What is the Percentage Difference from 40 to 5?
From 40 to 5 is a 87.5% decrease
Step by step
- Difference: 5 − 40 = -35
- Divide by the starting value: -35 ÷ 40 = -0.875
- Multiply by 100: -87.5%
How the answer is worked out
Percentage change measures a difference against the value you started with. The value went from 40 to 5, a difference of 35. Compared with the starting value of 40, that difference is 87.5%, so this is a 87.5% decrease.
The new value is 12.5% of the old one: for every 100 at the start there are now 12.5, so 87.5 out of every 100 have gone.
Why calculate this?
Percentage change compares a new value with an old one regardless of size: price rises, growth, discounts, score changes.
- Sales: a price cut from $40 to $5 is a 87.5% discount.
- Weight: going from 40 to 5 kilograms is a loss of 87.5% of the starting weight.
- Results: if a team scores 5 points this season after 40 last season, its total has dropped by 87.5%.
A quicker way
Find 1% of the starting value: 40 ÷ 100 = 0.4. The difference of 35 is 87.5 of those steps.
Percentage change is not the same as percentage points. If a rate moves from 40% to 5%, it changes by 35 percentage points, but by 87.5% relative to where it started.
Check the answer
Work forwards from the start: 40 × (1 − 0.875) = 40 × 0.125 = 5. Getting 5 shows the answer is right.
Rounding
Rounded to a whole number the change is -87, to one decimal place -87.5 and to two decimal places -87.50. Round only at the end: rounding halfway through a calculation can change the last digit.
The formula explained
percentage change = (new value − old value) ÷ old value × 100. A positive result is an increase and a negative result is a decrease. The old value is always the base, which is why the change from A to B and from B to A are different percentages.
Another worked example: 8 to 33
- Difference: 33 − 8 = 25
- Divide by the starting value: 25 ÷ 8 = 3.125
- Multiply by 100: 312.5%
Why the change back is different
A 87.5% fall followed by a 87.5% rise does not bring you back to 40: it gives 9.375. The second percentage is taken of 5, not of 40, so to undo this change you need 700% instead.
Other ways to ask this
The same calculation is often asked in other words. All of these have the answer above:
- Percentage decrease from 40 to 5
- What percent less is 5 than 40?
- 40 to 5 as a percent change
- How much did 40 fall going to 5, in percent?
- Relative change between 40 and 5
Terms used on this page
- Old value: the starting amount, used as the base of the percentage.
- New value: the amount after the change.
- Increase: a positive change: the new value is bigger.
- Percentage point: the plain difference between two rates, not a relative change.
The answer in other forms
| Change | -87.5% |
|---|---|
| Difference | -35 |
| New ÷ old | 0.125 |
| Direction | decrease |
Related results
| 40 to 3 | From 40 to 3 is a 92.5% decrease |
| 40 to 4 | From 40 to 4 is a 90% decrease |
| 40 to 6 | From 40 to 6 is a 85% decrease |
| 40 to 7 | From 40 to 7 is a 82.5% decrease |
| 40 to 15 | From 40 to 15 is a 62.5% decrease |
The other way round: Percentage difference from 5 to 40
Doing it in a spreadsheet
In Excel, Google Sheets or Numbers type =(5-40)/40*100 into any cell. Replace the numbers with cell references (for example A1 and B1) to reuse the formula for a whole column.
Common mistakes
Always divide by the starting value, not the new one. A rise from 40 to 50 is +25%, but the fall from 50 back to 40 is −20%.
Practice examples
| 8 to 33 | Show answerFrom 8 to 33 is a 312.5% increase |
| 68 to 99 | Show answerFrom 68 to 99 is a 45.5882% increase |
| 50 to 65 | Show answerFrom 50 to 65 is a 30% increase |
| 80 to 32 | Show answerFrom 80 to 32 is a 60% decrease |
| 18 to 68 | Show answerFrom 18 to 68 is a 277.7778% increase |
| 69 to 28 | Show answerFrom 69 to 28 is a 59.4203% decrease |
| 59 to 19 | Show answerFrom 59 to 19 is a 67.7966% decrease |
| 97 to 53 | Show answerFrom 97 to 53 is a 45.3608% decrease |
| 69 to 84 | Show answerFrom 69 to 84 is a 21.7391% increase |
| 74 to 75 | Show answerFrom 74 to 75 is a 1.3514% increase |
How this answer was calculated
The result is worked out from the numbers in this page's address when the page is opened, using exact arithmetic wherever possible and rounding only for display. Nothing is copied from a printed table. If you think an answer is wrong, please tell us through the contact page and we will check it.
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Questions
What is the Percentage Difference from 40 to 5?
Going from 40 to 5 is a 87.5% decrease. Formula and steps.
Is going from 40 to 5 an increase or a decrease?
A decrease: the value fell by 35, which is 87.5% of the starting value.
What is the percentage change from 5 back to 40?
700%. It is a different number because the starting value is now 5, not 40.
What is the percentage difference between 40 and 5?
When neither value is the starting point, use the average as the base: 35 ÷ 22.5 × 100 = 155.5556%. That is the symmetric percentage difference.
How do I calculate percentage change in Excel or Google Sheets?
Put the old value in A1 and the new value in B1, then type =(B1-A1)/A1 and format the cell as a percentage. For these numbers it shows -87.5%.