Percentages and Ratios
Four calculators, and the distinctions students lose marks on.
These four cover the comparisons that come up most often in class, and the distinctions between them are where marks are usually lost. Percent change and percent difference are not the same calculation and do not give the same answer.
Ratio calculatorSimplify a ratio, split a total, solve a proportion
Percent change calculatorIncrease or decrease from a starting value
Percent difference calculatorCompare two values of equal standing
Fraction to percent calculatorConvert any fraction to a percentage
Which one does the question want?
| Percent change | Percent difference | |
|---|---|---|
| Use when | One value came first | Neither value is the baseline |
| Divide by | The original value | The mean of the two |
| Sign | Signed: increase or decrease | Always positive |
| Example | Price rose from $50 to $75 | Two labs measured 50 and 75 |
Those two examples use the same numbers and give different answers: 50% change, 40% difference. Reading the question is the whole skill.