They are inverse operations. Percentage increase gives you a rate from two values. Increasing by a percentage gives you a value from a rate.
Same two numbers, opposite direction, and the answer to one is the input to the other.
The two questions side by side
| You know | You want | Question | Answer |
|---|---|---|---|
| 80 and 100 | the rate | “80 to 100 is what % increase?” | 25% |
| 80 and 25% | the value | “increase 80 by 25%” | 100 |
Read those twice. Every number appears in both rows. The only thing that changes is which one is missing.
Finding the rate
You have a before and an after, and you want to know how much it moved.
((new − old) ÷ old) × 100Revenue went from 80 to 100. The rise is 20. Divide by the original 80:
20 ÷ 80 = 0.25 → 25% increaseThe trap here is dividing by the wrong number. Divide by 100 instead of 80 and you get 20%, which is a real answer to a different question — “what proportion of the new figure is the growth?” Nobody asks that.
Growth is always measured against where you started.
Finding the value
You have a starting number and a rate, and you want the result.
number × (1 + rate ÷ 100)Increase 80 by 25%: multiply by 1.25 to get 100. One step, no addition required.
Plenty of people do it in two — find 25% of 80, which is 20, then add it back. Same answer, and there is nothing wrong with it. The one-step version just breaks less often when the numbers are awkward.
Why the confusion costs money
The two questions produce different numbers from the same inputs, so getting them backwards produces an answer that looks plausible.
Say a supplier raises a price from 80 to 100 and you need to know the increase for a budget. The right answer is 25%. If you instead calculate “80 increased by 100%” you get 160 — obviously wrong, and you would catch it.
But if you calculate “what percentage of 100 is 20” you get 20%, and 20% looks completely reasonable. It is the wrong answer to the right question, and nothing about it looks wrong. That is what makes it dangerous.
The check that catches it
Run your answer backwards.
If 80 to 100 is a 25% increase, then increasing 80 by 25% should give you 100. Multiply 80 by 1.25 — you get 100. Correct.
Try it with the wrong answer: increase 80 by 20% and you get 96, not 100. The check fails immediately.
Any percentage result can be verified this way in about five seconds, and it catches nearly every direction error before it reaches a spreadsheet.