# Percentage Change Calculator

Initial Value
Final Value
Percent Change  =  13.3333%
GENERATE WORK

## Percentage Change - work with steps

Input Data :
Initial Value = 7500
Final Value = 8500

Objective :
Find what is % change for given input data?

Formula

\text{% change} = \frac{\text{Final Value} - \text{Initial Value}}{\text{Initial Value}} \times 100

Solution :
% change = \frac{8500 - 7500}{7500} \times 100
 = \frac{1000}{7500} \times 100

 = \frac{100000}{7500}
% change = 13.3333

Percentage change calculator uses two values, $X$ and $Y$, and calculate the percent of change from $X$ to $Y$. It is an online a mathematical tool requires two real numbers, original and final values such that the original (initial) number is nonzero real number, to determine the difference from the original value to the final value in terms of percent.
It is necessary to follow the next steps:

1. Enter original and final values in the box. The final value must be a real number, while the original value must be nonzero real number;
2. Press the "GENERATE WORK" button to make the computation;
3. Percentage change calculator will give the percent of change from the original to the final value.
Input : Two real numbers. Note that the first entered value, the original amount, must be be nonzero real number.
Output : The result is a percent value, i.e. the result is a real number and $\%$ after the number.

Percent of Change Formula:
If the original amount is nonzero real number, the percent of change is determined by the following formula
$$\rm{percent\;change}=\Big(\frac{\rm{final\;amount-original\;amount}}{|\rm{original\;amount}|}\Big)\times 100\%$$
or equivalently
$$\frac{\rm{percent\;change}}{100}=\Big(\frac{\rm{actual\;change}}{|\rm{original\;amount}|}\Big)\times 100\%$$

## What is Percent of Change?

A useful way to express changes in amounts is through percents. A percent of change is increased or decreased the percent an amount in relation to the original amount. If the original amount is nonzero real number, the formula for the percent change is

$$\rm{percent\;change}=\Big(\frac{\rm{final\;amount-original\;amount}}{|\rm{original\;amount}|}\Big)\times 100\%$$
or
$$\frac{\rm{percent\;change}}{100}=\Big(\frac{\rm{actual\;change}}{|\rm{original\;amount}|}\Big)\times 100\%$$
There are two different kinds of percent of change.
• When the percent of change is positive, then the percent of change is a percent of increase;
• When the percent of change is negative, then the percent of change is a percent of decrease.
If the percent of increase or the percent of decrease and the original amount are known, we can find the final amount from the following formula:
$$\rm{final\;amount}={\rm{percent\;change}}\times|{\rm{original\;amount}}|+{\rm{original\;amount}}$$

### How to calculate Percent of Change

The percent of change is the difference between an original and final amount divided by the absolute value of the original amount and multiplied by $100\%$. The percentage change can be positive or negative.
The percentage change work with steps shows the complete step-by-step calculation for finding the percent of change from one amount to another with the original (initial) value of $10$ and the final value of $500$. For any other combinations of the original and final value such that the original number must not be a zero, just supply values and click on the "GENERATE WORK" button. The grade school students may use this percentage change calculator to generate the work, calculate the percent of change for two numbers, verify the results or do their homework problems efficiently.

### Real World Problems Using Percent of Change

Percentage change is a concept that represents the degree of change over time. It is used for many purposes in finance, for example to represent the price change of a security. Common applications of percent change are in trade for discounts and markups. A discount is a reduction in the original price. A markup is the difference between the cost of any item and its current selling price. Hence, one of the most important field of application in price supply-and-demand analysis.

### Percent Cahange Practice Problems

Practice Problem 1:
The population of France grew from $64,613,000$ to $66,991,000$ in seven years. Find the percent of change for this period.

Practice Problem 2:
Find the percent of change from $-10$ to $-20$.

The percentage change calculator, formula, example calculation (work with steps), real world problems and practice problems would be very useful for grade school students (K-12 education) to learn how to find percent of change from one number to another. This concept is very useful in real-life, for instance, to find the percent of change over multiple periods of time, to identify the percent of change as an increase or a decrease, etc.