Percentage change is a mathematical concept indicating the degree of change that has occurred over time. It is expressed as a percentage in relation to the initial quantity.

For example, if a company announces a five percent increase in profit for the third quarter, compared to the previous quarter of the financial year, they have reached this figure using a percentage increase calculation.

Percentage change is commonly encountered in finance when analysing profits, tracking prices of stocks and shares, or comparing currency values. It is also useful for expressing trends in scientific fields, such as changes in annual percentage rainfall or the percentage of environmental protected areas.

Quite simply, if a quantity has increased in value, you’ll be calculating percentage increase. If it has decreased instead, this requires a percentage decrease calculation.

If any quantity undergoes change over time, this difference can be pithily quoted as a percentage change. This expression aids with both understanding and communicating the shift that has occurred.

## A step-by-step guide to calculating percentage increase

Percentage change questions are often featured in numerical reasoning tests. As these are timed assessments, you’ll need to be able to perform the required calculations quickly and accurately.

There’s no need to worry about answering percentage increase questions though, as it’s simple to calculate – regardless of the scenario presented - if you know the steps involved.

## Step 1: Confirm it is a percentage increase question

The first step is to confirm what type of percentage change question you are dealing with. To check that the situation warrants a percentage increase calculation, review the data provided and ensure that it is increasing over time.

Don’t allow yourself to be distracted by any extra data provided in the question.

**For example:**

You are given a table containing historical data on the pollution levels within Central London and asked to calculate the percentage change to nitrogen oxide (NO2) from 2009 to 2013. From the data, you can see average nitrogen oxide levels stand at 44.4, 46.4, 51.5, 52.8 and 54.8 micrograms per cubic metre in July across the five-year period.

As the micrograms of NO2 are increasing over time, you can confirm that you are dealing with a percentage increase question.

## Step 2: Calculate the difference

Next, you need to calculate the difference – in this case the *increase* – between the two statistics in question.

This increase can be found by subtracting the original value from the new value.

**Difference = new value – original value**

So, using the NO2 example:

Difference = 54.8 – 44.4

= 10.4

## Step 3: Calculate the increase as a percentage of the original

For the next step, divide the identified increase by the original value. We’ll address the percentage conversion in the last step.

**% increase = (Increase ÷ original value)**x 100

For our example, you need to calculate what percentage 10.4 is of 44.4 micrograms.

Start by dividing 10.4 micrograms by 44.4.

10.4 ÷ 44.4 = 0.234

## Step 4: Convert to a percentage

Finally, to convert your increase into a percentage, multiple the value by 100.

**% increase = (Increase ÷ original value) x 100**

For our example:

0.234 x 100 = 23.4%

This tells us that nitrogen oxide levels in Central London increased by 23.4% in the five-year period concerned.

## Example questions

To help you get a hang of the steps in context, here are some further examples of how to calculate percentage increase.

If you learn how to apply the different stages, you’ll be able to use them to solve percentage increase problems involving anything from weekly working hours to the sales of household items.

### Example question 1

Marine Protected Areas (MPAs) are important for protecting our UK coastal and marine environments. Biodiversity and ecosystem services are key to the social, economic, and environmental prosperity of our island nation. Three tranches of MPAs have been legislated since 2012.

By the end of tranche two, 326,349 km² of waters had been protected.

In 2018, tranche three added a further 41 sites. By mid-2021, an area of 338,049 km² stood as protected.

What was the percentage change in protected areas seen by implementing tranche three MPAs across the UK?

#### Step 1: Confirm it’s a percentage increase question

From the data provided, we know the number of square kilometres protected has *increased* over time. We can therefore confirm that this is a percentage increase calculation.

#### Step 2: Calculate the difference (increase)

Take the two square kilometre values provided and calculate the increase that has taken place.

**Difference = 338,049 km² (new value) – 326,349 km² (original value)**

= 11,700 km²

#### Step 3: Calculate the increase as a percentage of the original

Next, as % increase = (increase ÷ original value) x 100, divide the increase (which in this case is 11,700km²) by the original square kilometre value of 326,349km².

**11,700** (increase) **÷ 326,349** (original value) **= 0.036**

#### Step 4: Convert to a percentage

To convert to a percentage and reach the answer, multiple the resulting value by 100.

0.036 x 100 = 3.6

**Answer:** UK MPA coverage increased by 3.6% due to the further designations implemented in 2018.

### Example question 2

A large corporate company is partnered with a children’s cancer charity as part of its corporate social responsibility and employee volunteering programme. Alongside volunteer work, it has been contributing funds to support the initiative over the last five years.

As performance and profits have improved, the company has been able to provide increased support. By what percentage has the company’s contribution changed since they began supporting the charity?

Financial Year | Contribution (£) |
---|---|

2016 - 17 | 278,000 |

2017 - 18 | 250,000 |

2018 - 19 | 396,000 |

2019 - 20 | 412,000 |

2020 - 21 | 462,000 |

#### Step 1: Confirm it’s a percentage increase question

Although the data fluctuates in the 2017 – 18 financial year, overall the contribution for the 2020 – 21 period is greater than that for the 2016 – 17 period. This means we are dealing with a percentage increase calculation.

#### Step 2: Calculate the difference (increase)

Calculate the difference between the first contribution in 2016 – 17 and the last contribution.

Increase = **462,000** (new value) **– 278,000** (original value)

= 184,000

#### Step 3: Calculate the increase as a percentage of the original

As, % increase = (increase ÷ original value) x 100, next divide the increase (£184,000) by the original contribution value of£278,000.

**£184,000 ÷ £278,000 = 0.66**

#### Step 4: Convert to a percentage

To convert to a percentage and reach the answer, multiple the resulting value by 100.

0.66 x 100 = 66

**Answer:** The company’s charitable contributions have increased by 66% over the last five years.