From one value to another, as a percentage
Work out the percentage change between two numbers, whether prices rose, traffic fell or a salary moved. Shows the direction and the absolute gap.
Percentage change measures movement between a starting figure and a final one. Which number you treat as the start completely changes the answer, and that is where most errors creep in.
Going from 80 to 100 is a 25% rise. Going back from 100 to 80 is a 20% fall. Same two numbers, same gap of 20, different percentages — because the base changed.
The percentage change from your first value to your second The raw difference between the two, for a sanity check A negative result when the value dropped, so direction is never ambiguous The change is always measured against the first value as the base. If the starting value is zero, percentage change is mathematically undefined — nothing can be a percentage of nothing. Why isn't a 25% rise cancelled by a 25% fall? Because the fall is calculated on a bigger number. 100 rises to 125, then 25% of 125 is 31.25, leaving you at 93.75 — down almost 6%.
What is the difference between percent change and percentage points? If a rate moves from 4% to 6%, that is a rise of 2 percentage points but a 50% increase. News reports blur these two constantly.
How do I express a fall as a percentage? Subtract the new value from the old, divide by the old, then multiply by 100. From 250 to 200 that gives 50 ÷ 250 = 20% down.
Can the change exceed 100%? Increases can, without limit — doubling is +100%, tripling is +200%. Decreases stop at −100%, which means the value reached zero.
Worked example A price rise
Input: From 80 to 100
Output: +25%
Note: Reversing it gives −20%. Percentage changes are not symmetrical, which is why 'we lost 50% then gained 50%' leaves you down overall.
