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Formula
Percentage change = ((New − Original) ÷ |Original|) × 100
- New
- the later or current value
- Original
- the starting value you are comparing against
- |Original|
- the size of the original value, ignoring its sign
What percentage change tells you
Percentage change expresses the gap between two values as a share of where you started. A $15 rise means something very different on a $30 item than on a $3,000 one. Dividing by the original value puts both on the same scale: the first is a 50% increase, the second is 0.5%.
The sign of the difference gives the direction. If the new value is larger, it’s an increase. If it’s smaller, it’s a decrease. The percentage change calculator shows the size of the change as the headline figure and states the direction next to it.
How to use the percentage change calculator
- Enter the original value, meaning the starting point or “before” figure.
- Enter the new value, meaning the “after” figure.
- The result updates as you type. Commas as thousands separators are fine, such as 12,500.
- Below the main result you’ll see:
- Difference (new − original): the raw change in the same units as your inputs.
- New value as % of original: useful for statements like “sales were 85% of last year’s”.
- Percentage difference (symmetric): a comparison that doesn’t treat either value as the starting point.
Getting the order right matters. Going from 40 to 50 is a 25% increase, but going from 50 to 40 is a 20% decrease. The gap is the same, but the bases differ.
How to calculate percentage change between two numbers
- Subtract the original value from the new value to get the difference.
- Divide the difference by the original value.
- Multiply by 100 to turn the decimal into a percentage.
Say a membership fee goes from $250 to $290. The difference is 290 − 250 = 40. Dividing by the original gives 40 ÷ 250 = 0.16, and 0.16 × 100 = 16%, so the fee rose 16%.
A decrease works the same way, and the negative sign tells you the direction. If a class shrinks from 75 students to 60, the difference is 60 − 75 = −15. Then −15 ÷ 75 = −0.2, which is a 20% decrease.
A quick sanity check: the new value divided by the original should equal 1 plus the change as a decimal. Here 290 ÷ 250 = 1.16 and 60 ÷ 75 = 0.80, which match a 16% rise and a 20% fall.
Percentage change with negative numbers
When the original value is negative, the difference is divided by the size of the original, ignoring its minus sign, so the sign of the result still shows the direction. From −40 to −10 the difference is 30, and 30 ÷ 40 × 100 gives a 75% increase, because the value rose toward zero. From −20 to −50 the difference is −30, a 150% decrease.
These results are consistent, but they can be hard to read when a figure such as profit swings between a loss and a gain, so report the raw difference alongside them. A change from zero has no percentage at all, because it would mean dividing by zero.
Growth factors and how to undo a change
Every percentage change corresponds to a multiplier, or growth factor. A 20% increase multiplies by 1.20, and a 20% decrease multiplies by 0.80. Because the base changes after the first move, undoing a change takes a different percentage than the one you started with.
| Change | Multiply by | Change needed to get back |
|---|---|---|
| +5% | 1.05 | −4.76% |
| +10% | 1.10 | −9.09% |
| +15% | 1.15 | −13.04% |
| +20% | 1.20 | −16.67% |
| +25% | 1.25 | −20% |
| +50% | 1.50 | −33.33% |
| +100% | 2.00 | −50% |
| −5% | 0.95 | +5.26% |
| −10% | 0.90 | +11.11% |
| −15% | 0.85 | +17.65% |
| −20% | 0.80 | +25% |
| −25% | 0.75 | +33.33% |
| −50% | 0.50 | +100% |
| −75% | 0.25 | +300% |
The pattern is lopsided. Small changes nearly cancel out, but large falls need much larger rises to recover. A 50% loss needs a 100% gain to get back to the starting point.
Percentage change vs percentage points
When the values are already percentages, such as interest rates or vote shares, there are two ways to describe a move. A rate going from 4% to 6% rose by 2 percentage points, the simple difference. It also rose by 50%, because 2 is half of 4. Both statements are true, but they answer different questions, so say which one you mean. Use percentage points for the absolute gap and percentage change for the relative one.
Real-life uses
Prices and the cost of living
If a gallon of milk goes from $3.49 to $3.89, the 40-cent rise is about an 11.46% increase. Comparing items by percentage rather than by cents makes it easy to see which prices are rising fastest, even when one item costs much more than another. When a package shrinks but the price stays the same, as in the coffee example below, the percentage decrease in quantity is the hidden price rise you’re paying.
Year-over-year sales and business figures
Quarterly sales that grow from $80,000 to $92,000 are up 15%. Businesses usually compare a period with the same period a year earlier (“year over year”) to avoid mistaking seasonal swings for growth. When you want a single yearly growth rate across several years, the change needs to be compounded rather than divided evenly. The compound interest calculator shows how a steady annual rate builds up.
Investments
A share bought at $85 that drops to $68 is down 20%, and it needs a 25% rise to get back to $85. For the return on money you put in, including gains and the amount invested, the ROI calculator is a closer fit.
Health and fitness
Going from 195 lb to 180 lb is about a 7.69% decrease in body weight. Using percentages makes progress comparable between people of different starting weights.
Tips for reading percentage changes
- Check the base. “Up 50%” from a tiny base can mean very little. Going from 2 complaints to 3 is a 50% rise.
- Look at the raw difference too. The calculator shows it beneath the main result for this reason.
- Watch for “times” language. “Three times as many” is a 200% increase, not 300%, because the new value is 300% of the original.
- Compare like with like. Use the same time period, units and definitions for both values.
Common mistakes
- Dividing by the new value. The base is always the original. Dividing by the new value understates increases and overstates decreases.
- Adding successive changes. Two years of 10% growth is 21% overall, not 20%, because the second 10% applies to an already larger number. The guide on how to calculate percentage change covers compounding in more detail.
- Reversing a change with the same percentage. After a 20% drop, you need a 25% rise to get back to the original value. To find the value a percentage was taken from, use the reverse mode of the percentage calculator.
- Averaging percentage changes. A 10% rise followed by a 10% fall averages to 0%, but the value ends 1% lower, because 1.10 × 0.90 = 0.99.
Related terms
- Percentage difference: the gap between two values divided by their average, used when neither is the starting point. For 60 and 75 it’s about 22.22%.
- Growth factor: 1 plus the change as a decimal. Multiplying growth factors combines successive changes.
- Percentage point: the plain difference between two percentages.
- Percentage of a number: for “what is 15% of 80?” rather than “how much did it change?”, use the percentage calculator. Other everyday math tools are on the math calculators page.
Worked examples
A price increase
A product’s price rises from $80 to $100.
Inputs: Original value = 80; New value = 100
((100 − 80) ÷ |80|) × 100 = 25
Answer: 25% increase from 80 to 100.
A drop in website visitors
Monthly visitors fell from 12,500 to 9,800.
Inputs: Original value = 12500; New value = 9800
((9,800 − 12,500) ÷ |12,500|) × 100 = −21.6
Answer: 21.6% decrease from 12,500 to 9,800.
A pay raise
An annual salary goes from $48,000 to $50,400.
Inputs: Original value = 48000; New value = 50400
((50,400 − 48,000) ÷ |48,000|) × 100 = 5
Answer: 5% increase from 48,000 to 50,400.
A smaller package at the same price
A bag of coffee shrinks from 16 oz to 14.5 oz while its price stays the same.
Inputs: Original value = 16; New value = 14.5
((14.5 − 16) ÷ |16|) × 100 = −9.375
Answer: 9.375% decrease from 16 to 14.5.
Assumptions and limitations
- The percentage change, the difference, the new value as a percent of the original, and the percentage difference are shown to up to 4 decimal places.
- The main result is shown without a sign and labeled as an increase, a decrease or no change.
- The original value must not be 0, because a change from zero can't be expressed as a percentage. The new value can be 0, which gives a 100% decrease from a positive original.
- Negative values are allowed. The change is divided by the size of the original value, so moving from −50 to −20 counts as a 60% increase.
- The symmetric percentage difference divides the gap by the average of the two values and doesn't depend on which value comes first. It and the "new value as % of original" figure are shown only when both values are positive, where they have a clear meaning.
- The calculator compares two values only. It doesn't combine several successive changes or convert a multi-year change into an annual rate.
Frequently asked questions
What's the difference between percentage change and percentage difference?
Percentage change measures movement from a starting point, so the original value is the reference and the order matters. Percentage difference compares two values with no starting point, using their average as the reference, so swapping them gives the same answer.
Why is a 25% rise followed by a 25% fall not back to the start?
Each change uses a different base. 200 rises 25% to 250, but 25% of 250 is 62.5, so falling 25% lands at 187.5. Successive changes multiply rather than add.
How do you calculate percentage change year over year?
Use the figure for a period last year as the original value and the figure for the same period this year as the new value. Third-quarter sales of $80,000 last year and $92,000 this year are up 15% year over year. Comparing the same period in each year keeps seasonal swings out of the result.
Can the percentage decrease be more than 100%?
Only if the new value goes below zero, or the original is negative. For quantities that can't be negative, such as prices or headcounts, the largest possible decrease is 100%, which means falling to zero.
What if the original value is zero?
Percentage change from zero is undefined, because it would mean dividing by zero. Going from 0 to 40 sales isn't an infinite increase. Report the absolute change instead, such as "up 40 sales from none".
How do I find the original value if I know the new value and the percentage change?
Divide the new value by the growth factor. If a price is $115 after a 15% increase, the original was 115 ÷ 1.15 = $100. After a 30% decrease, a value of $42 started at 42 ÷ 0.70 = $60.
How do I calculate percentage change in a spreadsheet?
With the original value in A2 and the new value in B2, use =(B2-A2)/ABS(A2) and format the cell as a percentage. Using ABS matches this calculator's handling of negative starting values; plain =(B2-A2)/A2 gives the same answer whenever A2 is positive.