Compare an old value with a new value to calculate percentage increase, percentage decrease, absolute change, and relative change. You can also reverse a percentage change, calculate chained changes, and compare percent change with percentage-point change.
Choose what you want to calculate, enter your numbers, and see the formula worked out.
Percentage change describes how much a value grew or shrank compared with where it started. It always needs two numbers to work: an old value (the starting point) and a new value (where things ended up). The result tells you the size of that move, expressed as a percentage of the original amount, so a $5 change means something very different depending on whether it started from $10 or from $1,000.
This is different from simply subtracting two numbers. If a price moves from $80 to $100, the raw difference is $20. But $20 relative to a starting point of $80 is a 25% increase, while the same $20 relative to a starting point of $1,000 would only be a 2% increase. Percentage change is what lets you compare movements of very different sizes on the same fair scale.
This calculator is built specifically around that before-and-after relationship. If you instead need a general percentage calculation, such as finding what X% of a number is, or what percent one number is of another with no clear starting point, the Percentage Calculator is the right tool for that.
Every percentage change starts as two numbers in order: an old value and a new value. The calculator measures the distance between them and expresses it as a percentage of the old value.
The core formula is: Percentage Change = (New Value − Old Value) ÷ |Old Value| × 100. Using the absolute value of the old value in the denominator keeps the sign of the result meaningful even when the starting value itself is negative, which matters for the negative-number examples later on this page.
Try it with a real example. Suppose a value moves from 64 to 120. First find the difference: 120 − 64 = 56. Now divide that difference by the old value: 56 ÷ 64 = 0.875. Multiply by 100 and the result is 87.5%. So 64 to 120 is an 87.5% increase.
Each piece of the formula has a specific job. Dividing by the absolute value of the old value, rather than the old value itself, is what keeps the direction of the result correct even when the starting value is negative.
The same numerical change can represent very different percentage changes depending on where it started. Compare two examples that both involve a 10-unit increase. First: 20 → 30. The increase is 10, and 10 ÷ 20 × 100 = 50%. Second: 100 → 110. The increase is also 10, but 10 ÷ 100 × 100 = 10%. Both examples moved by exactly the same absolute amount, yet one represents a 50% increase and the other only a 10% increase, purely because the starting values were different.
This is the entire reason percentage change exists as a concept separate from a plain difference. It answers "how big was this change relative to where things started," not just "how many units did this move."
Absolute change: +10
Absolute change: +10
Both examples increase by the same 10 units. The percentage change is completely different because each one is measured against a different starting value.
A percentage increase happens when the new value is larger than the old value. Suppose a value moves from 50 to 65. The difference is 65 − 50 = 15. Divide by the old value: 15 ÷ 50 = 0.30. Multiply by 100: 30%. So 50 to 65 is a 30% increase.
A percentage decrease happens when the new value is smaller than the old value. Suppose a value moves from 80 to 60. The difference is 60 − 80 = −20. Divide by the old value: −20 ÷ 80 = −0.25. Multiply by 100: −25%. So 80 to 60 is a 25% decrease, and the calculator's formula naturally produces the negative sign that signals a decrease rather than requiring you to track direction separately.
Because the old value is the reference point every percentage change is measured against, and swapping which number is "old" and which is "new" changes the answer, even when the two values themselves stay the same. Compare 50 → 100 with 100 → 50. Going from 50 to 100, the increase is 50, and 50 ÷ 50 × 100 = 100%, a 100% increase. Going the other direction, from 100 to 50, the decrease is also 50, but 50 ÷ 100 × 100 = 50%, only a 50% decrease. The two situations use the identical pair of numbers, yet the percentage change is not symmetric, because each one is divided by a different starting value.
Same two numbers, opposite directions. Because percentage change always divides by the starting value, reversing which number came first changes the result from +100% to −50%, not to −100%.
It is tempting to assume that increasing something by 20% and then decreasing it by 20% brings it right back to where it started. It does not, because each percentage is calculated from a different base. Start with 100. A 20% increase adds 20, bringing the value to 120. Now apply a 20% decrease, but 20% of 120 is 24, not 20, because the second percentage is calculated from 120, not from the original 100. Subtracting 24 from 120 leaves 96. The net result is a 4% decrease from the original 100, not a return to 100.
100 increased by 20% becomes 120. That 120, decreased by 20%, becomes 96, not 100, because the second 20% is measured against 120 rather than the original 100. The net change from 100 to 96 is a 4% decrease.
Sometimes you already know the starting value and the percentage change, and you want to find what the new value will be. The formula is: New Value = Old Value × (1 + Percentage Change ÷ 100). For an increase, suppose you start with 200 and apply a +15% change. Convert 15% to 0.15, add 1 to get 1.15, then multiply: 200 × 1.15 = 230. For a decrease, apply a −15% change to the same starting value of 200. Convert −15% to −0.15, add 1 to get 0.85, then multiply: 200 × 0.85 = 170. Entering the percentage change with its sign, positive for an increase or negative for a decrease, is what tells the formula which direction to move.
This is the reverse problem: you know the final value and the percentage change that produced it, and you need to recover the original value. A common mistake is to simply subtract the percentage from the final value, but that is not correct, because the percentage was originally applied to the old value, not the new one. The correct formula is: Original Value = Final Value ÷ (1 + Percentage Change ÷ 100). Suppose the final value is 120 after a +20% increase. Convert 20% to 0.20, add 1 to get 1.20, then divide: 120 ÷ 1.20 = 100. The original value was 100, not 96, which is what you would incorrectly get by subtracting 20% of 120 instead of dividing. For a broader set of percentage tools beyond this specific before-and-after reversal, the Percentage Calculator also includes a general reverse-percentage mode.
Percentage points measure the plain arithmetic difference between two percentages, while percentage change measures the relative change between them. Suppose an approval rating moves from 30% to 40%. The percentage-point change is simply 40 − 30 = 10 percentage points. But the relative percentage change treats 30% as the starting value and asks how much it grew: (40 − 30) ÷ 30 × 100 = 33.33%. Both numbers are correct descriptions of the same move, but they answer different questions, and mixing them up is one of the most common percentage mistakes in news reporting and everyday conversation.
Ten percentage points and a 33.33% relative increase describe the exact same move from 30% to 40%, but they are not interchangeable numbers. Always be clear about which one you are stating.
When the old value is zero, the percentage change formula breaks down, because it requires dividing by the old value, and division by zero is undefined. Suppose a value moves from 0 to 50. The absolute change is clear: +50. But there is no meaningful percentage to attach to that change, because there is no nonzero starting amount to compare it against. This calculator does not describe that as an "infinite percent increase." Instead it shows the absolute change plainly and explains that the percentage itself is undefined from a zero baseline, which is a more accurate and more useful description than a nonsensical infinite figure.
A related but different situation is when both the old and new values are zero. In that case the absolute change is 0, and while there is still no conventional percentage-change ratio to calculate, it is also true and worth stating plainly that the value simply did not change at all.
The absolute change from 0 to 50 is a real, calculable +50. The percentage change is undefined, not infinite, because there is no nonzero starting value to measure the change against.
Yes, and the calculator handles two distinct negative-number situations correctly. The first is when both the old and new values are negative. Suppose a value moves from −50 to −40. The value increased numerically, moving closer to zero, so the absolute change is +10. Dividing by the magnitude of the starting value, 10 ÷ 50 × 100 = 20%, gives a 20% increase, which correctly reflects that the value grew relative to its starting size, even though both numbers involved are negative.
The second situation is when a value crosses zero entirely. Suppose a value moves from −50 to +50. The absolute change is 100, and dividing by the magnitude of the starting value, 100 ÷ 50 × 100 = 200%, gives a 200% increase. That number is mathematically correct, but crossing zero can make a raw percentage feel less intuitive than it does for two same-sign values, so it is worth looking at the absolute change and the real-world meaning of the numbers alongside the percentage, rather than reading the percentage alone.
A chained percentage change is a sequence of two or more percentage changes applied one after another, where each one is calculated from the result of the previous step rather than from the original starting value. This is exactly why chained changes do not simply add together. Suppose a value starts at 100, increases by 10%, and then increases by another 20%. The first change: 100 × 1.10 = 110. The second change is applied to that new value of 110, not to the original 100: 110 × 1.20 = 132. The combined effect is a net change of 32%, which is not the same as simply adding 10% and 20% to get 30%, because the second percentage compounds on top of the first.
Chaining a 10% increase and a 20% increase multiplies the running value by 1.10 and then by 1.20. The combined multiplier is 1.32, a net change of +32%, not the +30% you would get by adding the two percentages directly.
Percentage change shows up anywhere something is compared before and after. Prices change from one week to the next. Sales figures change from one quarter to the next. Website traffic changes from one month to the next. Test scores change from one attempt to the next. Investments change in value over time, and tools like an Investment Calculator build directly on this same before-and-after relationship to project growth. Prices also change over time due to inflation, which an Inflation Calculator is built to measure specifically. Retail discounts describe a percentage decrease from an original price, which a Discount Calculator handles directly, and sales tax describes a percentage increase added on top of a price, which a Sales Tax Calculator is built for. In every one of these cases, the underlying question is the same one this calculator answers: given an old value and a new value, how big was the change relative to where things started?
The Percentage Calculator is built around general percentage relationships that do not require a before-and-after story, such as finding what X% of a number is, what percent one number is of another, or what number a given part and percentage came from. This Percentage Change Calculator is built specifically around the old-value-to-new-value relationship, along with the related questions that naturally come with it: finding a new value from a starting value and a percentage, finding an original value from a final value and a percentage, chaining multiple percentage changes together correctly, and distinguishing percentage change from percentage-point change. If your question starts with two numbers and a clear "before" and "after," this is the right calculator. If it does not, the Percentage Calculator is the better starting point.
For another explanation of percentage change from an independent educational source, Cuemath's percentage change lesson covers the same core concept from a classroom-oriented angle. It is provided here as a cross-reference for further reading, not as a source this page's explanations, examples, or visuals were drawn from.
The most common mistake is dividing by the wrong number, usually the new value instead of the old value. Percentage change always compares the change to where the value started, not to where it ended up. Another common mistake is assuming that an increase and a later matching decrease cancel out, when in fact a 20% increase followed by a 20% decrease leaves you 4% below where you started, because the second percentage is calculated from a different, larger base. A third mistake is treating percentage-point differences and percentage change as interchangeable, when a 10-percentage-point move from 30% to 40% is a 33.33% relative increase, not a 10% one. Finally, describing a change from a zero starting value as an "infinite percent increase" is not mathematically meaningful; the honest description is that the percentage change is undefined from a zero baseline.
And most importantly: you can see exactly how each answer was calculated instead of receiving a number with no explanation. That is what the CalculateThisWay Percentage Change Calculator is built to do.
A quick reference for every formula used on this page.
| What You Want | Formula |
|---|---|
| Absolute Change | New Value − Old Value |
| Percentage Change | (New − Old) ÷ |Old| × 100 |
| New Value After a Change | Old × (1 + Percentage ÷ 100) |
| Original Value | Final ÷ (1 + Percentage ÷ 100) |
| Percentage-Point Change | New % − Old % |
| Chained (Combined) Multiplier | (1 + r₁÷100) × (1 + r₂÷100) × ... |
| Net Chained Change | (Combined Multiplier − 1) × 100 |
I have an old value and a new value and want the increase, decrease, or reverse calculation between them.
You Are HereI need a general percentage calculation with no clear before-and-after, like X% of Y.
Open Calculator ›I need to calculate a shopping discount or sale price specifically.
Open Calculator ›I need to see how prices have changed due to inflation over time.
Open Calculator ›What is the formula for percentage change?
(New Value − Old Value) ÷ |Old Value| × 100.
What is the difference between percentage change and percent change?
Nothing. "Percent change" and "percentage change" refer to the same calculation and are used interchangeably.
How do I calculate percentage increase?
Subtract the old value from the new value, divide by the old value, then multiply by 100. If the result is positive, it is an increase.
How do I calculate percentage decrease?
Use the same formula as percentage increase. If the new value is smaller than the old value, the result comes out negative, indicating a decrease.
Why is my percentage change different when I swap the old and new values?
Because the formula always divides by the old value. Swapping which number is old and which is new changes the denominator, so the two directions are not symmetric. For example, 80 to 100 is a 25% increase, but 100 to 80 is only a 20% decrease.
Why doesn't a 20% increase followed by a 20% decrease return to the original value?
Because the second percentage is calculated from the new, larger value, not from the original one. A 20% increase on 100 gives 120, and a 20% decrease on 120 gives 96, not 100.
How do I find a new value after a percentage increase or decrease?
Multiply the old value by (1 + the percentage change divided by 100). Use a positive percentage for an increase and a negative percentage for a decrease.
How do I find the original value before a percentage change?
Divide the final value by (1 + the percentage change divided by 100). Do not simply subtract the percentage from the final value; that produces an incorrect answer.
Why can't I just subtract the percentage from the final value to find the original value?
Because the percentage was originally applied to the old value, not the final one. Subtracting it from the final value uses the wrong base and produces the wrong number.
What is a chained percentage change?
A sequence of two or more percentage changes applied one after another, where each change is calculated from the result of the previous step rather than from the original value.
Do chained percentage changes simply add together?
No. A +10% change followed by a +20% change results in a net +32% change, not +30%, because the second percentage compounds on the already-changed value.
What is the difference between percentage change and percentage points?
Percentage points are the plain arithmetic difference between two percentages. Percentage change is the relative change between them. A move from 30% to 40% is 10 percentage points, but a 33.33% relative percentage change.
What happens when the starting value is zero?
Percentage change is undefined from a zero baseline, because the formula requires dividing by the old value. The calculator still shows the absolute change, but does not describe it as an infinite percentage.
What if both the old and new values are zero?
The absolute change is 0, and there is no conventional percentage-change ratio to calculate, but the value itself simply did not change.
Can percentage change be calculated with negative numbers?
Yes. The calculator divides by the absolute value of the old value so the direction of the result stays meaningful, even when the old value, the new value, or both are negative.
What happens when a value crosses zero, like from -50 to 50?
The percentage change is still calculable, in this case +200%, but it can feel less intuitive than a same-sign change. It helps to look at the absolute change alongside the percentage in these cases.
What is the difference between percentage change and percentage difference?
Percentage change assumes a clear before-and-after relationship and divides by the old value. Percentage difference compares two values with neither one designated as the starting point, typically dividing by their average instead.
Is this the same as the regular Percentage Calculator?
No. The Percentage Calculator handles general percentage relationships like X% of Y. This calculator is built specifically around comparing an old value with a new value and the related forward and reverse calculations.
Can percentage change be greater than 100%?
Yes. If a value more than doubles, the percentage change will be greater than 100%. For example, 50 to 150 is a 200% increase.
Can the new value as a percentage of the original be over 100%?
Yes, whenever the new value is larger than the old value. If the old value is 80 and the new value is 100, the new value is 125% of the original.
Does the number of decimal places affect the accuracy of the result?
No. The calculator computes internally with full precision and only rounds the displayed figures. You can show more decimal places using the precision selector below the result.
How is percentage change used for prices and discounts?
A price drop from an original price to a sale price is a percentage decrease, and a price increase over time is a percentage increase. For shopping-specific discount math, the Discount Calculator applies this same relationship directly to sale prices.
How is percentage change used for investments?
Comparing an investment's starting value with its current value using this calculator's formula gives its percentage return over that period, which is the same core relationship an Investment Calculator builds on for longer-term projections.
Can I share or save my result?
Yes. You can copy the result as text, copy a link to this calculator, share it by email or social media, or use the print button to save a clean summary as a PDF.
This calculator uses the absolute value of the old value in the percentage-change denominator so the sign of the result stays meaningful when the starting value is negative. A zero starting value is treated as an undefined percentage change rather than an infinite one, and a −100% reverse-percentage input is guarded against so the calculator never divides by zero or returns an infinite or undefined final answer. Results may be rounded for display while calculations retain full internal precision; use the "Show more decimals" control to see additional digits.