A percentage decrease calculator measures a fall against the starting figure with (old - new) / old x 100, so a value that drops from 120 to 96 has fallen by 24, which is 24 / 120 x 100 = 20 percent.
The base is always the figure you began with. That one habit settles most confusion, including why 96 is 20 percent less than 120 while 120 is 25 percent more than 96. This page covers the reduction formula, how to cut a number by a percent, how to work backwards to the original, and a ready table of factors.
At a glance
Formula
(old - new) / old x 100Base
The starting or original figureCut a number by X%
number x (1 - X / 100)Recover the original
reduced value / (1 - X / 100)Example
120 down to 96 is a 20% decrease
Percentage decrease = (Old value - New value) / Old value x 100
Old value is the figure before the fall. New value is the lower figure after it. The answer is reported as a positive percent with the word decrease, or as a negative change.
What to type in the tool
Enter the original figure first and the lower figure second. The calculator above prints the drop as a number and as a percent of the original. Decimals work, so you can type an SGPA, a weight or a reading from a meter.
If the second figure turns out bigger, you have a rise rather than a fall, and the percentage increase calculator is the page to read. People also call this tool a reduction percentage calculator, a percentage less calculator or a decrease in percentage calculator, and some search for a reduce percentage calculator or a percentage of decrease calculator. The arithmetic does not change with the name.
- Write the original figure and the reduced figure.
- Subtract the reduced figure from the original to get the drop.
- Divide the drop by the original figure.
- Multiply by 100 and call the answer a decrease.
The percentage decrease calculator formula in detail
Drop = old - new
Percentage decrease = drop / old x 100
Three related sums come up again and again, and each has its own short rule:
| You want | Rule | Example |
|---|---|---|
| Percent fall between two figures | (old - new) / old x 100 | 120 to 96 = 20% |
| Reduce a number by a percent | number x (1 - X / 100) | 640 cut by 15% = 544 |
| Original before a cut | reduced / (1 - X / 100) | 360 after a 20% cut came from 450 |
Worked examples of reductions
Backlogs cleared. A student had 15 pending papers and cleared enough to leave 6. Drop 9. 9 / 15 x 100 = 60 percent reduction.
Hostel electricity. A floor used 450 units last month and 378 this month. Drop 72. 72 / 450 x 100 = 16 percent decrease. Any cost reduction percentage calculator works the same way, and units let you report the saving without quoting the bill.
SGPA dip. From 8.0 to 7.2 the drop is 0.8, and 0.8 / 8.0 x 100 = 10 percent. In grade points it is a fall of 0.8.
Working backwards. After a 20 percent cut, a batch has 360 seats. The original was 360 / 0.8 = 450, not 360 + 72 = 432.
Reduction factor table
Multiply by the factor to reduce a number by that percent. On the right you can read what 80 and 500 shrink to.
| Decrease | Multiply by | 80 becomes | 500 becomes |
|---|---|---|---|
| 5% | 0.95 | 76 | 475 |
| 10% | 0.90 | 72 | 450 |
| 15% | 0.85 | 68 | 425 |
| 20% | 0.80 | 64 | 400 |
| 25% | 0.75 | 60 | 375 |
| 30% | 0.70 | 56 | 350 |
| 40% | 0.60 | 48 | 300 |
| 50% | 0.50 | 40 | 250 |
| 60% | 0.40 | 32 | 200 |
| 75% | 0.25 | 20 | 125 |
| 90% | 0.10 | 8 | 50 |
A decrease can never pass 100 percent. A 100 percent fall takes any figure to zero.
How much less in percentage: why the answer flips
A how much less percentage calculator answers one question, and its mirror asks how much more. The question “how much less is 96 than 120” uses 120 as the base: 24 / 120 x 100 = 20 percent less. The question “how much more is 120 than 96” uses 96 as the base: 24 / 96 x 100 = 25 percent more. Same gap, different base, different answer.
This is also why a fall and a rise of the same percent do not cancel. Cut 200 by 20 percent and you get 160. Raise 160 by 20 percent and you reach 192, still short of 200. To get back you need a 25 percent rise.
Errors to avoid with a decrease
| Error | Result | Right way |
|---|---|---|
| Dividing the drop by the lower figure | 24 / 96 gives 25%, not 20% | Divide by the figure before the fall |
| Adding back the same percent | 360 + 20% of 360 is 432, not 450 | Divide the reduced figure by 0.8 |
| Quoting a fall in points as percent | Attendance 85% to 74% is 11 points, a 12.94% fall | Say which one you mean |
| Chaining cuts by adding | Two 10% cuts leave 81%, a 19% fall | Multiply the factors: 0.9 x 0.9 |
For attendance shortfalls in particular, the attendance calculator shows how many more classes bring you back above the line.
Questions students ask
How do I calculate percentage decrease?
Subtract the new figure from the old one, divide that drop by the old figure and multiply by 100. From 120 to 96, the drop of 24 is 20 percent of 120.
How do I reduce a number by a percentage?
Multiply by 1 minus the rate. To reduce 640 by 15 percent, 640 x 0.85 = 544.
How much less in percentage is 68 than 80?
The gap is 12 and the base is 80, so 68 is 15 percent less than 80. Seen the other way, 80 is about 17.65 percent more than 68.
Can a percentage decrease be more than 100?
No. A fall of 100 percent already takes the value to zero. If you see a bigger figure, the base was probably the smaller number.
How do I find the original value after a percentage reduction?
Divide the reduced figure by 1 minus the rate. If 360 is left after a 20 percent cut, the original was 360 / 0.8 = 450.
Is a decrease percentage calculator different from a percentage change calculator?
Only in sign. The decrease page reports a fall as a positive percent with the word decrease, and the change page shows it as a negative number.