Understanding percentage decrease results
The magnitude of the result describes what fraction of the original value was lost. The table below summarizes how to read common outcomes.
| Result | Meaning |
|---|---|
| 100% | The entire original value was lost (new value is 0) |
| 50% | The value halved |
| 25% | The new value is 75% of the original |
| 0% | No change between the two values |
| Negative result | The value increased; see the percentage increase calculator |
- Percentage decrease is not symmetric with percentage increase: a 20% decrease from 100 reaches 80, but restoring 100 from 80 requires a 25% increase, not 20%.
- For quantities that cannot go below zero (prices, counts), percentage decrease cannot exceed 100%; a claim of a '150% decrease' in such a quantity is not meaningful.
- Two successive 10% decreases compound to a 19% total decrease, not 20%, because the second reduction applies to the already-reduced value.
What is percentage decrease?
Percentage decrease is the relative reduction from an original value to a new, smaller value, expressed as a fraction of 100. It answers the question 'what proportion of the starting value was lost?'. Like percentage increase, it is a relative measure: losing 10 units is a 50% decrease from 20 but only a 1% decrease from 1000.
Percentage decrease always uses the original (earlier) value as the base of the calculation. A price falling from 100 to 75 is a 25% decrease because the reduction of 25 is divided by the starting value of 100. A percentage decrease can never exceed 100% for a quantity that stays at or above zero, because a 100% decrease means the entire original value was lost.
If the new value is larger than the original value, this calculator returns a negative percentage decrease, which indicates the value actually increased. A dedicated percentage increase calculator is available for that direction of change.
How to use this percentage decrease calculator
- Enter the original value — the earlier or starting quantity that serves as the base of the comparison.
- Enter the new value — the later or ending quantity.
- Read the percentage decrease and the absolute difference. A negative result means the value increased rather than decreased.
- To check the result by hand, subtract the new value from the original, divide by the original value, and multiply by 100.
The percentage decrease formula
Percentage decrease equals the reduction (original value minus new value) divided by the original value, multiplied by 100. When the original value is negative, the standard convention divides by its absolute value so the sign of the result still reflects the direction of change.
Worked example: from 100 to 75. Step 1 — find the reduction: 100 - 75 = 25. Step 2 — divide by the original value: 25 / 100 = 0.25. Step 3 — multiply by 100: 0.25 x 100 = 25%. A fall from 100 to 75 is therefore a 25% decrease.
Percentage decrease is undefined when the original value is zero, because division by zero has no meaning. This calculator returns no result in that case.
Common mistakes
- Dividing by the new value instead of the original value — the base of a percentage decrease is always the starting value.
- Assuming an X% decrease is undone by an X% increase — a 20% decrease from 100 to 80 requires a 25% increase to restore the original.
- Stacking discounts by addition: 10% off followed by another 10% off gives 19% off in total, not 20%, because the second discount applies to the reduced price.
- Reporting a decrease larger than 100% for a non-negative quantity — losing more than the whole of something is not meaningful in percent terms.
Frequently asked questions
How do I calculate percentage decrease?
Subtract the new value from the original value, divide the difference by the original value, and multiply by 100. For example, from 100 to 75: (100 - 75) / 100 x 100 = 25%, so the value fell by 25%. If the result is negative, the value actually increased.
What is a 25% decrease from 100?
A 25% decrease from 100 is 75. Multiply the original value by (1 - 25/100): 100 x 0.75 = 75. In general, to apply a known percentage decrease, multiply the original value by 1 minus the percentage expressed as a decimal.
If a price drops 50% and then rises 50%, is it back to the original?
No. A 50% decrease from 100 gives 50; a subsequent 50% increase applies to the new base of 50 and gives 75, not 100. Restoring the original after a 50% decrease requires a 100% increase. Percentage changes in opposite directions do not cancel because they use different bases.
Can a percentage decrease be more than 100%?
Only for quantities that can become negative, such as profit or temperature in Celsius. For non-negative quantities like prices or counts, a 100% decrease already means the value fell to zero, so decreases beyond 100% are not meaningful.
What is the difference between percentage decrease and percentage-point decrease?
Percentage decrease is relative: the reduction divided by the original value, times 100. A percentage-point decrease is the absolute difference between two values that are themselves percentages. An unemployment rate falling from 8% to 6% drops 2 percentage points, but the relative percentage decrease is (8 - 6) / 8 x 100 = 25%.
References
- Office for National Statistics (ONS). Style Guide: Percentages and percentage points. ons.gov.uk.
- National Institute of Standards and Technology (NIST). NIST/SEMATECH e-Handbook of Statistical Methods. nist.gov.
- Weisstein, Eric W. "Percent." MathWorld — A Wolfram Web Resource. mathworld.wolfram.com.