Percentage Calculator

How to Calculate Percentages

Percentage calculations are essential in many aspects of our daily lives, from financial planning to data analysis. Here's a guide on how to perform various percentage calculations:

Percentage Formulas

1. Finding a percentage of a number (P% of X):
   \[ \text{Result} = \frac{P}{100} \times X \]
2. Finding what percentage X is of Y:
   \[ \text{Percentage} = \frac{X}{Y} \times 100\% \]
3. Finding the total when a percentage is known (P% of what is X):
   \[ \text{Total} = \frac{X}{\frac{P}{100}} \]
4. Calculating percentage change:
   \[ \text{Percentage Change} = \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \times 100\% \]

Calculation Steps

Let's go through an example for each type of calculation:

1. Finding 25% of 80

1. Convert the percentage to a decimal: 25% = 25 ÷ 100 = 0.25
2. Multiply the decimal by the number: 0.25 × 80 = 20
3. Result: 25% of 80 is 20

2. Finding what percentage 15 is of 60

1. Divide the part by the whole: 15 ÷ 60 = 0.25
2. Multiply by 100 to get the percentage: 0.25 × 100 = 25%
3. Result: 15 is 25% of 60

3. Finding the total when 30% is 45

1. Convert the percentage to a decimal: 30% = 30 ÷ 100 = 0.3
2. Divide the known value by the decimal: 45 ÷ 0.3 = 150
3. Result: 30% of 150 is 45

4. Calculating the percentage change from 100 to 125

1. Calculate the difference: 125 - 100 = 25
2. Divide the difference by the original value: 25 ÷ 100 = 0.25
3. Multiply by 100 to get the percentage: 0.25 × 100 = 25%
4. Result: The percentage change from 100 to 125 is a 25% increase

Visual Representation

Visual aids can help in understanding percentages. Here's a simple diagram showing 25% of a whole:

This diagram illustrates how 25% relates to the whole (100%). The blue portion represents 25% of the entire bar.