Percentage Calculator
Whether calculating retail discounts, sales commissions, profit margins, exam score percentages, or year-over-year growth rates, this multi-mode percentage calculator provides instant, step-by-step arithmetic solutions.
What is X% of Y?
15% of 2400 is
X is what percent of Y?
45 is this percent of 180
Percentage Increase / Decrease
Percentage Increase
The Three Core Percentage Operations
1. Percentage of a Number (What is X% of Y?):
Result = (X × Y) / 100
Example: 15% tip on an $80 restaurant bill = (15 × 80) / 100 = $12.00.
2. Percentage Share (What percent is X of Y?):
Percentage (%) = (X / Y) × 100
Example: Scoring 45 marks out of 60 on a test = (45 / 60) × 100 = 75.0%.
3. Percentage Change / Growth (from X to Y):
Percentage Change (%) = [(New Value − Old Value) / Old Value] × 100
Example: A stock price rising from $50 to $65 represents: [(65 − 50) / 50] × 100 = +30.0% increase.
The Asymmetry of Percentage Increases vs Decreases
A common mathematical misconception is assuming that a percentage increase and decrease of the same nominal percentage cancel each other out. Because the denominator changes, they are asymmetrical:
| Initial Value | Percentage Drop | Trough Value | Required Gain to Break Even |
|---|---|---|---|
| $100 | −10% | $90 | +11.11% ($10 / $90) |
| $100 | −20% | $80 | +25.00% ($20 / $80) |
| $100 | −50% | $50 | +100.00% ($50 / $50) |
| $100 | −80% | $20 | +400.00% ($80 / $20) |
Key Rule: A 50% drop requires a 100% gain just to return to the starting baseline. Read our business guide on Markup vs Profit Margin vs Reverse Percentage.
Mental Math Shortcuts: The Reversibility Trick
Percentages are commutative: X% of Y is always equal to Y% of X.
- Calculating 16% of 50 in your head feels difficult.
- Flip it: 50% of 16 = 8. Therefore, 16% of 50 is exactly 8.
- Calculating 8% of 25: Flip to 25% of 8 = 2.
Frequently Asked Questions
What is the difference between Percent (%) and Percentage Points (pp)?+
A percentage represents a relative change, while percentage points measure the arithmetic difference between two percentage values. For example, if a central bank interest rate moves from 4% to 5%, it increased by 1 percentage point, but by 25 percent in relative terms.
How do I calculate a discount on retail shopping items?+
To calculate a discount, multiply the original price by the discount percentage and divide by 100 to find the savings amount. Then subtract that savings from the original price. For example: A $60 shirt with a 25% discount saves $15 (60 × 0.25), resulting in a sale price of $45.
How do I calculate reverse percentage to find the original price before tax or discount?+
Divide the final price by (1 − discount rate / 100) for discounts, or by (1 + tax rate / 100) for taxes. For example, if an item costs $80 after a 20% discount: Original Price = 80 / 0.80 = $100.
What is the formula for calculating profit margin vs markup?+
Markup = (Profit / Cost) × 100. Margin = (Profit / Selling Price) × 100. A product bought for $100 and sold for $150 has a 50% markup, but a 33.33% profit margin.
How do I calculate percentage difference between two numbers?+
Percentage difference compares two numbers when neither is considered the "original" baseline: Percentage Difference = [|A − B| / ((A + B) / 2)] × 100.
Can percentages exceed 100%?+
Yes. Percentages greater than 100% represent values that are larger than the original reference number. For example, if revenue grows from $10,000 to $35,000, the growth is 250%.
Is my input data private when using this online calculator?+
Yes. All calculations happen natively inside your client browser with zero network transmission or data logging.
Where can I learn more mental math percentage shortcuts?+
Visit our comprehensive guide on "Percentage Tricks: Calculate Discounts, Tips, and Changes in Your Head" in our Guides section.
Formulas on this calculator are reviewed by the AllYouTools Quantitative Research Team against official statutory standards. Read our Editorial Policy and explore full derivations in our Calculation Methodology.
Related Tools
Age Calculator
Find your exact age in years, months, and days from your date of birth, plus total days lived and next birthday.
BMI Calculator
Calculate your Body Mass Index from height and weight and understand which weight category you fall into.
Unit Converter
Convert length, weight, and temperature between metric and imperial units instantly and accurately.