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What is the Percentage Difference from 41 to 31?

From 41 to 31 is a 24.3902% decrease

Step by step

  1. Difference: 31 − 41 = -10
  2. Divide by the starting value: -10 ÷ 41 = -0.243902
  3. Multiply by 100: -24.3902%

How the answer is worked out

Percentage change measures a difference against the value you started with. The value went from 41 to 31, a difference of 10. Compared with the starting value of 41, that difference is 24.3902%, so this is a 24.3902% decrease.

The new value is 75.6098% of the old one: for every 100 at the start there are now 75.6098, so 24.3902 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 $41 to $31 is a 24.3902% discount.
  • Weight: going from 41 to 31 kilograms is a loss of 24.3902% of the starting weight.
  • Results: if a team scores 31 points this season after 41 last season, its total has dropped by 24.3902%.

A quicker way

Find 1% of the starting value: 41 ÷ 100 = 0.41. The difference of 10 is 24.3902 of those steps.

Percentage change is not the same as percentage points. If a rate moves from 41% to 31%, it changes by 10 percentage points, but by 24.3902% relative to where it started.

Check the answer

Work forwards from the start: 41 × (1 − 0.243902) = 41 × 0.756098 = 31. Getting 31 shows the answer is right.

Rounding

Rounded to a whole number the change is -24, to one decimal place -24.4 and to two decimal places -24.39. 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: 9 to 45

  1. Difference: 45 − 9 = 36
  2. Divide by the starting value: 36 ÷ 9 = 4
  3. Multiply by 100: 400%

Why the change back is different

A 24.3902% fall followed by a 24.3902% rise does not bring you back to 41: it gives 38.561. The second percentage is taken of 31, not of 41, so to undo this change you need 32.2581% 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 41 to 31
  • What percent less is 31 than 41?
  • 41 to 31 as a percent change
  • How much did 41 fall going to 31, in percent?
  • Relative change between 41 and 31

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-24.3902%
Difference-10
New ÷ old0.756098
Directiondecrease

Related results

41 to 29

From 41 to 29 is a 29.2683% decrease

41 to 30

From 41 to 30 is a 26.8293% decrease

41 to 32

From 41 to 32 is a 21.9512% decrease

41 to 33

From 41 to 33 is a 19.5122% decrease

The other way round: Percentage difference from 31 to 41

Doing it in a spreadsheet

In Excel, Google Sheets or Numbers type =(31-41)/41*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

9 to 45
Show answer

From 9 to 45 is a 400% increase

22 to 23
Show answer

From 22 to 23 is a 4.5455% increase

31 to 63
Show answer

From 31 to 63 is a 103.2258% increase

43 to 65
Show answer

From 43 to 65 is a 51.1628% increase

27 to 6
Show answer

From 27 to 6 is a 77.7778% decrease

97 to 93
Show answer

From 97 to 93 is a 4.1237% decrease

79 to 53
Show answer

From 79 to 53 is a 32.9114% decrease

87 to 47
Show answer

From 87 to 47 is a 45.977% decrease

44 to 50
Show answer

From 44 to 50 is a 13.6364% increase

81 to 8
Show answer

From 81 to 8 is a 90.1235% decrease

Calculate another

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 41 to 31?

Going from 41 to 31 is a 24.3902% decrease. Formula and steps.

Is going from 41 to 31 an increase or a decrease?

A decrease: the value fell by 10, which is 24.3902% of the starting value.

What is the percentage change from 31 back to 41?

32.2581%. It is a different number because the starting value is now 31, not 41.

What is the percentage difference between 41 and 31?

When neither value is the starting point, use the average as the base: 10 ÷ 36 × 100 = 27.7778%. 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 -24.3902%.