — Divide by 4. Example: 25% of $80 = $20
- 1% — Divide by 100. Example: 1% of $250 = $2.50
- Swap trick — X% of Y = Y% of X. So 8% of 50 = 50% of 8 = 4
Common Pitfalls
- Percentage change is not symmetric. A 50% increase followed by a 50% decrease does not return to the original value. $100 → +50% → $150 → −50% → $75 (a net loss of 25%).
- Percentage points vs. percentages. Going from 10% to 15% is a 5 percentage-point increase but a 50% relative increase.
- Compounding. Three consecutive 10% raises do not equal a 30% raise. They equal 1.1³ = 1.331, or 33.1%.
Frequently Asked Questions
How do I calculate a percentage on a calculator?
Divide the part by the whole, then multiply by 100. On most phone calculators you can also type the number, press ×, type the percentage, and press %.
How do I reverse a percentage?
To find the original price before a discount: divide the sale price by (1 − discount ÷ 100). A $60 item that was 25% off originally cost $60 ÷ 0.75 = $80.
What is the difference between margin and markup?
Margin is profit as a percentage of selling price; markup is profit as a percentage of cost. A $10 item sold for $15 has a 33% margin but a 50% markup.
How do I convert a fraction to a percentage?
Divide the numerator by the denominator and multiply by 100. For example, 3/8 = 0.375 × 100 = 37.5%.
Related Tools
- Discount Calculator — Find the sale price after any discount
- VAT Calculator — Add or remove sales tax / VAT
- Tip Calculator — Calculate the right tip amount
- Compound Interest Calculator — See how percentages compound over time
- GPA Calculator — Convert grades to GPA
Sources
- Khan Academy: Intro to Percentages
- Math is Fun: Percentages