To calculate a percentage increase, subtract the original value from the new value, divide the increase by the original value, then multiply by 100. As a formula: percentage increase = (increase ÷ original value) × 100. For example, if 120 increases to 168, the increase is 48, and 48 ÷ 120 × 100 = 40, so this is a 40% increase.
How to calculate percentage increase in 4 steps
- Confirm it is a percentage increase question.
- Calculate the difference between the two numbers being compared.
- Divide the increase by the original number.
- Multiply the answer by 100 to convert it to a percentage.
We’ll go through these stages in detail below.
Percentage change expresses how much a quantity has changed over time, as a percentage of its starting value. It is commonly encountered in finance when analysing profits, tracking prices of stocks and shares, or comparing currency values, and it is also useful for expressing trends in scientific fields, such as changes in annual rainfall.
Quite simply, if a quantity has increased in value, you’ll be calculating a percentage increase. If it has decreased instead, this requires a percentage decrease calculation, which follows the same structure: divide the decrease by the original value and multiply by 100.
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. The four steps below break the method down using a worked example.
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, multiply 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 the hang of the steps in context, here are some further examples of how to calculate percentage increase, starting with quick-fire questions in the format tests use most often: a value increases from one number to another, and you give the percentage increase.
Quick-fire practice questions
Q: 120 increases to 168. What percentage increase is this?
Increase = 168 - 120 = 48. Then 48 ÷ 120 = 0.4, and 0.4 x 100 = 40, so this is a 40% increase.
Q: A price rises from £50 to £65. What is the percentage increase?
Increase = 65 - 50 = 15. Then 15 ÷ 50 = 0.3, and 0.3 x 100 = 30, a 30% increase.
Q: Monthly sales grow from 80 units to 92 units. What is the percentage increase?
Increase = 92 - 80 = 12. Then 12 ÷ 80 = 0.15, and 0.15 x 100 = 15, a 15% increase.
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 = 0.662 (rounded to 3 decimal places)
Step 4: Convert to a percentage
To convert to a percentage and reach the answer, multiply the resulting value by 100.
0.662 x 100 = 66.2
Answer: The company’s charitable contributions have increased by 66.2% over the last five years.
Practice percentage increase questions
Percentage increase questions rarely appear on their own: numerical tests mix them with ratios, averages and data interpretation. Work through our numerical reasoning tests to apply the method under timed conditions, build up the fundamentals with our basic numeracy tests, or sample a range of question types with our free aptitude tests.
