Practical guide
Common percentage mistakes
Most percentage errors come from using the wrong starting value, treating percentage points as percentages, or assuming opposite changes cancel each other out.
Using the wrong base number
A percentage is always a percentage of something. For percentage change, the original value is the base: change ÷ original × 100.
From 80 to 100, the increase is 20. Using 80 as the base gives 20 ÷ 80 × 100 = 25%.
From 100 back to 80, the decrease is 20 ÷ 100 × 100 = 20%.
Assuming an increase and decrease cancel out
A 20% rise followed by a 20% fall does not return to the starting value. If 100 rises by 20%, it becomes 120. Reducing 120 by 20% removes 24, leaving 96. The second percentage acts on a different base.
Confusing percentage points with percent change
If an interest rate moves from 4% to 5%, it rises by one percentage point. Relative to the old 4% rate, that is a 25% increase. These statements describe different comparisons and should not be used interchangeably.
Adding successive percentages
Discounts, markups, and growth rates applied one after another compound. A 10% increase twice turns 100 into 110 and then 121 — a 21% overall increase, not 20%. Multiply the remaining or growth factors instead of adding the rates.
Mixing up markup and margin
Markup compares profit with cost. Margin compares profit with selling price. If an item costs $80 and sells for $100, the $20 profit is a 25% markup on cost but a 20% margin on the selling price.
Rounding too early
Keep the full number through each step and round currency only at the end. Repeatedly rounding intermediate values can move a final total by a cent or more, especially when a bill is split among several people.
Check the question before calculating
“What is 20% of 150?” and “30 is what percent of 150?” use different operations. Choose the matching mode in the percentage calculator, then make sure the answer is reasonable before using it.