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**Percentage Increase Formula**

**Introduction**

Percentage increase describes the eventual increase in the quantity in percent form. The percentage increase formula is used to compare the growth in a quantity from the initial value to its final value, over a period of time. Mathematically, this formula is represented as the difference between the final value and the initial value which is divided by the initial value and then multiplied by 100.

In this article, we will explore the concept of percentage increase and its formula. Let us learn more about the percentage increase formula in this article with the help of a few solved examples for a better understanding of the concept.

**What is Percentage Increase?**

Percentage increase is the difference between the final value and the initial value, expressed in the form of a percentage. To calculate the percentage, we need to have the initial value and the increased (new) value. In other words, we can say that percentage increase is a measure of percent change which gives the extent to which a quantity gains magnitude, intensity, or value. If the percentage increase is a negative value, then we can say that there is a percentage decrease of the same magnitude. Let us now explore the percentage increase formula.

**Percentage Increase Formula**

The percentage increase formula is a mathematical tool used to calculate the percentage change or growth between two values. It is commonly used in various fields such as finance, economics, and statistics to analyze data and track changes over time.

The formula ((New Value – Old Value) / Old Value) × 100 calculates the relative increase as a percentage. It involves subtracting the Old Value from the New Value to determine the difference, dividing it by the Old Value, and then multiplying by 100 to express the result as a percentage.

A positive percentage increase indicates growth or an upward trend, while a negative percentage increase indicates a decrease or a downward trend. The formula provides a standardized way to quantify and compare the magnitude of changes between different values.

It is essential to note that the percentage increase formula assumes that the Old Value is the baseline or starting point, and the New Value represents the updated or changed value. The formula can be applied to various scenarios, including calculating price changes, population growth rates, sales increases, and investment returns.

The percentage increase formula helps in understanding the relative change in values, allowing for comparisons, trend analysis, and decision-making based on the observed growth or decline.

**Solved Examples on Percentage Increase Formula:**

**Example 1:** A car’s original price was ₹20,000, and it increased to ₹25,000. What is the percentage increase?

Percentage Increase = ((New Value – Old Value) / Old Value) × 100

Percentage Increase = ((25,000 – 20,000) / 20,000) × 100

Percentage Increase = (5,000 / 20,000) × 100

Percentage Increase = 0.25 × 100

Percentage Increase = 25%

Therefore, the car’s price increased by 25%.

**Example 2:** A company’s stock was valued at ₹50 per share, and it increased to ₹70 per share. What is the percentage increase?

Percentage Increase = ((New Value – Old Value) / Old Value) × 100

Percentage Increase = ((70 – 50) / 50) × 100

Percentage Increase = (20 / 50) × 100

Percentage Increase = 0.4 × 100

Percentage Increase = 40%

Therefore, the stock price increased by 40%.

**Example 3:** A population increased from 10,000 to 15,000. What is the percentage increase in population?

Percentage Increase = ((New Value – Old Value) / Old Value) × 100

Percentage Increase = ((15,000 – 10,000) / 10,000) × 100

Percentage Increase = (5,000 / 10,000) × 100

Percentage Increase = 0.5 × 100

Percentage Increase = 50%

Therefore, the population increased by 50%.

** Frequently Asked Questions on Percentage Increase Formula:**

1: How do you calculate percentage increase?

Answer: To calculate the percentage increase, you need to know the original value and the new value. The formula for calculating the percentage increase is [(New Value – Original Value) / Original Value] x 100.

For example, if the original value is 50 and the new value is 75, you would subtract 50 from 75 to get 25. Then divide 25 by 50 to get 0.5. Multiply 0.5 by 100 to get the percentage increase, which is 50%. Therefore, in this case, there is a 50% increase from the original value of 50 to the new value of 75.

2: What is percentage increase with example?

Answer: Percentage increase is a measure that shows the relative growth between an original value and a new value. It is calculated by taking the difference between the new value and the original value, dividing it by the original value, and then multiplying by 100.

3: What is the difference between percent and percent increase?

Answer: Percent refers to a fraction of 100 and is used to express values relative to the whole. It is a general concept. Percent increase, however, specifically measures the relative growth between an original value and a new value. It quantifies the change in terms of a percentage. Percent increase is calculated by subtracting the original value from the new value, dividing by the original value, and multiplying by 100.

4: Why is percent increase important?

Answer: Percent increase is important because it provides a standardized measure to assess the relative growth or change between two values. It allows us to quantify and compare the magnitude of increases across different contexts. Percent increase is commonly used in various fields such as finance, economics, business, and statistics to analyze trends, track performance, and evaluate the impact of changes. It helps in making informed decisions, setting goals, measuring progress, and understanding the significance of changes over time.

5: What is the difference between increase and percentage increase?

Answer: The difference between increase and percentage increase lies in the way the change is expressed. Increase refers to the actual difference or amount by which something has grown or changed. It is a numerical value. Percentage increase, on the other hand, represents the relative growth in terms of a percentage compared to the original value. It provides a standardized measure that allows for easy comparison of changes across different scales or values.

6: What is the Difference Between Percentage Increase and Percentage Decrease?

Answer: Percentage increase is the increase in the initial value of a quantity over a period of time in percent form. On the other hand, the percentage decrease gives the decrease in the initial value over a period of time in percent form.

7: How to Calculate Percentage Increase Between Two Numbers?

Answer: To calculate the percentage increase between two numbers, we use the formula, Percentage Increase = [(Final Value – Initial Value)/Initial Value] × 100. For example, the height of an apple tree increases from 15 ft to 18 ft in a year. In order to find the percentage increase in the height of the tree, we can use the given formula and substitute the values as: Final value = 18, initial value = 15. After substituting the values in the formula, we get, [(18 – 15)/15] × 100 = (3/15) × 100 = 20%. Therefore, the percentage increase in the height of the apple tree is 20%.

8: How to Calculate Percentage Increase?

Answer: The percentage increase can be determined using its formula given by, Percentage Increase = [(Final Value – Initial Value)/Initial Value] × 100. We can substitute the initial and final values into the formula to find the percentage increase.

9: What is the Percentage Increase from 20 to 25?

Answer: In the given question, the percentage increase can be calculated with the help of the percentage increase formula, Percentage Increase = [(Final Value – Initial Value)/Initial Value] × 100. Here, the initial value is 20 and the final value is 25. Substituting the values in the formula, Percentage Increase = [(25 – 20)/20] × 100 = (5/20) × 100 = 25%.