Free Percentage Increase & Decrease Calculator – With Reverse Mode

How to Calculate Percentage Increase, Decrease, and Reverse a Change

A percentage increase and decrease calculator answers three closely related questions: by what percent did a number change, what do you get if you raise or lower a number by a percent, and what was the original number before a known percentage change. Each is a small rearrangement of the same relationship, but mixing them up is a common source of wrong answers, so this tool separates them into three clear modes and shows the working for the number you enter. It is useful for salaries, prices, marks, statistics, and any figure that moves up or down and needs to be expressed as a percentage. The percent change between an old value and a new value is (new minus old) divided by the absolute value of old, all multiplied by 100. A positive answer is an increase and a negative answer is a decrease. Using the absolute value of the old number in the denominator keeps the sign of the result meaningful even when the starting value is negative. To raise a value by a percent you multiply it by (1 plus the percent divided by 100); to lower it you multiply by (1 minus the percent divided by 100). The reverse mode undoes that step: if a number grew by a percent to reach a final value, the original is the final value divided by (1 plus the percent divided by 100), and if it fell, you divide by (1 minus the percent divided by 100). Here are results you can verify. Going from an old value of 50 to a new value of 75, the change is (75 minus 50) divided by 50 times 100, which is a 50 percent increase, with an absolute change of 25. Going from 80 down to 60 is (60 minus 80) divided by 80 times 100, which is a 25 percent decrease. Raising 200 by 15 percent gives 200 times 1.15, which is 230. Reversing that, a final value of 230 that resulted from a 15 percent increase came from 230 divided by 1.15, which returns the original 200. Those reverse and forward results match, which is the check that the reverse mode is doing the right inversion rather than simply subtracting the percentage again. A shopper works out that a price rising from 50 to 75 is a 50 percent increase, not a 25 percent one, because percent change is measured against the original, not the gap. An employee checks that a 15 percent raise on a salary of 200 units lands at 230. A finance user who sees a final figure and knows it already includes a markup uses reverse mode to strip the markup and recover the base amount. A student confirms that a mark falling from 80 to 60 is a 25 percent drop. Because the tool prints the formula with your numbers substituted in, each of these can be traced step by step rather than trusted blindly. The most important guard is division by zero. If the old value is zero, the percent change is undefined because you would be dividing by zero, and no finite percentage can describe going from nothing to something; the tool shows a dash and a short explanation rather than a misleading number. Similarly, in reverse mode a 100 percent decrease leaves a final value of zero regardless of the original, so there is no unique original to recover, and the tool flags that too. Empty or non-numeric entries also return a dash instead of a broken result. Remember that a percentage increase followed by a decrease of the same percentage does not return you to the start, because the two percentages are taken on different bases. Everything runs locally in your browser, so nothing you type is uploaded or stored.

Percentage Increase & Decrease Calculator Formula & Method

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