Percentage Decrease Calculator
Result
Percentage decrease (%)
- Amount of the drop (original − new)
- 20.0000
- Remaining (%)
- 80.0000%
A percentage decrease calculator compares two values and reports how far the second has fallen from the first, measured as a percentage of the first. Going from 100 down to 80 is a drop of 20%, and that figure is the size of the fall: it is the same arithmetic as a percentage increase, run in the other direction. The base is always the original value, so a fall from 100 to 80 and a rise from 80 to 100 are 20% and 25% rather than one number with two signs. The denominator decides what the movement is measured against, and it stays fixed at where the change started. Because the question on this page is specifically how much was given up, the drop is reported as a percent rather than as a signed change: the page answers how big the fall was, not which way it went. Feeding it a pair where the value rose gives a negative answer, which is the honest reading rather than a mistake, and the sibling page that reports the sign of every movement is a different question asked about the same two figures. The panel reports one fall three ways. The percentage is the headline and the figure most readers are after. The amount of decrease is the same fall stated in the original units, which is what a budget, a stock level or a measurement actually drops by. The remaining percentage is what is left of the original once the fall is taken out: 100 down to 80 leaves 80%, and it always adds up with the percentage beside it to a hundred, because the pair splits the original into the part that went and the part that stayed. Two properties of the base are worth knowing before reading the panel. An original value of zero has no percentage decrease at all: dividing by zero is undefined, so the page reports that the fall cannot be worked out instead of printing a figure. And a negative original value is accepted while reading backwards, because the division carries a sign of its own; a value that has moved upwards can come back with the drop shown as a fall.
Common falls and rises
| Original value | New value | Percentage decrease (%) | Remaining (%) |
|---|---|---|---|
| 100 | 100 | 0 | 100 |
| 100 | 90 | 10 | 90 |
| 100 | 80 | 20 | 80 |
| 100 | 75 | 25 | 75 |
| 100 | 50 | 50 | 50 |
| 100 | 25 | 75 | 25 |
| 100 | 0 | 100 | 0 |
| 80 | 60 | 25 | 75 |
| 200 | 150 | 25 | 75 |
| 100 | 120 | -20 | 120 |
The first seven rows all start from a hundred, which makes the percentage readable straight off the end value: a fall from 100 is a hundred minus the new value. Read down them and the ladder runs from 0% (unchanged) through 50% (halved) to 100% (nothing left), and the remaining column is the mirror of it, running from 100% down to 0%. The next two rows start somewhere else and exist to show that the base is what the percentage is measured against: 80 to 60 and 200 to 150 are both a 25% decrease even though one falls by 20 and the other by 50. The last row is the one that rises, and it is in the table because it is the clearest way to see what a negative decrease looks like: 100 up to 120 is -20%, with 120% remaining. Every row here comes out of the same formula, and no row is a special case of it.
Formula
Percentage decrease = (original − new) ÷ original × 100 (100 → 80) = 20 ÷ 100 × 100 = 20%
- Original value
- The value before the fall. It is the base every reading on the panel is measured against, and it is the one input that cannot be zero.
- New value
- The value after the fall. It may be larger than the original, which is what makes the answer a negative decrease rather than an error.
- Amount of decrease
- The original value minus the new one, in the same units as the two inputs: 20 for the default figures. It is the absolute half of the comparison, and the percentage is its size relative to the original.
- Remaining percentage
- The new value as a percentage of the original: 80% for the default figures, meaning four fifths of the value is still there. It is the reading to use when the question is what survived rather than what was lost, and it plus the percentage decrease always makes a hundred.
- Percentage decrease
- The amount of the fall divided by the original, then multiplied by a hundred. Positive for a fall, negative for a rise, and zero when the value did not move at all.
A percentage decrease is what gets reported here, and the report is useful in three places. The first is a price, a bill or a measurement that has come down, where the question is how big the fall was relative to where it started: a drop from 100 to 80 is a 20% decrease, and a figure like that is comparable across things of completely different sizes in a way the raw amount is not. The second is checking a claim: a listing that says something lost a fifth of its value should come back as 20% here, and if it comes back as 25% instead, the two figures were put in the wrong boxes. The third is tracking something that is running down, where the remaining percentage is the more useful of the three readings, because a battery at 80% and a budget with 80% left are both statements about what is still available rather than about what has gone. A percentage decrease is also the natural way to state a shortfall against a target or a drop from a previous period, which is the same calculation with the earlier figure as the original value.
Worked examples
100 down to 80
- Amount of the fall: 100 − 80 = 20
- Divide by the original: 20 ÷ 100 = 0.2
- Multiply by a hundred: 0.2 × 100 = 20%
- Remaining: 80 ÷ 100 × 100 = 80%
The default case. All three readings describe one fall: a fifth of the value gone, an amount of 20, and four fifths still there. The last two add up to a hundred, which is a quick way to check the panel.
100 up to 120
- Amount of the fall: 100 − 120 = -20
- Divide by the original: -20 ÷ 100 = -0.2
- Multiply by a hundred: -0.2 × 100 = -20%
- Remaining: 120 ÷ 100 × 100 = 120%
A rise is reported as a negative decrease rather than as an error, so one reading covers both directions. The remaining percentage goes above a hundred for the same reason: more of the value is there than the original had.
3 down to 2
- Amount of the fall: 3 − 2 = 1
- Divide by the original: 1 ÷ 3 = 0.333333...
- Multiply by a hundred: 33.3333% to four decimal places
- Remaining: 2 ÷ 3 × 100 = 66.6667%
A third does not terminate, so this is where the four decimal places on the panel show. The two percentages are rounded separately and still add to a hundred, which is not true of every pair of figures once the rounding is in.
A negative base, -50 up to -25
- Amount of the fall: -50 − (-25) = -25
- Divide by the original: -25 ÷ (-50) = 0.5
- Multiply by a hundred: 50%
- Remaining: -25 ÷ -50 × 100 = 50%
The value has risen and the page reports a decrease of 50%, because the base it is measured against sits below zero. The arithmetic is right and the reading is the one to be careful with: a negative base is where a percentage decrease stops matching the instinct it was built on.
Limitations
The base is the original value and never the new one. That is what makes a fall and its reverse asymmetric: 100 down to 80 is a decrease of 20%, while 80 up to 100 is an increase of 25% and not 20%. A change and its opposite therefore do not cancel, and a quantity that falls by a fifth and then rises by a fifth does not end up where it started. An original value of zero has no percentage decrease at all, and the page reports an error rather than a figure: dividing by zero is undefined, not infinite, and saying that something fell from nothing by some percentage would be answering a question that has no answer. A negative original value is accepted and does have an answer, but the sign of that answer describes the division rather than the movement, so a value that rose from -50 to -25 comes back as a decrease of 50%. The panel prints four decimal places, so a percentage that does not terminate is rounded there: a fall from 3 to 2 displays as 33.3333%, and the exact figure is a repeating decimal that only a fraction can write down. The remaining percentage is rounded in the same way, so the two figures shown side by side can miss a hundred by one in the last place. This page compares two plain numbers and has no idea whether they are already percentages: a move from 3% to 2% is a fall of one percentage point as well as a fall of 33.3333%, and the panel reports the second, which is the relative one. It also does not report the signed change that a percentage increase page gives for the same pair, which is a different question about the same two figures and the reason both pages exist.
Frequently asked questions
- How do I work out a percentage decrease?
- Subtract the new value from the original, divide that difference by the original value, and multiply by a hundred. Going from 100 down to 80 is 20 ÷ 100 × 100, which is 20%. It is the same formula as a percentage increase, with the two values subtracted the other way round.
- Is the answer positive when the value goes down?
- Yes. This page reports the size of the fall, so a drop comes back as a positive percentage and a rise comes back as a negative one. The sign is not describing which way the value moved here, it is describing whether the question was answered or contradicted.
- What does the remaining percentage mean?
- It is the new value as a percentage of the original, so it says how much is still there: 100 down to 80 leaves 80%. It is the companion reading to the decrease, and the two always add up to a hundred, because together they split the original into what went and what stayed.
- How is this different from the percentage increase calculator?
- The arithmetic has the same shape and the base is the same original value, but the two pages answer different questions. That page reports the signed change, so a fall from 100 to 90 is -10% there; this page reports the size of the drop and what is left, so the same pair is a 10% decrease with 90% remaining.
- Why is the original value used as the base rather than the new one?
- Because the fall is being measured against where it started. Dividing by the new value instead would answer a different question about the same pair of figures: 100 down to 80 would come back as 25%, which is what fraction of the new value was lost, not how much the original value fell.
- Why does the page show an error when the original value is zero?
- Because the percentage decrease from zero is undefined: the formula divides by the original value, and dividing by zero has no result. Nothing fell from zero by any finite percentage, so there is no figure to print.
- Can a percentage decrease be more than 100%?
- Not while the original value is positive: the biggest possible fall is everything, so 100 down to 0 is exactly a 100% decrease and that is the ceiling. A new value below zero goes past it, because the value has fallen further than to nothing: 100 down to -50 is a decrease of 150%.
References
- Percentage Change — the change from a nonzero initial value to a final value, where a negative result is a percentage decrease; the entry states that the change is undefined for a zero initial value and that it is not symmetric, which are the two properties this page is built around — Wolfram MathWorld (United States)
- Percent — a ratio or fraction converted to a percentage by multiplying by a hundred, illustrated with an investment: the new value as a percentage of the old one, and what is left after a fall, are the two relative readings this page prints — Wolfram MathWorld (United States)
- Relative Error — the relative form of a difference divides by the reference value rather than by the measured one, and the percentage form is a hundred times that relative figure, which is the shape of the headline reading here and of the remaining percentage beside it — Wolfram MathWorld (United States)