How to Calculate Percentage: A Complete Guide with Step-by-Step Examples

Percentages are a fundamental concept in both everyday life and in various fields such as mathematics, finance, and business. Whether you’re trying to figure out how much a product costs after a discount or how to calculate a percentage increase in your salary, understanding how to calculate percentages is essential. In this guide, we will walk you through the process of how to calculate percentages, including several common scenarios such as percentage increase, change, and conversions.

What is a Percentage?

A percentage is a way of expressing a number as a fraction of 100. It is often used to represent proportions, comparisons, and changes between numbers. When you see a percentage, such as 25%, it means 25 out of every 100 units.

For example, if a class has 25 students, and 10 are absent, the percentage of students absent is calculated by dividing the number of absent students (10) by the total number of students (25), then multiplying by 100 to convert it into a percentage:$$\left( \frac{10}{25} \right) \times 100 = 40\%$$(2510​)×100=40%

This shows that 40% of the students are absent.

How to Calculate Percentage: The Basics

The basic formula for calculating a percentage is:$$\text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100$$Percentage=(WholePart​)×100

Where:

• Part is the specific value you’re interested in (for example, a number of items or a portion of a total).
• Whole is the total value or the base you’re comparing against.

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Example 1: How to Calculate For the Percentage

Let’s say you scored 80 marks out of 100 in a test. To find your percentage score:$$\text{Percentage} = \left( \frac{80}{100} \right) \times 100 = 80\%$$Percentage=(10080​)×100=80%

You’ve scored 80% in the test.

Example 2: How to Calculate From Percentage

Now, if you want to find the value from a percentage, you can use this formula:$$\text{Value} = \left( \frac{\text{Percentage}}{100} \right) \times \text{Total}$$Value=(100Percentage​)×Total

Let’s say you need to find 30% of 200. Using the formula:$$\text{Value} = \left( \frac{30}{100} \right) \times 200 = 60$$Value=(10030​)×200=60

So, 30% of 200 is 60.

How to Calculate Percentage Increase

Calculating percentage increase is often used when comparing an old value to a new, higher value, such as the price of a product before and after a price hike.

The formula for percentage increase is:$$\text{Percentage Increase} = \left( \frac{\text{New Value} – \text{Old Value}}{\text{Old Value}} \right) \times 100$$Percentage Increase=(Old ValueNew Value−Old Value​)×100

Example 3: How to Calculate Percentage Increase

Suppose the price of a product was $50 and is now $60. To calculate the percentage increase:$$\text{Percentage Increase} = \left( \frac{60 – 50}{50} \right) \times 100 = \left( \frac{10}{50} \right) \times 100 = 20\%$$Percentage Increase=(5060−50​)×100=(5010​)×100=20%

So, the price increased by 20%.

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How to Calculate Increase as a Percentage

If you want to calculate how much an increase represents as a percentage, use the same formula for percentage increase as above.

Example 4: How to Calculate Increase as a Percentage

Let’s say you earned $1000 last month, and this month you earned $1200. To find the percentage increase in your earnings:$$\text{Percentage Increase} = \left( \frac{1200 – 1000}{1000} \right) \times 100 = \left( \frac{200}{1000} \right) \times 100 = 20\%$$Percentage Increase=(10001200−1000​)×100=(1000200​)×100=20%

You received a 20% increase in your earnings.

How to Calculate Percentage Change

Percentage change can refer to either an increase or a decrease. To calculate percentage change, the formula is:$$\text{Percentage Change} = \left( \frac{\text{New Value} – \text{Old Value}}{\text{Old Value}} \right) \times 100$$Percentage Change=(Old ValueNew Value−Old Value​)×100

If the new value is smaller than the old value, this results in a negative percentage, indicating a decrease.

Example 5: How to Calculate Percentage Change

Let’s say your sales decreased from 500 units to 300 units. To calculate the percentage change:$$\text{Percentage Change} = \left( \frac{300 – 500}{500} \right) \times 100 = \left( \frac{-200}{500} \right) \times 100 = -40\%$$Percentage Change=(500300−500​)×100=(500−200​)×100=−40%

This means your sales have decreased by 40%.

How to Calculate Percentage Increase of a Percentage

In some cases, you may need to calculate the increase of a percentage, such as when an increase is applied to a given percentage. The process follows the same steps as calculating a regular percentage increase.

Example 6: How to Calculate Percentage Increase of a Percentage

Let’s say you have a discount rate of 10%, and you want to increase that rate by 15%. To calculate the new discount percentage:$$\text{Percentage Increase} = \left( \frac{15}{100} \right) \times 10 = 1.5$$Percentage Increase=(10015​)×10=1.5

Now, add this increase to the original percentage:$$\text{New Percentage} = 10\% + 1.5\% = 11.5\%$$New Percentage=10%+1.5%=11.5%

So, the new discount rate is 11.5%.

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How to Calculate by Percentage

Calculating by percentage is a common method for determining values based on a given percentage. This approach is typically used in financial calculations or when determining commissions or taxes.

The formula for calculating by percentage is:$$\text{Value} = \text{Percentage} \times \text{Amount}$$Value=Percentage×Amount

Example 7: How to Calculate by Percentage

If you need to calculate 5% of $200:$$\text{Value} = \frac{5}{100} \times 200 = 10$$Value=1005​×200=10

So, 5% of $200 is $10.

How to Calculate Into Percentage

Converting a value into a percentage involves dividing the value by the total and then multiplying by 100 to express it as a percentage.

The general formula is:$$\text{Percentage} = \left( \frac{\text{Value}}{\text{Total}} \right) \times 100$$Percentage=(TotalValue​)×100

Example 8: How to Calculate Into Percentage

Suppose you scored 45 points out of 50 on a quiz. To calculate the percentage score:$$\text{Percentage} = \left( \frac{45}{50} \right) \times 100 = 90\%$$Percentage=(5045​)×100=90%

Thus, your score is 90%.

Practical Applications of Calculating Percentages

Knowing how to calculate percentages can help you in a wide variety of practical situations. Here are a few examples:

• Shopping Discounts: Understanding how to calculate percentage discounts can help you determine the final price after a sale.
• Finance and Budgeting: Calculating interest rates, tax rates, and investment returns often involves percentage-based calculations.
• Work and Productivity: Tracking performance metrics like sales growth, efficiency rates, and employee bonuses often requires percentage calculations.

Conclusion

Understanding how to calculate percentage is a crucial skill, whether you’re dealing with finance, shopping, or simply calculating performance metrics. By mastering the various methods of percentage calculation, including percentage increase, percentage change, and conversion between values and percentages, you can make more informed decisions in everyday life.

The key formulas for calculating percentages can be summarized as follows:

1. Basic Percentage: $$\text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100$$Percentage=(WholePart​)×100
2. Percentage Increase: $$\text{Percentage Increase} = \left( \frac{\text{New Value} – \text{Old Value}}{\text{Old Value}} \right) \times 100$$Percentage Increase=(Old ValueNew Value−Old Value​)×100
3. Percentage Change: $$\text{Percentage Change} = \left( \frac{\text{New Value} – \text{Old Value}}{\text{Old Value}} \right) \times 100$$Percentage Change=(Old ValueNew Value−Old Value​)×100
4. Calculating From a Percentage: $$\text{Value} = \left( \frac{\text{Percentage}}{100} \right) \times \text{Total}$$Value=(100Percentage​)×Total
5. Calculating Into Percentage: $$\text{Percentage} = \left( \frac{\text{Value}}{\text{Total}} \right) \times 100$$Percentage=(TotalValue​)×100

FAQs

Q1: How do I calculate percentage increase?
To calculate percentage increase, subtract the old value from the new value, then divide by the old value and multiply by 100.

Q2: How can I calculate a percentages of a number?
Multiply the percentage by the number and divide by 100.

Q3: How do I calculate percentages decrease?
Use the percentage change formula, but if the new value is smaller than the old value, you will get a negative result indicating a decrease.