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.

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,

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

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

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