Percentage Calculator
How do you calculate percentage change between two numbers?
A percentage is a number expressed as a fraction of 100. This calculator handles three common percentage calculations: finding a percentage of a number, finding what percent one number is of another, and calculating percentage change. — also see our fraction to percentage converter. Continue your calculation with the Percentage Change Calculator, or check the Discount Calculator.
Common percentage mistakes to avoid
Percentages can be confusing when the base number changes. A 20% increase followed by a 20% decrease does not return to the original value. Always check what number the percentage is being applied to before using the result.
What should you know before using this tool?
The Percentage Calculator is built for people who want a fast answer without losing context. It keeps the calculation simple, shows the result clearly, and helps you understand what the number means before you use it in a real decision.
This tool is built for quick everyday math. It can help with shopping, invoices, schoolwork, reports, and checking manual calculations.
Understanding percentage calculations
A percentage is a way of expressing a number as a fraction of 100. The word "percent" comes from the Latin "per centum" meaning "by the hundred." Percentages are used in virtually every area of daily life — from discounts and tax rates to exam scores, interest rates, and health statistics.
The four most common percentage calculations
1. What is X% of Y? (Finding a percentage of a number)
Formula: Result = (X ÷ 100) × Y
Example: What is 15% of $2,400? = (15 ÷ 100) × 2,400 = $360
2. X is what percent of Y? (Finding what percentage one number is of another)
Formula: Percentage = (X ÷ Y) × 100
Example: 45 is what percent of 180? = (45 ÷ 180) × 100 = 25%
3. Percentage increase
Formula: % Increase = [(New Value – Old Value) ÷ Old Value] × 100
Example: Price increased from $800 to $920: = [(920 – 800) ÷ 800] × 100 = 15% increase
4. Percentage decrease
Formula: % Decrease = [(Old Value – New Value) ÷ Old Value] × 100
Example: Salary reduced from $50,000 to $45,000: = [(50,000 – 45,000) ÷ 50,000] × 100 = 10% decrease
Real-world percentage examples
- Shopping discount: A $3,500 jacket with a 30% discount: Discount = $1,050. Final price = $2,450
- Salary hike: Monthly salary of $40,000 with a 12% increment: New salary = 40,000 × 1.12 = $44,800
- GST calculation: Product at $5,000 with 18% GST: GST amount = $900. Total price = $5,900
- Exam score: Scored 68 out of 80: Percentage = (68 ÷ 80) × 100 = 85%
- Weight loss: Starting weight 90 kg, current weight 81 kg: % lost = (9 ÷ 90) × 100 = 10%
Percentage points vs percentage change
This is one of the most commonly misunderstood concepts in percentage calculations. If an interest rate rises from 5% to 8%, it has increased by 3 percentage points — but by 60% in relative terms (since 3 is 60% of 5). In financial news and economic reporting, always clarify which measure is being used.
Successive discounts — a common trap
Two successive discounts of 20% and 10% do NOT equal a 30% total discount. On $1,000: After 20% off = $800. After 10% off $800 = $720. Total discount = $280 on $1,000 = 28% total, not 30%.
Successive percentage changes must be applied sequentially, not added. The formula for the combined effect of two successive percentage changes (a% then b%) is: Combined = a + b + (a × b ÷ 100)
How to calculate X% of a number (part of a whole)
To find X% of a number: multiply the number by X, then divide by 100. Formula: Part = (Whole × Percentage) ÷ 100. Examples: 15% of 200 = (200 × 15) ÷ 100 = 30. 8% of ₹5,000 = ₹400. 0.5% of 1,000 = 5. This is the most common percentage calculation — used for discounts, taxes, tips, and interest.
How to find what percentage A is of B
Formula: Percentage = (Part ÷ Whole) × 100. Examples: 30 is what % of 200? (30 ÷ 200) × 100 = 15%. You scored 42 out of 50: (42 ÷ 50) × 100 = 84%. A shirt costs ₹800, discounted from ₹1,000: (800 ÷ 1000) × 100 = 80% (you're paying 80% of original price).
How to calculate percentage increase and decrease
Percentage change = (New − Old) ÷ Old × 100. Increase: price rose from ₹500 to ₹625: (625−500)÷500 × 100 = +25%. Decrease: salary cut from ₹60,000 to ₹51,000: (51,000−60,000)÷60,000 × 100 = −15%. A negative result is a percentage decrease; positive is an increase.
Frequently asked questions about percentages
How do I calculate 20% of a number quickly? Divide by 10 (to get 10%) then double it. For $450: 10% = $45, so 20% = $90.
How do I find the original price before a discount? Divide the discounted price by (1 – discount rate). If an item costs $680 after a 15% discount: Original = $680 ÷ 0.85 = $800.
What is the percentage difference between two numbers? Use the percentage change formula. The direction matters — always use the original (starting) value as the denominator.
Is percentage the same as percentile? No. Percentage is a proportion out of 100. Percentile is a ranking position — the 90th percentile means you scored higher than 90% of the group.
Percentage change reference table
| Scenario | Original | New Value | % Change |
|---|---|---|---|
| Price rise (common) | ₹100 | ₹110 | +10% |
| Salary increment | ₹50,000 | ₹54,000 | +8% |
| Stock gain | $200 | $250 | +25% |
| Sale discount | $80 | $60 | −25% |
| Weight loss | 90 kg | 81 kg | −10% |
| Revenue decline | $1M | $850K | −15% |
Quick percentage calculations — mental math shortcuts
| To find | Shortcut | Example |
|---|---|---|
| 10% of X | Move decimal one place left | 10% of 850 = 85 |
| 5% of X | Half of 10% | 5% of 850 = 42.5 |
| 15% of X | 10% + 5% | 15% of 850 = 127.5 |
| 20% of X | Double the 10% | 20% of 850 = 170 |
| 25% of X | Divide by 4 | 25% of 850 = 212.5 |
| 50% of X | Divide by 2 | 50% of 850 = 425 |
| 1% of X | Move decimal two places left | 1% of 850 = 8.5 |
Sources & References
Sources: Common Core State Standards (CCSS.MATH.CONTENT.6.RP.A.3); OECD PISA Mathematics Framework 2022 — Percentage and ratio competency.
Which calculator should I use: percentage, change, or discount?
Stay here for the three classic part-whole questions: X% of Y, X is what % of Y, and finding the original value. Jump to the percentage change calculator when measuring increase or decrease between two values, and the discount calculator when it’s shopping math — sale prices, stacked discounts, and money saved.