# Percentage Change Calculator - Percent Increase, Decrease and the Original Value

Page: https://hirantha.me/tools/percentage-change-calculator
Part of: Hirantha Sandaruwan Lakshan free tools (https://hirantha.me/tools)
Updated: 2026-10-13

Find the percentage increase or decrease between two numbers, the value after a percentage change, or the original before it, with working shown.

This is a free tool that runs in the browser: open the page to use it. File tools process files on the visitor's own device; files are never uploaded or stored. No account, sign-up, payment or watermark.

Enter an old value and a new value to see the percentage increase or decrease, the difference, and the change you would need to get back. Or start from a value and a percentage to find the result, or work backwards from the result to the original. The working is shown, an old value of zero and negative numbers are handled openly, and nothing you type leaves your browser.

Percentage change = (new - old) / old x 100. The result is positive for an increase and negative for a decrease. From 2,000 to 2,500 the difference is 500, and 500 / 2,000 = 0.25, so the change is +25%. A change is always measured against the old value, which is why the same gap is a different percentage in the other direction: from 2,500 back to 2,000 is a fall of 500 / 2,500 = 20%.

A 50% rise followed by a 50% fall does not return to the start. 100 rising by 50% becomes 150. The 50% fall is then taken from 150, not from 100, so it removes 75 and leaves 75. The two changes use different starting points. Put another way, the factors multiply: 1.5 x 0.5 = 0.75, an overall fall of 25%. To get from 150 back to 100 you need a fall of 50 / 150 = 33.333333%.

To find the value after a change, multiply by 1 plus the percentage for an increase or 1 minus it for a decrease. To find the original before a change, divide by the same factor: 1,150 after a 15% rise was 1,150 / 1.15 = 1,000. Do not take 15% off 1,150, which gives 977.50 and is wrong, because the 15% was worked out on the original, not on the new value.

Zero and negative values need care. If the old value is 0, the percentage change is not defined, because you cannot divide by 0; the calculator says so and still shows the difference. If the old value is negative, this tool divides by its size (its absolute value, the number without its minus sign): (new - old) / |old| x 100. That keeps a rise positive, so -50 to -25 is +50% and -10 to -6 is +40%. Without the absolute value the sign flips and a rise looks like a fall. Other tools may use another convention for negative numbers. The reverse calculation (the value before a change) assumes the original was positive and says so if your numbers cannot work with that.

The change needed to get back to the start:
| After a change of | You need, to get back |
| --- | --- |
| A rise of 10% | A fall of 9.090909% |
| A rise of 20% | A fall of 16.666667% |
| A rise of 25% | A fall of 20% |
| A rise of 50% | A fall of 33.333333% |
| A rise of 100% | A fall of 50% |
| A fall of 10% | A rise of 11.111111% |
| A fall of 20% | A rise of 25% |
| A fall of 25% | A rise of 33.333333% |
| A fall of 50% | A rise of 100% |

Q: How do I calculate a percentage increase?
A: Subtract the old value from the new value, divide by the old value and multiply by 100. From 80 to 100: (100 - 80) / 80 = 0.25, so it is a 25% increase.

Q: How do I calculate a percentage decrease?
A: Use the same formula. A negative answer is a decrease. From 160 to 116: (116 - 160) / 160 = -0.275, so it is a decrease of 27.5%. Many people drop the minus sign and say 27.5% decrease.

Q: Why does a 50% rise followed by a 50% fall not return to the start?
A: Because the second percentage is taken from a different number. 100 rises 50% to 150, and 50% of 150 is 75, so the fall leaves 75. The two changes multiply (1.5 x 0.5 = 0.75), giving an overall fall of 25%. To get from 150 back to 100 you need a fall of 33.333333%.

Q: How do I find the original value before a percentage increase?
A: Divide the new value by 1 plus the percentage as a decimal. If a price is Rs. 1,150 after a 15% increase, the original was 1,150 / 1.15 = Rs. 1,000. For a decrease, divide by 1 minus the percentage: Rs. 750 after a 25% decrease was 750 / 0.75 = Rs. 1,000.

Q: What if the old value is zero?
A: The percentage change is not defined. The formula divides by the old value, and nothing can be divided by 0. Wikipedia's article on relative change says the same: it is not defined if the reference value is zero. The calculator still shows the difference between the two values.

Q: How does the calculator treat negative numbers?
A: It divides the change by the size of the old value, ignoring its sign, so (new - old) / |old| x 100. A rise then always shows as a positive percentage: -10 to -6 is +40%. Wikipedia's article on relative change suggests this fix for negative reference values. It is a convention, and other sources may handle negatives differently.

Q: Is percentage change the same as percentage difference?
A: Not always. Percentage change measures from an old value to a new one, so it depends on the direction. A symmetric percentage difference, which divides by the average of the two values and gives the same answer in both directions, is a different calculation and this tool does not do it.

Q: Is anything I type sent to a server?
A: No. The sums run in your browser and nothing is stored or sent anywhere.

Sources: Relative change - Wikipedia (not defined when the reference value is zero; dividing by the absolute value of the reference works for negative values; +50% then -50% totals -25%), checked 2026-10-13 (https://en.wikipedia.org/wiki/Relative_change); Percentage - Wikipedia (a 25% increase must be followed by a 20% decrease to restore the initial amount), checked 2026-10-13 (https://en.wikipedia.org/wiki/Percentage); Percentage Change - Maths is Fun (160 to 116 worked example; its formula divides by the absolute value of the old value), checked 2026-10-13 (https://www.mathsisfun.com/numbers/percentage-change.html)

Related tools:

- [Percentage calculator](https://hirantha.me/tools/percentage-calculator.md): Find X% of a number, what percent one number is of another, the whole from a part, or add and subtract a percentage, with the working shown.
- [Discount calculator](https://hirantha.me/tools/discount-calculator.md): Find the sale price and amount saved after a discount, the original price from a sale price, or the combined effect of two or three discounts in a row.
- [Compound interest calculator](https://hirantha.me/tools/compound-interest-calculator.md): Final balance, interest earned and a year-by-year table for a lump sum with optional regular deposits, compounded annually to daily.
- [Simple interest calculator](https://hirantha.me/tools/simple-interest-calculator.md): Find the interest, principal, rate or time from the other three with I = P x r x t, shown with the working.