Percentage Calculator

Percentages show up everywhere: grades, discounts, tips, test scores and statistics. This calculator answers the five questions students ask most, each in its own form, and gives the answer as a full sentence so you can check it reads the way you meant.

How to Use It

1. Choose a Question, such as “What is X% of Y?” or “Percent change from X to Y”.
2. Fill in the two numbers. The labels change to match the question.
3. Press Calculate to see the answer and a sentence explaining it.

How It Works

Every question here comes from one relationship between a part, a percent and a whole:

• X% of Y solves it for the part.
• X is what percent of Y solves it for the percent: $\text{part} \div \text{whole} \times 100$.
• X is Y% of what solves it for the whole: $\text{part} \div \text{percent} \times 100$.

Percent change measures a move from an original value to a new one, relative to the original:

Percent difference compares two values with their average, so the order doesn’t matter:

Worked Example

• 15% of 200: $0.15 \times 200 = 30$.
• 30 is what percent of 200: $30 \div 200 \times 100 = 15\%$.
• 45 is 15% of what: $45 \div 15 \times 100 = 300$.
• Change from 200 to 230: $(230 - 200) \div 200 \times 100 = +15\%$.
• Difference between 40 and 50: $10 \div 45 \times 100 \approx 22.22\%$.

Tips and Common Mistakes

• Pick the right base. “Percent of what?” is the question to ask: a 15% change is 15% of the original, not the new value.
• Changes don’t cancel. A 50% rise followed by a 50% drop leaves you at 75% of where you started.
• Change or difference? Use change when there’s a before and after; use difference when neither value comes first.
• Percent vs percentage points. Going from 40% to 50% is a rise of 10 percentage points, but a 25% increase.
• Check the sentence. The answer’s sentence repeats your numbers, which catches a swapped X and Y.