Percent Change Calculator

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Initial Value

Final Value

Please provide your input and click the calculate button

About the Percent Change Calculator

This percent change calculator lets you calculate the percent change if you know the initial and final values. It can also calculate for you the initial (final) value if you know the final (initial) value and the percent change.

The calculator will give tell not just the answer, but also how to calculate the precent change or initial/final value.

Usage Guide

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i. Valid Inputs

Each input can be a real number in any format — integers, decimals, fractions, or even mixed numbers. Here are a few examples.

Whole numbers or decimals → $\hspace{0.2em} 2 \hspace{0.2em}$ , $\hspace{0.2em} -4.25 \hspace{0.2em}$ , $\hspace{0.2em} 0 \hspace{0.2em}$ , $\hspace{0.2em} 0.33 \hspace{0.2em}$
Fractions → $\hspace{0.2em} 2/3 \hspace{0.2em}$ , $\hspace{0.2em} -1/5 \hspace{0.2em}$
Mixed numbers → $\hspace{0.2em} 5 \hspace{0.5em} 1/4 \hspace{0.2em}$

ii. Example

If you would like to see an example of the calculator's working, just click the "example" button.

iii. Solutions

As mentioned earlier, the calculator won't just tell you the answer but also the steps you can follow to do the calculation yourself. The "show/hide solution" button would be available to you after the calculator has processed your input.

iv. Share

We would love to see you share our calculators with your family, friends, or anyone else who might find it useful.

By checking the "include calculation" checkbox, you can share your calculation as well.

Here's a quick overview of what we mean by percent change and how to calculate it.

For those interested, we have a more comprehensive tutorial on percent change and its calculation.

Percent Change

Percent change refers to the change in a value expressed as a percent of the initial value.

Writing the above statement as a mathematical expression, we get the formula for percent change.

\text{percent change} \hspace{0.25em} = \hspace{0.25em} \frac{\text{change}}{| \hspace{0.15em}\text{initial value} \hspace{0.15em}|} \times 100 \hspace{0.25em} \%

Here change is the different between the initial and final values. So,

\text{change} \hspace{0.25em} = \hspace{0.25em} \text{final value} - \text{initial value}

A Useful Formula

Combining the two formulas above and rearranging, we get the relation between the percent change $\hspace{0.2em} (P \hspace{0.1em} \%) \hspace{0.2em}$ and the initial $\hspace{0.2em} (X) \hspace{0.2em}$ and final value $\hspace{0.2em} (Y) \hspace{0.2em}$ .

Y = \frac{100 + P}{100} \times X

Examples

Here are a couple of examples of how we use the formula above to calculate the percent change and other related values.

Example

The number of dogs in a housing society increased from $\hspace{0.2em} 40 \hspace{0.2em}$ in $\hspace{0.2em} 2021 \hspace{0.2em}$ to $\hspace{0.2em} 46 \hspace{0.2em}$ in $\hspace{0.2em} 2022 \hspace{0.2em}$ . Find the percent change in the number of dogs.

Solution

We'll start by finding the change in the number of dogs in the society.

\begin{align*} \text{change} \hspace{0.25em} &= \hspace{0.25em} \text{final value} - \text{initial value} \\[1em] &= \hspace{0.25em} 46 - 40 \\[1em] &= \hspace{0.25em} 6 \end{align*}

And now we can use the formula for percent change.

\begin{align*} \text{percent change} \hspace{0.25em} &= \hspace{0.25em} \frac{\text{change}}{| \hspace{0.15em}\text{initial value} \hspace{0.15em}|} \times 100 \hspace{0.25em} \% \\[1.75em] &= \hspace{0.25em} \frac{6}{| \hspace{0.15em} 40 \hspace{0.15em}|} \times 100 \hspace{0.25em} \% \\[1.75em] &= \hspace{0.25em} 15 \hspace{0.25em} \% \end{align*}

So the number of dogs in the society saw a $\hspace{0.2em} 15 \hspace{0.1em} \% \hspace{0.2em}$ increase.

Example

During the 2008 housing crisis, the market value of a house dropped by $\hspace{0.2em} 45 \% \hspace{0.2em}$ to $\hspace{0.2em} \$ \hspace{0.2em} 220,000 \hspace{0.2em}$ . What was the house's market value before the drop?

Solution

The question tells us that there was drop in the price, so we are dealing with a case of percent decrease (a negative percent change).

Let's start by listing what the question tells us.

\begin{align*} \text{percent change} \hspace{0.25em} (P) \hspace{0.25em} &= \hspace{0.25em} -45 \hspace{0.2em} \% \\[1em] \text{final price} \hspace{0.25em} (Y) \hspace{0.25em} &= \hspace{0.25em} \$ \hspace{0.15em} 220,000 \end{align*}

Now, we can find the initial price $\hspace{0.2em} X \hspace{0.2em}$ using the formula from earler.

\begin{align*} Y \hspace{0.25em} &= \hspace{0.25em} \frac{100 + P}{100} \times X \\[1.75em] \$ \hspace{0.1em} 220000 \hspace{0.25em} &= \hspace{0.25em} \frac{100 - 45}{100} \times X \end{align*}

Solving for $\hspace{0.2em} X \hspace{0.2em}$ , we get

X \hspace{0.25em} = \hspace{0.25em} \$ \hspace{0.1em} 400000