## Percentage Change

What Is Percentage Change?

Percentage change can be applied to any quantity. Let’s say you are tracking the the grow of height. If the height increased, use the formula

(New Height – Old Height)/Old Height

Then, multiply that number by 100%.

If the price decreased, use the formula

(Old Height – New Height)/Old Height

Then multiply that number by 100%.

This formula is used both to track the height of someone / something.

Percentage change show the degree of change

Percentage change can be used for any quantity

Positive values show a percentage increase whereas negative values show percentage decrease.

## Definition of Change

To find a change, subtract old value from new value.

Example

You had 4 pens, but now have 7.

The change is: 7-4 = 3.

## Definition of Percentage Change

Percentage change is a concept of mathematics that represents the degree of change over time. There are many purposes to use this in finance, for ecample: to represent the price change in supermarket.

Percentage change shows the change as a percent of the old value.

To find the percentage change divide by the old value and make it a percentage:

So the percentage change from 4 to 7 is:

3/4 = 0.75 = 75%

## How to find percentage change

There are 2 ways to calculate a percentage change, use the one you prefer:

### Method 1

1. subtract old value from the new value
2. divide that change by the old value
3. multiply by 100 and adding a “%” sign

Note:

when the new value is greater then the old value, it is a percentage increase, otherwise it is a decrease.

### Method 2

1. divide the New Value by the Old Value
2. multiply by 100 and adding a “%” sign
3. subtract 100% from that

Note:

when the result is positive it is a percentage increase, if negative, just remove the minus sign and call it a decrease.

Example

A Bag went from \$5 to \$10, what is the percentage change?

Method 1:

Step 1: \$10 – \$5 = \$5 change

Step 2: \$5/\$5 = 1

Step 3: 1×100 = 100% rise.

That means a 100% rise.

Method 2:

Step 1: \$10/\$5 = 2

Step 2: 2×100 = 200%

Step 3: 200% – 100% = 100%

Same result with method 1

## Formula

To calculate a percentage change, use this formula

Change = New Number – Original Number

Next, divide the change by the original number and multiply the result by 100%:

% change = change ÷ Original Number × 100%.

If the answer is a positive number, then the percentage change is increase.

If the answer is a negative number, then the percentage change is a decrease.

Other Formula

You can also put the values into this formula:

(The “|” symbols mean absolute value, so negatives become positive)

Example

There were 100 apples yesterday, and 120 today:

A 20% increase.