To calculate a percentage decrease, subtract the new value from the original value, divide that decrease by the original value, then multiply by 100. For example, a fall from 16 to 12 is a decrease of 4, and 4 ÷ 16 × 100 = 25, so it is a 25% decrease. You always divide by the original, larger figure.
Percentage decrease questions are a staple of every free numerical reasoning test, where you compare two figures from a table or chart, such as costs, headcount or sales falling between two periods.
The percentage decrease formula
Percentage decrease = (original value − new value) ÷ original value × 100
The top part, original value minus new value, is the size of the fall. Dividing it by the original value tells you what share of the starting amount was lost. Multiplying by 100 turns that share into a percentage.
How to calculate percentage decrease step by step
A company van was valued at £30,000 last year and is valued at £24,000 this year. What is the percentage decrease in its value?
- Find the decrease. Subtract the new value from the original: 30,000 − 24,000 = 6,000.
- Divide by the original value. 6,000 ÷ 30,000 = 0.2.
- Multiply by 100. 0.2 × 100 = 20.
The van’s value fell by 20%.
How to find the percentage decrease between two numbers
The step people get wrong is choosing the original value. It is the earlier figure, or the one the question says the change is measured “from”. Test questions do not always give the figures in time order, so read carefully before you subtract.
A town had a population of 17,560 this year. Three years earlier it was 20,410. What is the percentage decrease?
The original figure is the earlier one, 20,410, even though it is mentioned second.
- 20,410 − 17,560 = 2,850
- 2,850 ÷ 20,410 = 0.1396 (to four decimal places)
- 0.1396 × 100 = 13.96
The population fell by 13.96%.
Percentage decrease examples
Example 1: falling profit. A business made a gross profit of £28,120 in its first year and £21,950 in its second. What is the percentage decrease?
The decrease is 28,120 − 21,950 = 6,170. Then 6,170 ÷ 28,120 = 0.2194, so profit fell by 21.94%.
Example 2: figures in millions. A firm’s total liabilities were £1.24 million at the end of one year and £0.93 million at the end of the next. What is the percentage decrease?
You can work in millions without converting. The decrease is 1.24 − 0.93 = 0.31, and 0.31 ÷ 1.24 = 0.25, a 25% decrease.
Example 3: a sale price. A laptop’s price is cut from £680 to £578. What percentage discount is this?
The decrease is 680 − 578 = 102, and 102 ÷ 680 = 0.15, a 15% discount.
Using one formula for increase and decrease
You can also use the general percentage change formula: (new value − original value) ÷ original value × 100. With a fall, the answer comes out negative. For the van, (24,000 − 30,000) ÷ 30,000 × 100 = −20, which means a 20% decrease. If your answer is positive, the value actually went up, and you need our guide to calculating percentage increase.
Mistakes to avoid
- Dividing by the new value. A fall from 16 to 12 is 4 ÷ 16 = 25%. Dividing by 12 instead gives 33.3%, which is wrong but will often be among the options.
- Getting an answer above 100%. A percentage decrease can never be more than 100%, because a value cannot fall by more than all of itself. If you get one, you have divided by the wrong figure.
- Assuming a rise and an equal fall cancel out. A salary of £40,000 that rises by 10% becomes £44,000. A 10% fall from there takes it to £39,600, which is 1% below where it started, because the fall is taken from a larger amount.
- Adding successive decreases. A 20% cut followed by a 10% cut is not 30%. Use multipliers: 0.8 × 0.9 = 0.72, so the overall fall is 28%.
Working backwards from a decrease
Sometimes you know the price after a reduction and need the original. A dress costs £50 after 40% off. Taking 40% off £50 and adding it back gives the wrong answer. Instead, note that £50 is 60% of the original price, so divide by 0.6: 50 ÷ 0.6 = £83.33. Our guide to reverse percentages explains this method in full.
Percentage decrease in a numerical test
In a real test you will usually pull the two figures out of a larger table, so start by finding the right row and the right two columns, then name the original value before you calculate anything. Keep four decimal places until the end and round only to the level the question asks for.
For more question formats that combine percentage change with charts, averages and ratios, see our numerical reasoning test examples. When you are ready to practise against the clock, take a numerical reasoning test with worked solutions for every answer.
