Percentage Calculator — Increase, Decrease, Difference & More

The five percentage questions

Almost every percentage problem is one of five shapes. Pick the tab that matches your question and the calculator handles the arithmetic.

1. What is X% of Y?

The most common case — tips, discounts, tax, commission. Divide the percentage by 100 and multiply: 20% of 150 is 0.20 × 150 = 30.

2. X is what percent of Y?

Turns two raw numbers into a proportion. If 37 of 200 customers renewed, that is 37 ÷ 200 × 100 = 18.5%.

3. Percentage increase or decrease

Measures change relative to where you started: (new − old) ÷ old × 100. Revenue moving from 80,000 to 92,000 is a 15% increase. Note that the original value is always the denominator — swapping the two numbers gives a different answer.

4. Increase or decrease a number by a percentage

Applies a change you already know. An item at 45 with 8% sales tax comes to 45 × 1.08 = 48.60. The tool shows both the increased and the decreased result, since discounts and markups use the same input.

5. Reverse percentage

Works backwards from a result. If 60 is 75% of the original price, the original was 60 ÷ 75 × 100 = 80. This is how you recover a pre-discount price or a pre-tax total.

Two mistakes worth avoiding

Percentages do not reverse symmetrically. Drop 100 by 50% and you get 50; add 50% back and you reach 75, not 100. Each percentage applies to a different base, so undoing a 50% cut takes a 100% rise.

Percent and percentage point are not the same word. An interest rate moving from 4% to 6% rose by two percentage points — but by 50 percent. Financial and political reporting mix these up constantly, usually in whichever direction sounds more dramatic.

Quick mental shortcuts

• 10% — move the decimal one place left.
• 5% — take 10% and halve it.
• 15% — 10% plus half of that 10%. Handy for tips.
• Swap the terms — 8% of 50 is awkward, but 50% of 8 is obviously 4. X% of Y always equals Y% of X.