A percentage is a way of expressing a number as a fraction of 100. It is often denoted by the symbol "%" or simply as "percent" or "pct". For example, 50% means 50 out of 100, or 1/2.
The basic percentage formula is used to express a part of a whole as a fraction of 100. It's most commonly stated as:
Percentage = (Value / Total Value) × 100%
Let's break down the components and provide some examples:
Value (Part): This is the specific amount or quantity you want to express as a percentage.
Total Value (Whole): This is the overall amount or quantity that the "Value" is a part of.
Example 1: Finding the percentage of a score
If you scored 45 marks out of a total of 50 marks on a test, what percentage did you get?
Percentage = (45 / 50) × 100%
Percentage = 0.9 × 100%
Percentage = 90%
Other common percentage formulas:
Percentage Increase: To calculate how much something has increased as a percentage of its original value.
Percentage Increase = ((New Value - Original Value) / Original Value) × 100%
Example: If a product's price increased from $100 to $120.
Percentage Increase = (($120 - $100) / $100) × 100%
Percentage Increase = ($20 / $100) × 100%
Percentage Increase = 0.2 × 100%
Percentage Increase = 20%
Percentage Decrease: To calculate how much something has decreased as a percentage of its original value.
Percentage Decrease = ((Original Value - New Value) / Original Value) × 100%
Example: If a product's price decreased from $120 to $90.
Percentage Decrease = (($120 - $90) / $120) × 100%
Percentage Decrease = ($30 / $120) × 100%
Percentage Decrease = 0.25 × 100%
Percentage Decrease = 25%
Finding a percentage of a number: To find a specific percentage of a given number.
Amount = (Percentage / 100) × Number
Example: What is 15% of 200?
Amount = (15 / 100) × 200
Amount = 0.15 × 200
Amount = 30
Understanding these formulas allows you to calculate and work with percentages in various real-world situations, from discounts and sales to statistics and financial calculations.
The percentage difference formula is used to calculate the relative difference between two values, expressed as a percentage. Unlike percent change, which uses one value as the reference (the original value), percentage difference uses the average of the two values as the reference point. This makes the calculation symmetrical, so the percentage difference between A and B is the same as between B and A.
Formula:
The percentage change formula is used to measure the degree of change between an initial value and a final value, expressed as a percentage of the initial value. It is commonly used to track growth, decline, or trends over time.
Formula:
To calculate a percentage, divide the part by the whole and multiply by 100. Formula: Percentage = (Part / Whole) × 100%. For example, (25 / 200) × 100 = 12.5%.
Percentages are essential for comparing proportions, tracking changes, and interpreting data in fields like finance, science, and everyday life. They provide a standardized way to express ratios and make data more understandable.
Subtract the original value from the new value, divide by the original value, then multiply by 100. Formula: Percentage Increase = ((New Value - Original Value) / Original Value) × 100%. For example, ((120 - 100) / 100) × 100 = 20% increase.
Subtract the new value from the original value, divide by the original value, then multiply by 100. Formula: Percentage Decrease = ((Original Value - New Value) / Original Value) × 100%. For example, ((100 - 80) / 100) × 100 = 20% decrease.
Divide the first number by the second, then multiply by 100. Formula: Percentage = (First Number / Second Number) × 100%. For example, (30 / 200) × 100 = 15%.
Multiply Y by X and divide by 100. Formula: Result = (X × Y) / 100. For example, 20% of 150 is (20 × 150) / 100 = 30.
Subtract the original value from the new value, divide by the original value, then multiply by 100. Formula: Percentage Change = ((New Value - Original Value) / Original Value) × 100%. For example, ((120 - 100) / 100) × 100 = 20% increase.
Multiply the number by the percentage (as a decimal). Formula: Result = Number × (Percentage / 100). For example, 25% of 200 is 200 × 0.25 = 50.
Divide the part by the total and multiply by 100. Formula: Percentage = (Part / Total) × 100%. For example, (25 / 200) × 100 = 12.5%.
A percentage is a number out of 100, while a decimal is a number between 0 and 1 (or greater). To convert a percentage to a decimal, divide by 100. For example, 75% = 0.75. To convert a decimal to a percentage, multiply by 100 and add the % sign. For example, 0.2 = 20%.