What is the Percentage Difference from 20 to 21?
From 20 to 21 is a 5% increase
Step by step
- Difference: 21 − 20 = 1
- Divide by the starting value: 1 ÷ 20 = 0.05
- Multiply by 100: 5%
How the answer is worked out
Percentage change measures a difference against the value you started with. The value went from 20 to 21, a difference of 1. Compared with the starting value of 20, that difference is 5%, so this is a 5% increase.
The new value is 1.05 times the old one: for every 100 at the start there are now 105.
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 $20 to $21 has gone up by 5%.
- Pay: a wage that rises from $20 to $21 an hour is a 5% pay rise.
- Audiences: a channel that grows from 20 to 21 subscribers has grown by 5%.
A quicker way
Find 1% of the starting value: 20 ÷ 100 = 0.2. The difference of 1 is 5 of those steps.
Percentage change is not the same as percentage points. If a rate moves from 20% to 21%, it changes by 1 percentage points, but by 5% relative to where it started.
Check the answer
Work forwards from the start: 20 × (1 + 0.05) = 20 × 1.05 = 21. Getting 21 shows the answer is right.
Rounding
Rounded to a whole number the change is 5, to one decimal place 5.0 and to two decimal places 5.00. 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 8
- Difference: 8 − 4 = 4
- Divide by the starting value: 4 ÷ 4 = 1
- Multiply by 100: 100%
Why the change back is different
A 5% rise followed by a 5% fall does not bring you back to 20: it gives 19.95. The second percentage is taken of 21, not of 20, so to undo this change you need 4.7619% 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 20 to 21
- What percent more is 21 than 20?
- 20 to 21 as a percent change
- How much did 20 grow going to 21, in percent?
- Relative change between 20 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 | 5% |
|---|---|
| Difference | 1 |
| New ÷ old | 1.05 |
| Direction | increase |
Related results
| 20 to 19 | From 20 to 19 is a 5% decrease |
| 20 to 22 | From 20 to 22 is a 10% increase |
| 20 to 23 | From 20 to 23 is a 15% increase |
| 20 to 31 | From 20 to 31 is a 55% increase |
The other way round: Percentage difference from 21 to 20
Doing it in a spreadsheet
In Excel, Google Sheets or Numbers type =(21-20)/20*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 8 | Show answerFrom 4 to 8 is a 100% increase |
| 38 to 60 | Show answerFrom 38 to 60 is a 57.8947% increase |
| 77 to 94 | Show answerFrom 77 to 94 is a 22.0779% increase |
| 46 to 31 | Show answerFrom 46 to 31 is a 32.6087% decrease |
| 4 to 97 | Show answerFrom 4 to 97 is a 2,325% increase |
| 14 to 48 | Show answerFrom 14 to 48 is a 242.8571% increase |
| 4 to 89 | Show answerFrom 4 to 89 is a 2,125% increase |
| 4 to 90 | Show answerFrom 4 to 90 is a 2,150% increase |
| 65 to 99 | Show answerFrom 65 to 99 is a 52.3077% increase |
| 20 to 11 | Show answerFrom 20 to 11 is a 45% 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 20 to 21?
Going from 20 to 21 is a 5% increase. Formula and steps.
Is going from 20 to 21 an increase or a decrease?
An increase: the value grew by 1, which is 5% of the starting value.
What is the percentage change from 21 back to 20?
-4.7619%. It is a different number because the starting value is now 21, not 20.
What is the percentage difference between 20 and 21?
When neither value is the starting point, use the average as the base: 1 ÷ 20.5 × 100 = 4.878%. 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 5%.