General
Percentage Decrease Calculator
Works a percentage decrease, where reversing it needs a different percentage.
Result
A decrease and the increase required to reverse it are never the same percentage, because they are measured from different bases.
Get a Free Business AuditHow the calculation works
The decrease divided by the original value, multiplied by a hundred. The asymmetry worth understanding is that reversing a percentage decrease requires a larger percentage increase, because the base has shrunk: a 50% decrease then a 50% increase leaves 75 from a starting 100.
What moves the number
- The original value as the base.
- Whether the decrease is being reversed or compounded.
- Successive decreases, which compound.
- Whether a decrease to zero is possible.
Where this one goes wrong
A 50% fall followed by a 50% rise does not return to the start, it leaves three quarters of it, and that asymmetry explains why a volatile series can trend downward while the average percentage change is zero. It is the single most useful thing to understand about percentage decreases. Successive decreases also compound, so two 10% falls leave 81% rather than 80%.
Before you quote
- Remember that reversing a decrease needs a larger increase.
- Compound successive decreases rather than adding them.
- Show absolute figures where the base is small.
Questions
About this calculator
Does a 50% fall then a 50% rise return to the start?
No, it leaves 75 from a starting 100, because the rise applies to the reduced base. That asymmetry explains why a volatile series can trend downward while the average percentage change is zero.
What increase reverses a 20% decrease?
25%, because the base has shrunk to 80 and returning to 100 requires adding 20 to 80. Reversing any percentage decrease always requires a larger percentage increase than the decrease that caused it.
Do successive decreases add?
No, they compound. Two 10% decreases leave 81% rather than 80%, which is a small difference over two periods and a meaningful one over many, particularly in anything describing decline over years.
The formula
(original − new) ÷ original × 100 = % decrease
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How to use this calculator
- Original value. Enter your own figure; the page starts at 1,500.
- New value. Enter your own figure; the page starts at 1,200.
- Or apply a decrease of (%). Enter your own figure; the page starts at 10%.
The result updates as you type, so you can try a figure, see what it does to percentage decrease, and change it back. Nothing you enter is sent anywhere or saved.
A worked example
These are the figures the calculator opens with. Every number in the results column below is produced by the same calculation the page runs, so you can follow it through before putting your own figures in.
What goes in
| Input | Value |
|---|---|
| Original value | 1,500 |
| New value | 1,200 |
| Or apply a decrease of | 10% |
What comes out
| Result | Value |
|---|---|
| Percentage decrease main result | 20.00% |
| Absolute change | 300 |
| Original reduced by that % | 1,350 |
| Increase needed to undo it | 25.00% |
Falling from 1500 to 1200 is a decrease of 20.00%. Getting back would take an increase of 25.00%.
How sensitive the answer is
Holding everything else steady and changing only original value, this is what happens to percentage decrease. It is worth knowing which of your inputs the answer actually hinges on, and which barely move it.
| Original value | Percentage decrease |
|---|---|
| 750 | -60.00% |
| 1,125 | -6.67% |
| 1,500 example above | 20.00% |
| 2,250 | 46.67% |
| 3,000 | 60.00% |
Every other input is held at the example value while this one changes, which is not how a real job behaves. Treat it as a guide to which number matters most, not as five separate quotes.
What each figure means
- Original value
- A number, starting at 1,500.
- New value
- A number, starting at 1,200.
- Or apply a decrease of (%)
- A percentage, between 0 and 100, starting at 10%.
What the results tell you
| Result | What it is |
|---|---|
| Percentage decrease | The headline result. A percentage. |
| Absolute change | A number. |
| Original reduced by that % | A number. |
| Increase needed to undo it | A percentage. |
Keep going
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