Percentage Calculator — Free Online Percent Calculator
Percentages appear in everyday math: calculating discounts, tax, tips, grade scores, profit margins, growth rates, and more. Our free online Percentage Calculator solves all common percentage problems instantly — with clear formulas shown so you understand the math, not just the answer. 100% private, works in your browser with no data uploaded.
What Is a Percentage?
A percentage is a way of expressing a ratio as a fraction of 100. The word comes from the Latin per centum, meaning “by the hundred.” The percent symbol is %.
Percentage = (Part / Whole) × 100
For example, if 45 out of 60 students passed an exam:
Pass rate = (45 / 60) × 100 = 75%
Percentage Calculation Types
Our calculator handles the four most common percentage problems:
1. What is X% of Y?
Formula: Result = (X / 100) × Y
Example: What is 20% of $350?
(20 / 100) × 350 = $70
2. What percentage is X of Y?
Formula: Percent = (X / Y) × 100
Example: 45 is what percent of 180?
(45 / 180) × 100 = 25%
3. X is Y% of what number?
Formula: Whole = X / (Y / 100)
Example: 60 is 40% of what number?
60 / (40 / 100) = 60 / 0.4 = 150
4. Percentage Change (Increase or Decrease)
Formula: Change% = ((New - Old) / Old) × 100
Example: Price went from $80 to $100. What is the percentage increase?
((100 - 80) / 80) × 100 = (20 / 80) × 100 = 25% increase
Common Percentage Examples
| Scenario | Calculation | Result |
|---|---|---|
| 15% tip on $60 meal | (15/100) × 60 | $9.00 |
| 30% discount on $200 | 200 × (1 - 0.30) | $140 |
| GST at 18% on $500 | 500 × 0.18 | $90 |
| Grade: 72 out of 90 | (72/90) × 100 | 80% |
| Salary increase from ₹40,000 to ₹48,000 | ((48k-40k)/40k) × 100 | 20% increase |
| Population growth 1M to 1.05M | ((1.05-1)/1) × 100 | 5% growth |
How to Calculate Percentage in Your Head
Quick mental math tricks:
- 10%: Move the decimal point one place left (10% of 250 = 25)
- 5%: Half of 10% (5% of 250 = 12.5)
- 25%: Divide by 4 (25% of 200 = 50)
- 50%: Divide by 2 (50% of 80 = 40)
- 1%: Move the decimal two places left (1% of 450 = 4.5)
Frequently Asked Questions
How do I calculate a percentage increase?
Use the formula: ((New Value − Old Value) / Old Value) × 100. A positive result means an increase; a negative result means a decrease. Example: a product priced at ₹800 that rises to ₹1,000 has a ((1000−800)/800)×100 = 25% increase.
How do I find the original price after a discount?
If a product costs $70 after a 30% discount, the original price = 70 / (1 − 0.30) = 70 / 0.70 = $100. This is the reverse percent calculation.
What is a percentage point vs a percentage?
A percentage point is an absolute difference between two percentages. If interest rates rise from 3% to 5%, that’s a 2 percentage point increase. But it’s a ((5−3)/3)×100 = 66.7% increase in the rate itself. These two phrasings mean very different things.
How do I calculate compound percentage change?
For compound growth over multiple periods, use: Final = Initial × (1 + rate)^n. For example, $1,000 growing at 5% per year for 3 years = 1000 × 1.05³ = $1,157.63.
How do I reverse a percentage (find the whole from a part)?
If 35 represents 14% of a total, the total = 35 / 0.14 = 250. The formula: Whole = Part / (Percent / 100).
