What is the Percentage Difference from 45 to 51?
From 45 to 51 is a 13.3333% increase
Step by step
- Difference: 51 − 45 = 6
- Divide by the starting value: 6 ÷ 45 = 0.133333
- Multiply by 100: 13.3333%
How the answer is worked out
Percentage change measures a difference against the value you started with. The value went from 45 to 51, a difference of 6. Compared with the starting value of 45, that difference is 13.3333%, so this is a 13.3333% increase.
The new value is 1.1333 times the old one: for every 100 at the start there are now 113.3333.
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 $51 has gone up by 13.3333%.
- Pay: a wage that rises from $45 to $51 an hour is a 13.3333% pay rise.
- Audiences: a channel that grows from 45 to 51 subscribers has grown by 13.3333%.
A quicker way
Find 1% of the starting value: 45 ÷ 100 = 0.45. The difference of 6 is 13.3333 of those steps.
Percentage change is not the same as percentage points. If a rate moves from 45% to 51%, it changes by 6 percentage points, but by 13.3333% relative to where it started.
Check the answer
Work forwards from the start: 45 × (1 + 0.133333) = 45 × 1.133333 = 51. Getting 51 shows the answer is right.
Rounding
Rounded to a whole number the change is 13, to one decimal place 13.3 and to two decimal places 13.33. 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 71
- Difference: 71 − 9 = 62
- Divide by the starting value: 62 ÷ 9 = 6.888889
- Multiply by 100: 688.8889%
Why the change back is different
A 13.3333% rise followed by a 13.3333% fall does not bring you back to 45: it gives 44.2. The second percentage is taken of 51, not of 45, so to undo this change you need 11.7647% 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 51
- What percent more is 51 than 45?
- 45 to 51 as a percent change
- How much did 45 grow going to 51, in percent?
- Relative change between 45 and 51
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 | 13.3333% |
|---|---|
| Difference | 6 |
| New ÷ old | 1.133333 |
| Direction | increase |
Related results
| 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 52 | From 45 to 52 is a 15.5556% increase |
| 45 to 53 | From 45 to 53 is a 17.7778% increase |
| 45 to 61 | From 45 to 61 is a 35.5556% increase |
The other way round: Percentage difference from 51 to 45
Doing it in a spreadsheet
In Excel, Google Sheets or Numbers type =(51-45)/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 71 | Show answerFrom 9 to 71 is a 688.8889% increase |
| 4 to 42 | Show answerFrom 4 to 42 is a 950% increase |
| 69 to 16 | Show answerFrom 69 to 16 is a 76.8116% decrease |
| 8 to 63 | Show answerFrom 8 to 63 is a 687.5% increase |
| 37 to 23 | Show answerFrom 37 to 23 is a 37.8378% decrease |
| 27 to 63 | Show answerFrom 27 to 63 is a 133.3333% increase |
| 60 to 20 | Show answerFrom 60 to 20 is a 66.6667% decrease |
| 94 to 67 | Show answerFrom 94 to 67 is a 28.7234% decrease |
| 70 to 40 | Show answerFrom 70 to 40 is a 42.8571% decrease |
| 20 to 81 | Show answerFrom 20 to 81 is a 305% increase |
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 51?
Going from 45 to 51 is a 13.3333% increase. Formula and steps.
Is going from 45 to 51 an increase or a decrease?
An increase: the value grew by 6, which is 13.3333% of the starting value.
What is the percentage change from 51 back to 45?
-11.7647%. It is a different number because the starting value is now 51, not 45.
What is the percentage difference between 45 and 51?
When neither value is the starting point, use the average as the base: 6 ÷ 48 × 100 = 12.5%. 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 13.3333%.