To calculate a percentage increase, subtract the original value from the new value, divide that increase by the original value, then multiply by 100. For example, if 120 rises to 168, the increase is 48, and 48 ÷ 120 × 100 = 40, so it is a 40% increase. The original value is always the number you divide by.
Percentage increase is one of the most common calculations in a free numerical reasoning test, usually applied to figures you read from a table or chart.
The percentage increase formula
Percentage increase = (new value − original value) ÷ original value × 100
The top part of the formula, new value minus original value, is the increase. Dividing it by the original value tells you what fraction of the starting amount the increase represents. Multiplying by 100 turns that fraction into a percentage.
How to work out percentage increase in three steps
Take a question that gives average nitrogen dioxide readings for a city of 44.4 micrograms per cubic metre in the first year and 54.8 in the fifth year. What is the percentage increase across the period?
- Find the increase. Subtract the original value from the new value: 54.8 − 44.4 = 10.4.
- Divide by the original value. 10.4 ÷ 44.4 = 0.234 (to three decimal places).
- Multiply by 100. 0.234 × 100 = 23.4.
The readings rose by 23.4%. The figures for the years in between do not matter here. Only the first and last values go into the calculation.
How to find the percentage increase between two numbers
The only judgement you need to make is which number is the original. It is the earlier value, the “before” figure, or the value the question says the change is measured “from”.
A price rises from £50 to £65. The increase is 65 − 50 = 15. Then 15 ÷ 50 = 0.3, and 0.3 × 100 = 30, a 30% increase.
Monthly sales grow from 80 units to 92 units. The increase is 92 − 80 = 12. Then 12 ÷ 80 = 0.15, a 15% increase.
A savings balance of £150 grows by £35. Here the question hands you the increase directly, so you skip the subtraction: 35 ÷ 150 = 0.2333, a 23.3% increase.
A useful check: if the new value is double the original, the increase is 100%. If it is one and a half times the original, the increase is 50%. Your answer should sit sensibly against those markers.
Worked example from a data table
Numerical tests rarely give you two clean numbers. More often you pick them out of a table that contains figures you do not need.
A company has donated to a children’s charity for five years. By what percentage has its annual contribution increased from the first year to the fifth?
| Year | Contribution (£) |
|---|---|
| Year 1 | 278,000 |
| Year 2 | 250,000 |
| Year 3 | 396,000 |
| Year 4 | 412,000 |
| Year 5 | 462,000 |
- Pick the right two values. The question asks about Year 1 and Year 5, so the dip in Year 2 is irrelevant.
- Find the increase. 462,000 − 278,000 = 184,000.
- Divide by the original. 184,000 ÷ 278,000 = 0.662 (to three decimal places).
- Multiply by 100. The contribution rose by 66.2%.
How to work out percentage increase or decrease
The same formula handles both directions. Work out (new value − original value) ÷ original value × 100. A positive answer is an increase and a negative answer is a decrease. If revenue falls from £80,000 to £68,000, you get (68,000 − 80,000) ÷ 80,000 × 100 = −15, which is a 15% decrease.
Many people find it easier to treat a fall separately and subtract the smaller number from the larger. Our guide to calculating percentage decrease walks through that version with its own examples.
Two increases in a row
When one percentage increase follows another, you cannot add them, because the second increase is applied to a value the first has already raised.
Say a value of 300 rises by 10% and then by a further 20%. Turn each change into a multiplier by adding it to 100% and writing it as a decimal: 1.10 and 1.20. Then apply them in turn:
- 300 × 1.10 = 330
- 330 × 1.20 = 396
The total rise is 96, and 96 ÷ 300 × 100 = 32, so the overall increase is 32%, not 30%. A quicker way to get the same answer is to multiply the multipliers: 1.10 × 1.20 = 1.32.
The same method works when a rise is followed by a fall. A 15% rise and then an 8% fall gives 1.15 × 0.92 = 1.058, an overall rise of 5.8%. Subtracting 8 from 15 gives 7%, and that wrong answer is often among the options.
Common mistakes to avoid
- Dividing by the new value. If revenue goes from £240,000 to £276,000, the increase is £36,000. Divided by the original £240,000 that is 15%. Divided by the new £276,000 it is 13.0%, which is wrong but will often appear as an option.
- Confusing percentages with percentage points. A conversion rate moving from 4% to 6% has risen by 2 percentage points, which is a 50% increase. Read which one the question wants.
- Picking the biggest absolute rise. When a question asks which row grew the most in percentage terms, the largest rise in pounds or units is often not the answer, because it may come from the largest starting figure.
- Rounding too early. Keep three or four decimal places until the final step, then round to what the question asks for.
If you know the value after an increase and need the value before it, you need a different method. Our guide to reverse percentages explains why you divide by the multiplier rather than taking the percentage off.
Calculating percentage increase quickly in a test
Even with a calculator allowed, a rough mental estimate catches keying errors. Work in 10% and 1% chunks: 10% of 1,240 is 124 and 1% is 12.4, so a rise of 434 on 1,240 is 35%, because 372 + 62 = 434.
It also helps to be fluent at moving between fractions, decimals and percentages, since 48 ÷ 120 is easier when you can see it as 2 ÷ 5. Our guide to converting fractions, decimals and percentages covers the conversions you will use most.
To put the method into practice under time pressure, try a numerical reasoning test with worked solutions for every question.
