A price rise: from 40 to 50
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40 → 50The change is 50 - 40 = 10. As a share of the start: 10/40 = 1/4. Times 100% gives a 25% increase. Three lines, and each one answers a natural question: how much, what share, what percentage.
Percent Change Calculator
From one value to another, as a percentage of where you started.
Last updated
Want to solve these without the calculator?
The Coddy math course teaches the method itself - you work each step on an interactive board and get told exactly where a move went wrong.
Percent change is measured against where you started
Percent change answers one question: by what share of the ORIGINAL value did it move? The method is three lines. Subtract the old value from the new one to get the change; divide that change by the old value; multiply by 100% to read the result as a percentage. From 40 to 50, the change is 10, the share is 10/40 = 1/4, and the answer is a 25% increase.
The single most important word in that method is "original". Dividing by the new value answers a different question, and it is why a rise and the fall that undoes it are not the same size: 40 to 50 is +25%, but 50 back down to 40 is -20%, because the second journey is measured against 50. That asymmetry confuses more people than any other fact about percentages, and the worked steps below make it visible instead of mysterious.
The arithmetic is exact throughout. From 30 to 40 is a 33⅓% increase - written as the fraction it is, not as 33.33% - because a rounded percentage compounds into a wrong answer the moment anyone multiplies by it.
What to notice
- The base is the starting value, always. Percent change from a to b divides by a - dividing by b answers "what percent would undo this".
- Up then down the same percent does not return home. +25% then -25% of the new value lands at 93.75% of where you began - the two percents have different bases.
- The sign carries the direction: positive is an increase, negative a decrease. This page says the word as well, so the sign never has to be decoded.
- A change past -100% is impossible for quantities that cannot go negative; a change past +100% just means it more than doubled.
- Percent change and percentage points are different units. From 10% to 15% is a 5 percentage-point rise, but a 50% percent change - say which one you mean.
How to calculate percent change
Subtract: new minus old
From 40 to 50 the change is 50 - 40 = 10. If the result is negative, the value fell - keep the sign, it is the direction.
Divide by the old value
The change as a share of where you started: 10/40 = 1/4. This is the step where the wrong base sneaks in - the denominator is the value you started from, not the one you ended at.
Multiply by 100%
1/4 × 100% = 25%. Positive means an increase, negative a decrease - from 40 to 50 the value rose by 25%.
Percent change at a glance
A few journeys and their exact percent change - including the pairs that look like they should match and do not.
| From | To | Percent change |
|---|---|---|
| 40 | 50 | +25% |
| 50 | 40 | -20% |
| 30 | 40 | +33⅓% |
| 80 | 60 | -25% |
| 60 | 80 | +33⅓% |
| 100 | 250 | +150% |
| 250 | 100 | -60% |
| 20 | 20 | 0% |
| 10 | 5 | -50% |
| 5 | 10 | +100% |
Worked examples
The same journey backwards: from 50 to 40
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50 → 40The change is 40 - 50 = -10, and the base is now 50, so the share is -10/50 = -1/5, a 20% decrease. Not 25% - the fall that undoes a 25% rise is always smaller in percent, because it is measured against the bigger number.
A repeating answer: from 30 to 40
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30 → 40The change is 10 and the share is 10/30 = 1/3, which is 33⅓% exactly. Writing 33.33% is close but wrong, and using the rounded figure to reconstruct the new value gives 39.996 instead of 40 - exactness is not pedantry here.
Negative values: from -10 to -5
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-10 → -5The change is -5 - (-10) = 5: the value moved up. Measured against the size of the start, |−10| = 10, that is 5/10 = 50% - an increase. Dividing by the signed value would call a move toward zero a decrease, which is why the convention divides by the absolute value.
Common mistakes
- Dividing by the new value. Percent change measures against where you STARTED - 40 to 50 divides by 40. Dividing by 50 answers a different question.
- Expecting a rise and its reverse to match. +25% up is undone by -20% down, not by -25% - the two moves have different bases.
- Averaging percent changes across periods. +50% then -50% is not 0%: it lands at 75% of the start. Percent changes compound; they do not add.
- Confusing percent change with percentage points. An interest rate going from 4% to 5% rose one percentage point, and 25 percent - the two statements are both true and mean different things.
- Rounding the share before multiplying by 100. Keep the fraction exact until the last line, or the error you introduce multiplies into everything downstream.
- Dropping the sign. The minus IS the word "decrease" - report -20%, or say "a 20% decrease", but never just "20%" for a fall.
Percent change FAQ
How do I calculate percent change between two numbers?
Subtract the old value from the new one, divide by the old value, and multiply by 100%. From 40 to 50: (50 - 40) / 40 = 1/4 = 25%, an increase. A negative result is a decrease.
Why is 40 to 50 a 25% rise but 50 to 40 only a 20% fall?
Because each journey is measured against its own starting point. Going up, the change of 10 is compared with 40; coming down, the same 10 is compared with 50. Same distance, different base, different percentage - and it is why undoing a rise always takes a smaller percent than the rise itself.
What is the difference between percent change and percentage difference?
Percent change has a direction: it goes from an old value to a new one and divides by the old. Percentage difference compares two values with no order, dividing by their average. When someone says "percentage difference" about a before-and-after, they almost always mean percent change - which is what this page computes.
What does a percent change over 100% mean?
The value more than doubled. From 100 to 250 is a 150% increase: the change of 150 is one and a half times the starting value. Nothing is wrong - percent change has no ceiling on the way up.
How does it handle negative starting values?
The change keeps its sign, and the division uses the absolute value of the start, so a move from -10 to -5 reads as the 50% increase it is - the value moved up by half its size. Dividing by the signed value would flip the direction and call it a decrease.
What is the reverse question - undoing a percent change?
To undo a p% increase you divide by (1 + p/100), not subtract p%. A 25% rise is undone by dividing by 1.25 - equivalently a 20% fall. If you need to grow or shrink a value by a percentage, the percentage increase calculator one page over does exactly that with the working shown.
Why does the answer sometimes come as a fraction?
Because the exact percentage does not terminate. From 30 to 40 the rise is 33⅓% - exactly a third - and any decimal form is a rounding of it. When the answer terminates, you get the decimal; when it repeats, you get the exact mixed fraction.
