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What is the Percentage Difference from 31 to 33?

From 31 to 33 is a 6.4516% increase

Step by step

  1. Difference: 33 − 31 = 2
  2. Divide by the starting value: 2 ÷ 31 = 0.064516
  3. Multiply by 100: 6.4516%

How the answer is worked out

Percentage change measures a difference against the value you started with. The value went from 31 to 33, a difference of 2. Compared with the starting value of 31, that difference is 6.4516%, so this is a 6.4516% increase.

The new value is 1.0645 times the old one: for every 100 at the start there are now 106.4516.

Why calculate this?

Percentage change compares a new value with an old one regardless of size: price rises, growth, discounts, score changes.

  • Prices: an item whose price rises from $31 to $33 has gone up by 6.4516%.
  • Pay: a wage that rises from $31 to $33 an hour is a 6.4516% pay rise.
  • Audiences: a channel that grows from 31 to 33 subscribers has grown by 6.4516%.

A quicker way

Find 1% of the starting value: 31 ÷ 100 = 0.31. The difference of 2 is 6.4516 of those steps.

Percentage change is not the same as percentage points. If a rate moves from 31% to 33%, it changes by 2 percentage points, but by 6.4516% relative to where it started.

Check the answer

Work forwards from the start: 31 × (1 + 0.064516) = 31 × 1.064516 = 33. Getting 33 shows the answer is right.

Rounding

Rounded to a whole number the change is 6, to one decimal place 6.5 and to two decimal places 6.45. 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: 7 to 59

  1. Difference: 59 − 7 = 52
  2. Divide by the starting value: 52 ÷ 7 = 7.428571
  3. Multiply by 100: 742.8571%

Why the change back is different

A 6.4516% rise followed by a 6.4516% fall does not bring you back to 31: it gives 30.871. The second percentage is taken of 33, not of 31, so to undo this change you need 6.0606% instead.

Other ways to ask this

The same calculation is often asked in other words. All of these have the answer above:

  • Percentage increase from 31 to 33
  • What percent more is 33 than 31?
  • 31 to 33 as a percent change
  • How much did 31 grow going to 33, in percent?
  • Relative change between 31 and 33

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

Change6.4516%
Difference2
New ÷ old1.064516
Directionincrease

Related results

31 to 32

From 31 to 32 is a 3.2258% increase

31 to 34

From 31 to 34 is a 9.6774% increase

31 to 35

From 31 to 35 is a 12.9032% increase

31 to 43

From 31 to 43 is a 38.7097% increase

The other way round: Percentage difference from 33 to 31

Doing it in a spreadsheet

In Excel, Google Sheets or Numbers type =(33-31)/31*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

7 to 59
Show answer

From 7 to 59 is a 742.8571% increase

60 to 57
Show answer

From 60 to 57 is a 5% decrease

65 to 26
Show answer

From 65 to 26 is a 60% decrease

67 to 66
Show answer

From 67 to 66 is a 1.4925% decrease

58 to 60
Show answer

From 58 to 60 is a 3.4483% increase

86 to 66
Show answer

From 86 to 66 is a 23.2558% decrease

20 to 17
Show answer

From 20 to 17 is a 15% decrease

51 to 29
Show answer

From 51 to 29 is a 43.1373% decrease

75 to 72
Show answer

From 75 to 72 is a 4% decrease

27 to 90
Show answer

From 27 to 90 is a 233.3333% increase

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 31 to 33?

Going from 31 to 33 is a 6.4516% increase. Formula and steps.

Is going from 31 to 33 an increase or a decrease?

An increase: the value grew by 2, which is 6.4516% of the starting value.

What is the percentage change from 33 back to 31?

-6.0606%. It is a different number because the starting value is now 33, not 31.

What is the percentage difference between 31 and 33?

When neither value is the starting point, use the average as the base: 2 ÷ 32 × 100 = 6.25%. 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 6.4516%.