Percentage Calculator
Calculate percentages, increases, and decreases.
Number
Counts
About this topic
Find X% of Y Calculate a specific portion of a total number.
To find X% of a number, think of the percentage as a part out of 100. Convert it to a decimal, then multiply by the total. For example, 20% of 500 means 0.20 × 500, which gives 100. This is useful whenever you need to calculate a portion of an amount, such as a discount on a product, tax on a bill, or a tip at a restaurant.
Key formulas & rules
- •Formula: (Percentage / 100) × Total
- •Converts percentage to a decimal
- •Result is always smaller than the total (if % < 100)
- •Used for taxes, tips, and discounts
- •Commutative: X% of Y = Y% of X
Examples
| Input | Output | Note |
|---|---|---|
| 20% of 500 | 100 | Standard calculation |
| 15% of 80 | 12 | Common tip amount |
| 50% of 30 | 15 | Equivalent to dividing by 2 |
| 5% of 200 | 10 | Small percentage |
Real-world uses
Find the Whole Find the original total from a known part and percentage.
When you know how much a part is worth and what percentage of the total it represents, you can work backwards to find the original whole. Divide the known part by the percentage written as a decimal. For example, if 50 represents 10% of a price, the full price is 50 ÷ 0.10 = 500. This is useful for recovering an original price, total score, or budget from a partial amount.
Key formulas & rules
- •Formula: (Part / Percentage) × 100
- •Reverses the X% of Y calculation
- •Result is always larger than the part (if % < 100)
- •Requires a non-zero percentage
- •Useful for reverse-engineering totals
Examples
| Input | Output | Note |
|---|---|---|
| 50 is 10% of? | 500 | Simple reverse |
| 15 is 20% of? | 75 | Original price before 20% off |
| 12 is 15% of? | 80 | Original bill before tip |
| 25 is 50% of? | 50 | Equivalent to doubling |
Real-world uses
Percentage Change Calculate the relative increase or decrease.
Percentage change compares a new value with its starting value and expresses the difference relative to the starting value. A positive answer means the value increased; a negative answer means it decreased. For example, a price rising from 200 to 250 has increased by 25%, while a fall from 200 to 150 is a 25% decrease. It is commonly used to compare price changes, business growth, marks, and other measurements over time.
Key formulas & rules
- •Formula: ((Final - Initial) / |Initial|) × 100
- •Positive result = Increase
- •Negative result = Decrease
- •Uses |Initial| to handle negative baselines
- •Zero change = 0%
Examples
| Input | Output | Note |
|---|---|---|
| 100 to 150 | +50% | 50% increase |
| 100 to 50 | -50% | 50% decrease |
| -100 to -50 | +50% | Debt reduction is positive |
| 50 to 50 | 0% | No change |
Real-world uses
Find Percentage Find what percentage one number is of another.
This calculation tells you how large one value is compared with a total, expressed per hundred. Divide the part by the whole and multiply by 100. For example, getting 40 questions correct out of 50 gives (40 ÷ 50) × 100 = 80%. The part can also be greater than the whole, so a result can exceed 100%—for example, 60 is 120% of 50.
Key formulas & rules
- •Formula: (Part / Whole) × 100
- •Part must be smaller than Whole for < 100%
- •Whole cannot be zero
- •Result is dimensionless
- •Commonly used for test scores
Examples
| Input | Output | Note |
|---|---|---|
| 40 of 50 | 80% | Standard test score |
| 25 of 200 | 12.5% | Small proportion |
| 1 of 4 | 25% | Equivalent to a quarter |
| 60 of 50 | 120% | Greater than 100% |
Real-world uses
Modes & formulas
Find X% of Y
Dividing by 100 converts the percentage into a decimal (e.g., 20% becomes 0.20). Multiplying this decimal by the number gives you the portion.
Find the Whole
Part is the known value, and Percentage is what that part represents. For example, if 50 is 10% of a number, the total number is (50 / 10) × 100 = 500.
Percentage Change
Final is the new value, and Initial is the starting value. Using the absolute value ensures correct behavior with negative baselines.
Find Percentage
Part is the smaller piece, and Whole is the total. For example, if you score 40 out of 50 on a test, the percentage is (40 / 50) × 100 = 80%.