Work out everyday percent problems: what is X% of Y, X is what percent of Y, X is Y% of what, percentage change between two numbers, and increase or decrease a value by a percent.
Classroom check: part of a whole versus percent change
Imagine a class had 30 students at the start of a term and 24 attended today. These are two different questions, with different numerators:
| Question | Calculator mode and inputs | Answer |
|---|---|---|
| What percent of the class attended? | X is what % of Y? · X = 24, Y = 30 | 24 ÷ 30 × 100 = 80% |
| What was the change in attendance? | Change · From = 30, To = 24 | (24 − 30) ÷ 30 × 100 = −20% |
The first answer describes the part that remains. The second describes the change relative to the original 30. A useful self-check is that 80% attended and 20% did not; the attendance count fell by 20% from the starting count. This follows the OpenStax percent-equation and percent-change lesson, which uses the original amount as the comparison base for a change.
Try another check: start at 100, decrease by 15%, then increase the result by 15%. The values are 100 → 85 → 97.75, not 100. The two 15% adjustments use different bases. Use Increase/Decrease twice to test it.
Examples
What is 20% of 50
0.20 × 50 = 10.
500 increased by 10%
500 × 1.10 = 550. Decreased by 10% is 500 × 0.90 = 450.
Formula
The core relationship is:
P × V1 = V2
P is the percent as a decimal (20% → 0.20), V1 is the original value, and V2 is the result. Rearrange to solve for any one of the three.
Percentage change compares a new value to a start:
change % = (new − start) ÷ start × 100
Increase / decrease applies a percent to a single number:
increased = value × (1 + P)
decreased = value × (1 − P)
A 10% decrease followed by a 10% increase does not return to the start — you end below the original because the increase is applied to a smaller base.
Percentage interpretation
Percent change uses the starting value as its denominator, so reversing a change does not generally produce the negative of the original percentage. A change from zero has no finite percent-change value. Percentage points and percent change answer different questions: moving from 20% to 25% is 5 percentage points and a 25% relative increase.
Percentage change and the return trip
In Change mode, the original value is the baseline: (new − original) / original × 100. Moving from 80 to 100 is a 25% increase. Returning from 100 to 80 is a 20% decrease, because the return trip has a different denominator. The result now shows that reverse percentage and the new/original multiplier.
A 50% fall needs a 100% rise to recover. Equal increases and decreases do not cancel: increasing 100 by 10% gives 110, and reducing that by 10% gives 99. For sequential changes, multiply their factors rather than adding percentages.
Zero, negative values and percentage points
A zero original value has no defined relative percentage change, so the calculator asks for a nonzero baseline. A change to zero is −100% from a positive start; the reverse percentage is omitted because its new baseline would be zero. For negative starts, this tool retains the signed denominator and explains why the sign can differ from an ordinary increase/decrease description.
When comparing rates, distinguish relative change from percentage points. A rate moving from 20% to 25% rises by five percentage points and by 25% relative to its starting rate. The Change tab calculates the latter; simple subtraction gives the percentage-point difference.