What is the Percentage Difference from 100 to 71?
From 100 to 71 is a 29% decrease
Step by step
- Difference: 71 − 100 = -29
- Divide by the starting value: -29 ÷ 100 = -0.29
- Multiply by 100: -29%
How the answer is worked out
Percentage change measures a difference against the value you started with. The value went from 100 to 71, a difference of 29. Compared with the starting value of 100, that difference is 29%, so this is a 29% decrease.
The new value is 71% of the old one: for every 100 at the start there are now 71, so 29 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 $100 to $71 is a 29% discount.
- Weight: going from 100 to 71 kilograms is a loss of 29% of the starting weight.
- Results: if a team scores 71 points this season after 100 last season, its total has dropped by 29%.
A quicker way
Find 1% of the starting value: 100 ÷ 100 = 1. The difference of 29 is 29 of those steps.
Percentage change is not the same as percentage points. If a rate moves from 100% to 71%, it changes by 29 percentage points, but by 29% relative to where it started.
Check the answer
Work forwards from the start: 100 × (1 − 0.29) = 100 × 0.71 = 71. Getting 71 shows the answer is right.
Rounding
Rounded to a whole number the change is -29, to one decimal place -29.0 and to two decimal places -29.00. 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: 19 to 93
- Difference: 93 − 19 = 74
- Divide by the starting value: 74 ÷ 19 = 3.894737
- Multiply by 100: 389.4737%
Why the change back is different
A 29% fall followed by a 29% rise does not bring you back to 100: it gives 91.59. The second percentage is taken of 71, not of 100, so to undo this change you need 40.8451% 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 100 to 71
- What percent less is 71 than 100?
- 100 to 71 as a percent change
- How much did 100 fall going to 71, in percent?
- Relative change between 100 and 71
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 | -29% |
|---|---|
| Difference | -29 |
| New ÷ old | 0.71 |
| Direction | decrease |
Related results
| 100 to 69 | From 100 to 69 is a 31% decrease |
| 100 to 70 | From 100 to 70 is a 30% decrease |
| 100 to 72 | From 100 to 72 is a 28% decrease |
| 100 to 73 | From 100 to 73 is a 27% decrease |
| 100 to 81 | From 100 to 81 is a 19% decrease |
The other way round: Percentage difference from 71 to 100
Doing it in a spreadsheet
In Excel, Google Sheets or Numbers type =(71-100)/100*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
| 19 to 93 | Show answerFrom 19 to 93 is a 389.4737% increase |
| 88 to 42 | Show answerFrom 88 to 42 is a 52.2727% decrease |
| 92 to 55 | Show answerFrom 92 to 55 is a 40.2174% decrease |
| 5 to 75 | Show answerFrom 5 to 75 is a 1,400% increase |
| 64 to 38 | Show answerFrom 64 to 38 is a 40.625% decrease |
| 27 to 99 | Show answerFrom 27 to 99 is a 266.6667% increase |
| 93 to 27 | Show answerFrom 93 to 27 is a 70.9677% decrease |
| 4 to 23 | Show answerFrom 4 to 23 is a 475% increase |
| 54 to 68 | Show answerFrom 54 to 68 is a 25.9259% increase |
| 96 to 83 | Show answerFrom 96 to 83 is a 13.5417% decrease |
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 100 to 71?
Going from 100 to 71 is a 29% decrease. Formula and steps.
Is going from 100 to 71 an increase or a decrease?
A decrease: the value fell by 29, which is 29% of the starting value.
What is the percentage change from 71 back to 100?
40.8451%. It is a different number because the starting value is now 71, not 100.
What is the percentage difference between 100 and 71?
When neither value is the starting point, use the average as the base: 29 ÷ 85.5 × 100 = 33.9181%. 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 -29%.