Start with the right base value
A percentage means a number per hundred. The key to choosing a calculation is identifying what counts as the whole: the original price, the total possible score, or the starting value before a change. The same difference can produce different percentages when you change that base.
Choose the mode that matches the question
What is X% of Y?
Use this when you know the rate and the base amount. Multiply X ÷ 100 by Y. For 15% of 200, enter 15 and 200; the answer is 30, an amount rather than a percentage.
X is what percent of Y?
Use this when you know a part and a total. Divide X by Y and multiply by 100. For 30 out of 120, enter 30 and 120; the answer is 25%. The total cannot be zero.
Percentage change
Use this to compare an old value with a new one. Enter the old value in From and the new value in To. From 80 to 100 gives +25%; reversing those inputs gives −20%.
Enter 15 for fifteen percent, not 0.15, in the percentage field. Use the same units for amounts you compare: for example, compare monthly counts with monthly counts rather than mixing a monthly total with an annual total.
Everyday examples with the arithmetic shown
A 30% discount on a price of 2,500
Use “What is X% of Y?” with 30 and 2500. The discount is 0.30 × 2500 = 750. Subtract it from the original price: 2500 − 750 = 1,750 to pay. The calculator's first result is the saving, not the final price.
A 15% tip on a bill of 1,200
Enter 15 and 1200 in the same mode. The tip is 180, so the bill plus that tip is 1,380. This example assumes the chosen tip base is the full 1,200; decide which amount you intend to use before calculating.
A score of 42 out of 50
Use “X is what percent of Y?” with 42 and 50. The calculation is 42 ÷ 50 × 100 = 84%. This gives the share of available marks, not a grading category or pass/fail decision.
A price rising from 80 to 100
Choose Percentage change, From 80, To 100. The difference is 20, and the starting base is 80: 20 ÷ 80 × 100 = 25% increase. Dividing by 100 instead would answer a different question.
Finding the price before a discount
If a price is 800 after a 20% discount, it represents 80% of the original. Divide 800 by 0.80 to get 1,000. Adding 20% to 800 gives 960, not the original price. Reverse-percentage division is a manual calculation; there is no dedicated reverse mode above.
Percentage change versus percentage points
Suppose a completion rate rises from 40% to 50%. Subtracting the two rates gives an increase of 10 percentage points. The relative percentage increase is (50 − 40) ÷ 40 × 100 = 25%.
Both describe the same change, but answer different questions. Percentage points describe the gap between rates; percentage change describes that gap relative to the original rate. Enter From 40 and To 50 in change mode for the relative result. Subtract the rates separately for the percentage-point gap.
For a decrease from 50% to 40%, the gap is −10 percentage points and the relative change is −20%. State which measure you mean when reporting results.
Why a 20% decrease and a 20% increase do not cancel
Starting at 100, a 20% decrease removes 20 and leaves 80. A 20% increase then adds 16, because it is calculated from 80. The final amount is 96. Move the slider to compare other rates.
100 × 0.80 × 1.20 = 96.00. The final value is 4.00% below the starting value because the increase applies to the smaller amount.
This teaching example starts at 100 and does not change the calculator inputs above.
To return from 80 to 100, you need an increase of 20 ÷ 80 × 100 = 25%. For a decrease of d%, where d is below 100, the recovery percentage is d ÷ (100 − d) × 100. After a 100% decrease, the value is zero and no finite percentage increase of zero restores a positive original.
Sequential discounts also multiply rather than simply add. A 20% discount followed by a 10% discount leaves 0.80 × 0.90 = 0.72 of the original price: a 28% total discount, not 30%.
Zero, negative values, and rounding
This calculator uses (new − old) ÷ |old| × 100 for percentage change. For a positive starting value, that is the familiar difference divided by the original. For negative starting values, it uses the magnitude of the original as the denominator.
For example, From −100 to −50 produces +50% under this convention. Negative bases can make percentage descriptions ambiguous, so report the original and new values alongside the result rather than treating this convention as universal.
A dash appears when the total in part-of-whole mode is zero, or the starting value in change mode is zero. That is division by zero. It does not mean percentages of zero are impossible: 15% of 0 is simply 0.
Keep unrounded values through intermediate steps where possible and round at the end. A displayed result is a rounded representation; rounding early can change totals across several calculations.