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What is the Percentage Difference from 45 to 48?

From 45 to 48 is a 6.6667% increase

Step by step

  1. Difference: 48 − 45 = 3
  2. Divide by the starting value: 3 ÷ 45 = 0.066667
  3. Multiply by 100: 6.6667%

How the answer is worked out

Percentage change measures a difference against the value you started with. The value went from 45 to 48, a difference of 3. Compared with the starting value of 45, that difference is 6.6667%, so this is a 6.6667% increase.

The new value is 1.0667 times the old one: for every 100 at the start there are now 106.6667.

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 $45 to $48 has gone up by 6.6667%.
  • Pay: a wage that rises from $45 to $48 an hour is a 6.6667% pay rise.
  • Audiences: a channel that grows from 45 to 48 subscribers has grown by 6.6667%.

A quicker way

Find 1% of the starting value: 45 ÷ 100 = 0.45. The difference of 3 is 6.6667 of those steps.

Percentage change is not the same as percentage points. If a rate moves from 45% to 48%, it changes by 3 percentage points, but by 6.6667% relative to where it started.

Check the answer

Work forwards from the start: 45 × (1 + 0.066667) = 45 × 1.066667 = 48. Getting 48 shows the answer is right.

Rounding

Rounded to a whole number the change is 7, to one decimal place 6.7 and to two decimal places 6.67. 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 63

  1. Difference: 63 − 9 = 54
  2. Divide by the starting value: 54 ÷ 9 = 6
  3. Multiply by 100: 600%

Why the change back is different

A 6.6667% rise followed by a 6.6667% fall does not bring you back to 45: it gives 44.8. The second percentage is taken of 48, not of 45, so to undo this change you need 6.25% 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 45 to 48
  • What percent more is 48 than 45?
  • 45 to 48 as a percent change
  • How much did 45 grow going to 48, in percent?
  • Relative change between 45 and 48

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

Change6.6667%
Difference3
New ÷ old1.066667
Directionincrease

Related results

45 to 46

From 45 to 46 is a 2.2222% increase

45 to 47

From 45 to 47 is a 4.4444% increase

45 to 49

From 45 to 49 is a 8.8889% increase

45 to 50

From 45 to 50 is a 11.1111% increase

45 to 58

From 45 to 58 is a 28.8889% increase

The other way round: Percentage difference from 48 to 45

Doing it in a spreadsheet

In Excel, Google Sheets or Numbers type =(48-45)/45*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 63
Show answer

From 9 to 63 is a 600% increase

78 to 74
Show answer

From 78 to 74 is a 5.1282% decrease

97 to 42
Show answer

From 97 to 42 is a 56.701% decrease

95 to 86
Show answer

From 95 to 86 is a 9.4737% decrease

29 to 50
Show answer

From 29 to 50 is a 72.4138% increase

93 to 49
Show answer

From 93 to 49 is a 47.3118% decrease

90 to 4
Show answer

From 90 to 4 is a 95.5556% decrease

57 to 94
Show answer

From 57 to 94 is a 64.9123% increase

89 to 82
Show answer

From 89 to 82 is a 7.8652% decrease

36 to 61
Show answer

From 36 to 61 is a 69.4444% 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 45 to 48?

Going from 45 to 48 is a 6.6667% increase. Formula and steps.

Is going from 45 to 48 an increase or a decrease?

An increase: the value grew by 3, which is 6.6667% of the starting value.

What is the percentage change from 48 back to 45?

-6.25%. It is a different number because the starting value is now 48, not 45.

What is the percentage difference between 45 and 48?

When neither value is the starting point, use the average as the base: 3 ÷ 46.5 × 100 = 6.4516%. 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 6.6667%.