Percentage Change Calculator — increase or decrease between two numbers

How it works

Percentage change tells you how big a rise or fall is compared with the starting point. Take the difference between the new and old values, then express it as a percentage of the original:

change = (new − old) ÷ old × 100

The sign carries the direction: a positive result is an increase, a negative one a decrease. The key is that you always divide by the old value — the change is measured relative to where you began, not where you ended up. That's also why a gain and the "same" loss aren't symmetric, as the examples below show.

Worked example

Going from 50 to 75:

change = (75 − 50) ÷ 50 × 100 = 25 ÷ 50 × 100 = +50%

And a fall, from 200 to 150:

change = (150 − 200) ÷ 200 × 100 = −50 ÷ 200 × 100 = −25%

Notice the asymmetry: 50 → 75 is +50%, but reversing it, 75 → 50, is only −33.3% — because the second time you divide by 75, not 50. Doubling a value is always +100%; halving it is −50%.

Frequently asked questions

How do I calculate percentage increase or decrease?

Both use the same formula — the sign tells them apart. Subtract the old value from the new, divide by the old, and multiply by 100. If the result is positive it's an increase; if negative, a decrease. From 40 to 46 is (46 − 40) ÷ 40 = 0.15 → +15%.

Why divide by the original value and not the new one?

Because percentage change describes movement *from* a baseline, so the baseline is the reference. A $50 item rising to $75 has gone up by $25 on a $50 base, which is 50%. Dividing by the new value instead would answer a different question, and wouldn't match how growth, inflation or returns are normally quoted.

Why isn't a 50% rise cancelled by a 50% fall?

Because the two percentages are taken on different bases. Start at 100, add 50% to reach 150, then take 50% off 150 — that's −75, landing at 75, not back at 100. To undo a +50% rise you need a −33.3% fall. Percentage changes don't simply add up for this reason.

What if the original value is zero?

Then percentage change is undefined — there's no baseline to measure against, and dividing by zero has no answer. Any move away from zero is an infinite percentage increase in the limit, so a percentage isn't a meaningful way to describe it; report the absolute change instead.

Is this the same as percentage difference?

No. Percentage change has a direction and a fixed reference (the old value), so order matters. Percentage *difference* compares two values without either being "first", dividing the difference by their average — it's always positive. This page computes change, the from→to version.

How do I apply a percentage change to get the new value?

Multiply the original by (1 + change), with the change as a decimal. A +20% change on 50 is 50 × 1.20 = 60; a −20% change is 50 × 0.80 = 40. That's the reverse of this calculator: here you have both values and want the change; there you have the change and want the result.