Percentage Change Calculator
This percentage change calculator works out the percentage increase or decrease between an old value and a new one, with the sign and the word “increase” or “decrease” spelled out. A second mode applies a percentage to a number instead. Either way you get the absolute change, the multiplier, the reverse change, the working steps and a bar chart of old against new.
How to use the percentage change calculator
The calculator has two modes, chosen with the buttons at the top.
Change between two values
- Enter the old (starting) value and the new value. The defaults are 80 and 100.
- The result reads +25% increase. Below it: the absolute change (20), the multiplier (1.25), and the reverse change, which says that going from 100 back to 80 is a 20% decrease.
- The numbered steps show the subtraction and the division, and the bar chart puts the two values side by side.
Increase or decrease by a %
- Enter a starting value and a percentage. The defaults are 80 and 25.
- Pick increase or decrease from the direction menu. Increasing 80 by 25% gives 100; decreasing it by 25% gives 60.
Use the first mode when you know both numbers and want the percent. Use the second when you know the percent and want the new number, such as a 4% raise or a 15% price cut. The percentage increase formula guide explains the reasoning behind both in more depth.
The percentage change formula
Subtracting gives the size of the change in the original units: dollars, people, pounds. Dividing by the old value turns it into a share of where you started, and multiplying by 100 writes that share as a percent. With the defaults:
The same formula covers decreases. When the new value is smaller, the subtraction comes out negative and so does the percent. You do not need a separate formula for a percentage decrease, only the sign.
The multiplier view
The calculator also shows the multiplier, which is just new ÷ old. For 80 to 100 it is 1.25. A multiplier above 1 is an increase, below 1 is a decrease, and the percent change is the distance from 1: 1.25 means +25%, 0.8 means −20%. The multiplier is the number to use when you need to apply a change, undo one, or chain several together.
Percentage increase: a worked example
Example: a rent increase from $1,450 to $1,595
Monthly rent goes up from $1,450 to $1,595 at renewal. What is the percentage increase?
The rent rose 10%, an extra $145 a month. To check, run it through the second mode: increasing $1,450 by 10% gives $1,595.
A percentage increase calculator is most useful when the numbers are not round. Here the dollar amount looks large, but relative to the old rent it is one tenth. Comparing percentages rather than dollar amounts is what lets you compare a $145 rise on one apartment with a $210 rise on a more expensive one.
Percentage decrease: a worked example
Example: monthly sales fall from 2,400 to 1,860 units
A product sold 2,400 units in March and 1,860 in April. What is the percentage decrease?
Sales fell 22.5%. The multiplier 0.775 says April was 77.5% of March, which is the same fact seen from the other side: 100% − 77.5% = 22.5%.
As a percentage decrease calculator, the tool always divides by the starting value, here March. That is what “decreased by” means in ordinary use. Divide by April instead and you get about 29.03%, which answers a different question: how much bigger March was than April.
Example: decrease a price by 35%
A $48 jacket is cut by 35%. Use the second mode with direction set to decrease.
The new price is $31.20. For shop discounts with sales tax or a second markdown, the percent off calculator is set up for exactly that.
Why the reverse change is a different percent
Going from 80 to 100 is +25%, but going from 100 back to 80 is only −20%. The calculator shows the reverse change for this reason: people expect the two to match, and they never do.
The change is 20 both ways. What differs is the base. On the way up you divide by 80; on the way down you divide by 100. A bigger base makes the same change a smaller percentage. The same thing explains why a 25% increase followed by a 25% decrease leaves you below where you started:
| Increase | Decrease that undoes it | Multiplier pair |
|---|---|---|
| +10% | ≈ −9.09% | 1.1 and ≈ 0.9091 |
| +20% | ≈ −16.67% | 1.2 and ≈ 0.8333 |
| +25% | −20% | 1.25 and 0.8 |
| +50% | ≈ −33.33% | 1.5 and ≈ 0.6667 |
| +75% | ≈ −42.86% | 1.75 and ≈ 0.5714 |
| +100% | −50% | 2 and 0.5 |
| +200% | ≈ −66.67% | 3 and ≈ 0.3333 |
Each pair of multipliers multiplies to exactly 1, which is what undoing a change means. If you know the value after a change and want the value before it, divide by the multiplier, or use the reverse percentage calculator, which is built for that.
Zero, negatives and percentage points
Starting from zero
If the old value is 0, the percentage change is undefined, because the formula divides by the old value. Going from 0 to 50 customers is an increase of 50 customers, but not any particular percent of zero. Report the absolute change instead.
Decreases cannot pass 100%
For a quantity that cannot go below zero, a 100% decrease means it has fallen to nothing, and no decrease can be larger. Increases have no ceiling: doubling is +100%, tripling is +200%. If you see a decrease of more than 100%, the value must have gone negative.
Negative starting values
When the old value is negative, such as a loss of $50 turning into a profit of $25, the plain formula gives 75 ÷ −50 = −150%, a “decrease” for what is clearly an improvement. A common convention divides by the absolute value of the old number, giving +150%, but many analysts avoid a percentage altogether when the sign flips and quote the dollar change. The absolute value calculator covers the |x| notation if you use that convention.
Percent versus percentage points
When the values are themselves percentages, keep the two measures apart. An interest rate going from 4% to 5% has risen by 1 percentage point, but by 25 percent, since (5 − 4) ÷ 4 = 0.25. Both are correct; they answer different questions. The guide to a percentage of a percentage covers points and stacked rates in detail.
Percentage change or percentage difference?
Percentage change has a direction: there is an old value and a new value, and the old one is the base. That fits prices over time, before-and-after measurements, and this year against last year.
When two values have no natural order, such as two stores’ prices for the same item or two labs’ readings of the same sample, there is no “old” to divide by. Picking one would make the answer depend on which you happened to list first. The percentage difference calculator divides by the average of the two instead, so the answer is the same either way round. The guide on percent difference vs percent change sets out when each one is the right tool.
A third relative, markup, is a percentage change from cost to selling price. If you are pricing products, the markup calculator uses the same arithmetic with business labels on the fields.
Common mistakes
- Dividing by the new value. 80 to 100 divided by 100 gives 20%, not 25%. The base is always the starting value.
- Adding successive changes. A 10% rise followed by another 10% rise is a 21% rise overall, because
1.1 × 1.1 = 1.21. Multiply the multipliers. - Expecting a decrease to undo an equal increase. +25% then −25% ends 6.25% lower than the start.
- Confusing points with percent. A rate moving from 4% to 5% is a 1-point rise and a 25% rise. Say which one you mean.
- Undoing a change by subtracting the percent. If a price is $120 after a 25% increase, the original is
120 ÷ 1.25 = $96, not 75% of $120, which is $90.
For a plain “what is 25% of 80” question with no before and after, the general percentage calculator is the simpler tool.
Frequently asked questions
How do I calculate percentage increase?
Subtract the old value from the new value, divide the result by the old value, and multiply by 100. From 80 to 100: (100 − 80) ÷ 80 × 100 = 25%. Always divide by the starting value, not the ending one. If the answer comes out negative, the value went down, and the number is a percentage decrease instead.
How do you calculate a percentage decrease?
Use the same formula: (new − old) ÷ old × 100. The result is negative for a decrease, and you can drop the minus sign when you say “decreased by.” From 2,400 to 1,860: the change is −540, and −540 ÷ 2,400 = −0.225, so the decrease is 22.5%. Dividing by the old value is what makes it a decrease “from” that starting point.
What is the percentage change from 50 to 35?
It is a 30% decrease. The change is 35 − 50 = −15, and −15 ÷ 50 = −0.3, or −30%. The multiplier is 0.7, meaning 35 is 70% of 50. Going back the other way, from 35 to 50, is an increase of about 42.86%, because the base is now the smaller number.
How do I add 20% to a number?
Multiply the number by 1.2. Adding 20% means keeping the whole original (1) plus 0.2 more. For example, 150 increased by 20% is 150 × 1.2 = 180. To take 20% off instead, multiply by 0.8. The calculator’s second mode does this with the direction menu set to increase or decrease.
Why doesn’t a 25% increase and a 25% decrease cancel out?
Because the second change is measured from a different starting point. 80 increased by 25% is 100. A 25% decrease is then taken from 100, which removes 25, not 20, and leaves 75. The overall effect is 1.25 × 0.75 = 0.9375, a 6.25% loss. To undo a 25% increase you need a 20% decrease.
Can a percentage increase be more than 100%?
Yes. An increase of 100% means the value has doubled, 200% means it has tripled, and there is no upper limit. Going from 40 to 140 is a 250% increase. A decrease, on the other hand, cannot exceed 100% for a quantity that cannot go below zero, since a 100% decrease already takes it to zero.
What is the difference between percent and percentage points?
Percentage points measure the plain gap between two percentages; percent measures that gap relative to the starting percentage. A rate rising from 4% to 5% is up 1 percentage point, and up 25 percent, because 1 is a quarter of 4. News reports on interest rates, polls and tax rates usually mean points, but should say so.
What happens if the old value is zero?
The percentage change cannot be calculated, because the formula divides by the old value and division by zero is undefined. Going from 0 to 50 is an increase of 50 units, but not any specific percent. In that situation, report the absolute change, or pick a different, nonzero baseline period to compare against.
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