These questions give an earlier value and a later value and ask how large the rise or fall is as a percentage. The essential decision is which value belongs in the denominator.
Use the earlier value as the base
First identify the earlier value: this is the original whole and therefore the base. Next find the size of the change by subtracting the smaller value from the larger one. Divide that change by the earlier value, then multiply by 100. Finally, label the direction from the order of the values: later above earlier means an increase, while later below earlier means a decrease.
| Question feature | Form to use |
|---|---|
| Later value is greater | (Later - earlier) / earlier x 100, described as an increase |
| Later value is smaller | (Earlier - later) / earlier x 100, described as a decrease |
| Rounding is requested | Keep the unrounded quotient through the multiplication by 100, then round once at the end |
For a rise example, suppose a value moves from 180 to 234. The change is 54, and the earlier value is 180, so 54 / 180 x 100 = 30%. For a fall example, suppose a value moves from 160 to 124. The change is 36, so 36 / 160 x 100 = 22.5% decrease.
The denominator is not simply the smaller value and it is not always the number written first in a calculation you are shown. It is the value at the earlier time. If the result does not terminate, retain the calculator value until the final step and follow the requested precision exactly.
Avoid these traps
| Tempting route | How to reject it |
|---|---|
| Divide the change by the later value | That compares the change with the destination rather than with the original whole. Mark the earlier value before subtracting, and keep it as the denominator. |
| Attach a percent sign to the raw numerical difference | Subtraction gives an amount, not a rate. The amount must still be divided by the earlier value and multiplied by 100. |
| Report the later value as a percentage of the earlier value | This measures how much of the original whole is present, not how much it changed. The numerator for percentage change is the difference between the values. |
| Assume reversing the journey keeps the same percentage | The absolute difference stays the same, but the earlier value changes. Recalculate with the new earlier value instead of copying the percentage from the opposite direction. |
A useful reasonableness check is to compare the change with familiar fractions of the earlier value. If the change is roughly one quarter of that base, the percentage should be near 25%, not near the raw change or the percentage represented by the later total.
Try it
Daily visitors to a garden rise from 240 on Monday to 300 on Tuesday. What is the percent increase? Enter the number of percent.
A production count rises from 120 to 150. Which method does NOT calculate its percent change correctly?
- 30 / 120 x 100
- 150 - 120 = 30, then 30 / 120 x 100
- 30 / 150 x 100
- Use the old value 120 as the base.
A bus route records 45 delays one month and 58 the next. What is the percent increase? Enter the number of percent, rounded to the nearest whole number.