Hi there. In this mathematics post, I cover the topic of calculating percentage changes. Knowing how to calculate percentage changes helps with shopping and for measuring growths of a financial stock or cryptocurrency.

## Topics

- Review Of Percents
- Calculating Percentage Changes
- Examples

## Review Of Percents

Before we get into calculating percentage changes, I do think that it is important to cover the concept of percents. Percents refer to a part of a whole. One hundred percent (100%) refers to all of the whole, 25% refers to one quarter of a whole, 10% refers to one tenth of a whole, 50% refers to half of a whole.

One percent refers to one hundredth of a whole. Something big like 300% refers to three times the whole. In general `x%`

as a fraction would be:

## Calculating Percentage Changes

Percentage changes allows us to see how much something went up or down in amount.

The percentage increase or decrease is given by this formula:

If the latest value is higher than the old value then the percentage change would be positive.

A new value being lower than the old value is a decrease. The percentage change for this case would be negative.

You can replace Old Value with Original Value or Original Price.

## Examples

Examples are important to show how percentage changes are calculated. I use mostly financial examples here.

**Example One**

A laptop computer that has a regular price of $1000 USD is now priced at $800 USD. What is the percentage discount?

The regular price went down by 20% from $1000 USD to $800USD. This is a discount of twenty percent.

**Example Two**

Peter wants to buy a new house in his area. His current house that he is trying to sell was at $500, 000 CAD two years ago. The current house is now worth $800 000 CAD. What is the percentage gain on the value of Peter's house?

Peter's house price has went up by 60% from five hundred thousand to eight hundred thousand.

**Example Three**

Jessie has received a pay raise at her job. Her hourly wages went up from $24 per hour to $30 per hour. What is the increase in percentage terms?

Jessie's wage increased by 25%.

**Example Four**

Tom's math course average went down from 80 to 70. What is the percentage change here?

Tom's math course average went down by 12.5% going from 80 to 70.

**Example Five**

Linus has invested $250 into stock AYZ. The price of stock AYZ tripled. What is the percentage change of stock AYZ?

This AYZ stock has tripled and went up by 200%. After doing this calculation, you do see that it is not actually 300% for a gain. This 3x is a 200% gain.

A 10x gain would correspond to a 900% gain. Something that was up 100x had a 9900% gain.

**Notes**

I think it important to point out that a lot of news reports mention percentages only when it comes to gains or losses in price or any numeric value. If you know the percentages only, you would not know about the two values that are used in the percentage gain/loss calculations.

If there are percentages of a number of people for a survey or something similar, the sample size is usually not specified. This is a different topic.

If calculations are not for you can consider this Percentage Change Calculator.