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Calculate any percentage instantly. Find percentages of numbers, calculate increases and decreases, or find the percentage difference between values.
Understanding Percentages
A percentage is a number expressed as a fraction of 100. The word comes from Latin "per centum" meaning "by the hundred." Percentages are one of the most practical mathematical concepts used in everyday life.
Basic Percentage Formulas
Finding a percentage of a number:
Result = (Percentage × 100) × Number
Finding what percent X is of Y:
Percentage = (X × Y) × 100
Percentage change:
Change = ((New - Old) × Old) × 100
Converting Between Forms
| Percentage |
Decimal |
Fraction |
How to Convert |
| 45% |
0.45 |
9/20 |
Divide by 100 for decimal |
| 0.75 (decimal) |
0.75 |
3/4 |
Multiply by 100 for percent |
| 2/5 (fraction) |
0.40 |
2/5 |
Divide, then ×100 |
Practical Percentage Applications
Shopping & Discounts
Calculate sale prices quickly:
- 20% off $80: $80 × 0.20 = $16 off ? Pay $64
- 30% off $150: $150 × 0.30 = $45 off ? Pay $105
- Quick tip: For 25% off, divide by 4. For 50% off, divide by 2.
Calculating Tips
- 10%: Move decimal one place left ($45.00 ? $4.50)
- 15%: Calculate 10%, add half (10% + 5%)
- 20%: Calculate 10%, double it
Tax Calculations
Add sales tax to a purchase:
- Item: $50, Tax: 8% ? $50 × 1.08 = $54
- Item: $120, Tax: 6.5% ? $120 × 1.065 = $127.80
Grade Calculations
Find your test score percentage:
- 42 correct out of 50: (42 × 50) × 100 = 84%
- 18 correct out of 25: (18 × 25) × 100 = 72%
Mental Math Trick
To find any percentage, break it into easy parts. For 35% of 200: Calculate 10% (20), multiply by 3 (60), add 5% (10) = 70!
Percentage Increase vs. Decrease
Understanding the Difference
Percentage change measures how much a value has grown or shrunk relative to its original value.
| Scenario |
Original |
New |
Change |
| Stock price rise |
$100 |
$125 |
+25% |
| Weight loss |
200 lbs |
180 lbs |
-10% |
| Salary increase |
$50,000 |
$55,000 |
+10% |
| Product discount |
$80 |
$60 |
-25% |
Important Note About Reversal
A key concept: if something increases by 50% and then decreases by 50%, you don't end up back at the start!
- Start: $100
- +50%: $150
- -50% of $150: $75
- Net result: 25% loss!
This is why recovering from stock market losses is harder than it seems.
Percentage Formulas: Reference Guide
These are the six core percentage calculations used in business, finance, science, and everyday life × with the exact formula and a worked example for each:
| Calculation Type |
Formula |
Example |
| Percentage of a number | Result = (% × 100) × Number | 15% of 200 = 30 |
| What % is X of Y? | Result = (X × Y) × 100 | 30 is 15% of 200 |
| Percentage increase | Result = ((New - Old) × Old) × 100 | $80?$100 = +25% |
| Percentage decrease | Result = ((Old - New) × Old) × 100 | $100?$75 = -25% |
| Add % to a number | Result = Number × (1 + % × 100) | $200 + 20% = $240 |
| Remove % from a number | Result = Number × (1 - % × 100) | $200 - 20% = $160 |
Common Percentage Mistakes
- A 50% increase followed by a 50% decrease ? 0%. $100 × 1.5 = $150, then $150 × 0.5 = $75. You're down 25%.
- Percentage points ? percent change. A rate going from 2% to 3% is +1 percentage point, but +50% relative change.
- Order matters in percentage change. $80 to $100 is +25%, but $100 to $80 is -20%. The base number changes.
? Frequently Asked Questions
How do I calculate percentage increase between two numbers?
+
Use this formula: ((New Value - Original Value) × Original Value) × 100. For example, if a price went from $80 to $100: ((100 - 80) × 80) × 100 = 25% increase.
What's the difference between percentage points and percent?
+
These are different concepts. If interest rates go from 3% to 5%, that's a 2 percentage point increase, but a 66.7% increase (2×3×100). News often confuses these, so pay attention to context.
How do I find the original price before a discount?
+
Divide the sale price by (1 - discount rate). If an item costs $75 after 25% off: $75 × 0.75 = $100 original price. Formula: Original = Sale Price × (1 - Discount%)
Can percentages be greater than 100%?
+
Absolutely! A 200% increase means something tripled (went from 100 to 300). If your investment doubled, that's a 100% increase. Stock market returns often exceed 100% over long periods.
How do I calculate compound percentages?
+
Multiple percentage changes apply sequentially, not additively. For 10% followed by 20%: multiply by 1.10, then by 1.20 (or 1.10 × 1.20 = 1.32, which is 32% total increase, not 30%).