PERCENTAGE CHANGE
Percentage Change
Subtract the old from the new, then divide by the old value. Show that as a Percentage.
Comparing Old to New
Change: subtract old value from new value.
Example: You had 5 books, but now have 7. The change is: 7-5 = 2.
Percentage Change: show that as a percent of the old value ... so divide by the old value and make it a percentage:
So the percentage change from 5 to 7 is: 2/5 = 0.4 = 40%
Percentage Change is all about comparing old to new values. See percentage change, difference and error for other options.
Change: subtract old value from new value.
Example: You had 5 books, but now have 7. The change is: 7-5 = 2.
| |
Percentage Change: show that as a percent of the old value ... so divide by the old value and make it a percentage:
So the percentage change from 5 to 7 is: 2/5 = 0.4 = 40%
|
Percentage Change is all about comparing old to new values. See percentage change, difference and error for other options.
How to Calculate
Here are two ways to calculate a percentage change, use whichever method you prefer:
Method 1
Step 1: Calculate the change (subtract old value from the new value)
Step 2: Divide that change by the old value (you will get a decimal number)
Step 3: Convert that to a percentage (by multiplying by 100 and adding a "%" sign)
Note: if the new value is greater then the old value, it is a percentage increase, otherwise it is a decrease.
Step 1: Calculate the change (subtract old value from the new value) |
Step 2: Divide that change by the old value (you will get a decimal number) |
Step 3: Convert that to a percentage (by multiplying by 100 and adding a "%" sign) |
Note: if the new value is greater then the old value, it is a percentage increase, otherwise it is a decrease. |
Method 2
Step 1: Divide the New Value by the Old Value (you will get a decimal number)
Step 2: Convert that to a percentage (by multiplying by 100 and adding a "%" sign)
Step 3: Subtract 100% from that
Note: if the result is positive it is a percentage increase, if negative, just remove the minus sign and call it a decrease.
Step 1: Divide the New Value by the Old Value (you will get a decimal number) |
Step 2: Convert that to a percentage (by multiplying by 100 and adding a "%" sign) |
Step 3: Subtract 100% from that |
Note: if the result is positive it is a percentage increase, if negative, just remove the minus sign and call it a decrease. |
Examples
Why Compare to Old Value?
Because you are saying how much a value has changed.
The Formula
You can also put the values into this formula:
New Value - Old Value
| × 100% |
|Old Value|
|
(The "|" symbols mean absolute value, so negatives become positive)
How to Reverse a Rise or Fall
Some people think that a percentage increase can be "reversed" by the same percentage decrease.But no!
Example: 10% of 100
How to do it properly
To "reverse" a percentage rise or fall, use the right formula here:
To Reverse: | Use this Percent: | Example 10% |
---|---|---|
An "x" percent rise: |
x/(1+x/100)
| 10/(1+10/100) = 10/(1.1) = 9.0909... |
An "x" percent fall: |
x/(1-x/100)
| 10/(1-10/100) = 10/(0.9) = 11.111... |
Percentage Difference,
Percentage Error,
Percentage Change
They are very similar ...
They all show a difference between two values as a percentage of one (or both) values
- Use Percentage Change when comparing an Old Value to a New Value
- Use Percentage Error when comparing an Approximate Value to an Exact Value
- Use Percentage Difference when both values mean the same kind of thing (one value is not obviously older or better than the other).
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