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What is the Percentage Difference from 40 to 61?

From 40 to 61 is a 52.5% increase

Step by step

  1. Difference: 61 − 40 = 21
  2. Divide by the starting value: 21 ÷ 40 = 0.525
  3. Multiply by 100: 52.5%

How the answer is worked out

Percentage change measures a difference against the value you started with. The value went from 40 to 61, a difference of 21. Compared with the starting value of 40, that difference is 52.5%, so this is a 52.5% increase.

The new value is 1.525 times the old one: for every 100 at the start there are now 152.5.

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 $40 to $61 has gone up by 52.5%.
  • Pay: a wage that rises from $40 to $61 an hour is a 52.5% pay rise.
  • Audiences: a channel that grows from 40 to 61 subscribers has grown by 52.5%.

A quicker way

Find 1% of the starting value: 40 ÷ 100 = 0.4. The difference of 21 is 52.5 of those steps.

Percentage change is not the same as percentage points. If a rate moves from 40% to 61%, it changes by 21 percentage points, but by 52.5% relative to where it started.

Check the answer

Work forwards from the start: 40 × (1 + 0.525) = 40 × 1.525 = 61. Getting 61 shows the answer is right.

Rounding

Rounded to a whole number the change is 53, to one decimal place 52.5 and to two decimal places 52.50. 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: 9 to 49

  1. Difference: 49 − 9 = 40
  2. Divide by the starting value: 40 ÷ 9 = 4.444444
  3. Multiply by 100: 444.4444%

Why the change back is different

A 52.5% rise followed by a 52.5% fall does not bring you back to 40: it gives 28.975. The second percentage is taken of 61, not of 40, so to undo this change you need 34.4262% 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 40 to 61
  • What percent more is 61 than 40?
  • 40 to 61 as a percent change
  • How much did 40 grow going to 61, in percent?
  • Relative change between 40 and 61

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

Change52.5%
Difference21
New ÷ old1.525
Directionincrease

Related results

40 to 59

From 40 to 59 is a 47.5% increase

40 to 60

From 40 to 60 is a 50% increase

40 to 62

From 40 to 62 is a 55% increase

40 to 63

From 40 to 63 is a 57.5% increase

40 to 71

From 40 to 71 is a 77.5% increase

The other way round: Percentage difference from 61 to 40

Doing it in a spreadsheet

In Excel, Google Sheets or Numbers type =(61-40)/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

9 to 49
Show answer

From 9 to 49 is a 444.4444% increase

51 to 29
Show answer

From 51 to 29 is a 43.1373% decrease

14 to 52
Show answer

From 14 to 52 is a 271.4286% increase

64 to 93
Show answer

From 64 to 93 is a 45.3125% increase

48 to 95
Show answer

From 48 to 95 is a 97.9167% increase

18 to 29
Show answer

From 18 to 29 is a 61.1111% increase

40 to 26
Show answer

From 40 to 26 is a 35% decrease

85 to 21
Show answer

From 85 to 21 is a 75.2941% decrease

71 to 91
Show answer

From 71 to 91 is a 28.169% increase

85 to 87
Show answer

From 85 to 87 is a 2.3529% 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 40 to 61?

Going from 40 to 61 is a 52.5% increase. Formula and steps.

Is going from 40 to 61 an increase or a decrease?

An increase: the value grew by 21, which is 52.5% of the starting value.

What is the percentage change from 61 back to 40?

-34.4262%. It is a different number because the starting value is now 61, not 40.

What is the percentage difference between 40 and 61?

When neither value is the starting point, use the average as the base: 21 ÷ 50.5 × 100 = 41.5842%. 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 52.5%.