How to Calculate Percentage Increase (Formula + Examples)

The whole thing fits on one line: percentage increase = ((new − old) ÷ old) × 100. Start with the change, the difference between where you ended and where you began, which is new minus old. If the number went up, that difference is positive. If it fell, it's negative. The same formula handles both directions, which is why the more general version is called percent change.

Next you divide that difference by the old value, the one you started from. This is the step that does the real work, because it scales the raw change against the original size. A jump of 25 means something very different depending on whether you started at 50 or at 5,000, and dividing by the base is what captures that. The result is a ratio. Multiply it by 100 to express the ratio as a percentage instead of a decimal, and you're done: 0.5 becomes 50%.

Take the numbers from the top. Going from 50 to 75, the change is 75 − 50 = 25 and the old value is 50, so (25 ÷ 50) × 100 = 50%. That's a 50% increase. Now run it the other way, from 75 down to 50. The change is 50 − 75 = −25, and the old value is 75 this time because that's where you started. So (−25 ÷ 75) × 100 = −33.3%. The sign is the whole point.

A decrease comes out negative. −33.3% tells you the direction as well as the size: down by about a third. Notice the asymmetry too. Rising from 50 to 75 is +50%, but falling from 75 back to 50 is only −33.3%, not −50%. The base shifted from 50 to 75, and the base is what the entire calculation hinges on. If you care about how big the drop was and not the direction, take the absolute value and call it a 33.3% decrease.

Here's where people get tangled, and it matters in finance, in politics, and in any news story that quotes rates. Say an interest rate moves from 5% to 7%. There are two honest ways to describe that. In percentage points, it rose by 2, which is plain subtraction: 7 − 5 = 2 percentage points. In percent terms, the relative change is (7 − 5) ÷ 5 = 0.4, or +40%.

Both are correct and they mean different things. Percentage points measure the absolute gap between two percentages. Percent change measures that gap relative to the starting figure. A headline reading 'rates jumped 40%' and one reading 'rates rose 2 points' describe the exact same move. Treating them as interchangeable is how a small shift gets made to sound alarming. When you quote a change between two percentages, say which one you mean.

The most common slip is dividing by the wrong number. The denominator is always the old value, the one you started from, never the new one. Swap them and you get a different, wrong percentage, which is exactly why 50 to 75 is +50% but 75 to 50 is only −33.3%. Close to this is a base of zero or a negative base. If the old value is 0, dividing by it is undefined and there's no meaningful percent change to report. A negative starting value flips the sign of the result in ways that rarely mean what you expect, so treat percent change on negative bases with suspicion.

The other big mistake is assuming percentages simply add up. They compound. A 10% rise followed by a 10% fall does not return you to even. Start at 100, add 10% to reach 110, then subtract 10% of 110, which is 11 and not 10, and you land on 99. You're below where you started after an equal-looking up-and-down. Each move applies to the current value rather than the original, so a series of percentage changes has to be chained, not summed.

Once the formula makes sense, you rarely need to work it out manually. A percentage calculator takes the old value and the new value, runs ((new − old) ÷ old) × 100 for you, and returns the increase or decrease instantly, sign included. There's nothing to misplace and no denominator to mix up.

It earns its keep anywhere you compare a before and an after: salary raises, month-over-month sales growth, a price change at the register, investment returns across a period, a grade that improved between two exams. Type in the two numbers, read the percent, move on. Keeping the formula in your head is still worth it for anything you check often, but for a quick answer the calculator is faster and far less error-prone.