What is the Percentage Difference from 16 to 21?
From 16 to 21 is a 31.25% increase
Step by step
- Difference: 21 − 16 = 5
- Divide by the starting value: 5 ÷ 16 = 0.3125
- Multiply by 100: 31.25%
How the answer is worked out
Percentage change measures a difference against the value you started with. The value went from 16 to 21, a difference of 5. Compared with the starting value of 16, that difference is 31.25%, so this is a 31.25% increase.
The new value is 1.3125 times the old one: for every 100 at the start there are now 131.25.
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 $16 to $21 has gone up by 31.25%.
- Pay: a wage that rises from $16 to $21 an hour is a 31.25% pay rise.
- Audiences: a channel that grows from 16 to 21 subscribers has grown by 31.25%.
A quicker way
Find 1% of the starting value: 16 ÷ 100 = 0.16. The difference of 5 is 31.25 of those steps.
Percentage change is not the same as percentage points. If a rate moves from 16% to 21%, it changes by 5 percentage points, but by 31.25% relative to where it started.
Check the answer
Work forwards from the start: 16 × (1 + 0.3125) = 16 × 1.3125 = 21. Getting 21 shows the answer is right.
Rounding
Rounded to a whole number the change is 31, to one decimal place 31.3 and to two decimal places 31.25. 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: 4 to 3
- Difference: 3 − 4 = -1
- Divide by the starting value: -1 ÷ 4 = -0.25
- Multiply by 100: -25%
Why the change back is different
A 31.25% rise followed by a 31.25% fall does not bring you back to 16: it gives 14.4375. The second percentage is taken of 21, not of 16, so to undo this change you need 23.8095% 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 16 to 21
- What percent more is 21 than 16?
- 16 to 21 as a percent change
- How much did 16 grow going to 21, in percent?
- Relative change between 16 and 21
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 | 31.25% |
|---|---|
| Difference | 5 |
| New ÷ old | 1.3125 |
| Direction | increase |
Related results
| 16 to 19 | From 16 to 19 is a 18.75% increase |
| 16 to 20 | From 16 to 20 is a 25% increase |
| 16 to 22 | From 16 to 22 is a 37.5% increase |
| 16 to 23 | From 16 to 23 is a 43.75% increase |
| 16 to 31 | From 16 to 31 is a 93.75% increase |
The other way round: Percentage difference from 21 to 16
Doing it in a spreadsheet
In Excel, Google Sheets or Numbers type =(21-16)/16*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
| 4 to 3 | Show answerFrom 4 to 3 is a 25% decrease |
| 40 to 15 | Show answerFrom 40 to 15 is a 62.5% decrease |
| 32 to 50 | Show answerFrom 32 to 50 is a 56.25% increase |
| 99 to 98 | Show answerFrom 99 to 98 is a 1.0101% decrease |
| 43 to 74 | Show answerFrom 43 to 74 is a 72.093% increase |
| 38 to 72 | Show answerFrom 38 to 72 is a 89.4737% increase |
| 3 to 27 | Show answerFrom 3 to 27 is a 800% increase |
| 70 to 93 | Show answerFrom 70 to 93 is a 32.8571% increase |
| 69 to 26 | Show answerFrom 69 to 26 is a 62.3188% decrease |
| 52 to 45 | Show answerFrom 52 to 45 is a 13.4615% decrease |
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 16 to 21?
Going from 16 to 21 is a 31.25% increase. Formula and steps.
Is going from 16 to 21 an increase or a decrease?
An increase: the value grew by 5, which is 31.25% of the starting value.
What is the percentage change from 21 back to 16?
-23.8095%. It is a different number because the starting value is now 21, not 16.
What is the percentage difference between 16 and 21?
When neither value is the starting point, use the average as the base: 5 ÷ 18.5 × 100 = 27.027%. 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 31.25%.