Why Your Percentage Change Calculation Came Out Wrong
The most common mistake is dividing by the new value instead of the original (old) value — percentage change is always ((new − old) ÷ old) × 100, and swapping which number goes in the denominator produces a different, incorrect result, especially noticeable for large changes.
This is consistently the single most common percentage-related mistake, and it's worth understanding exactly why it happens, not just what the correct formula is.
The mistake, demonstrated
A value goes from 50 to 75. Correct: (75 − 50) ÷ 50 × 100 = 50% increase. Incorrect (dividing by the new value instead): (75 − 50) ÷ 75 × 100 = 33.3% — a meaningfully different, wrong answer, purely from using the wrong denominator.
Why this specific mistake is so common
It often happens because the new value is the more prominent or recent number in someone's mind while working through the problem, making it feel like the natural denominator — but percentage change is always relative to the starting point, not the ending point, since it's answering "how much did this change, relative to where it started."
A reliable way to avoid it
Before calculating, explicitly label which number is "old" (the starting point) and which is "new" (the result) — writing this down before applying the formula removes the ambiguity that leads to picking the wrong denominator under time pressure.