Percentage Calculator

How This Calculator Works

A percentage is a way of expressing a number as a fraction of 100. This calculator covers the five questions people most often need answered:

• What is X% of Y? — for example, figuring out a 20% discount on a $50 item, or how much a 15% tip on a $60 bill comes to.
• X is what percent of Y? — for example, working out that 45 correct answers out of 60 questions is 75%.
• X is Y% of what? — the “reverse percentage” question. For example, if a $45 deposit was 15% of the total price, the full price was $300.
• What is the percent change from X to Y? — for example, how much a price, a salary, or a measurement went up or down between two points in time.
• What is the percent difference between X and Y? — how far apart two values are relative to their average, without treating either one as the “starting” value.

Pick the question that matches what you’re trying to find, enter the two numbers, and the calculator does the rest — no need to remember which number goes on top of the fraction.

The Formula

All three questions come from the same underlying relationship: a percentage is a part divided by a whole, multiplied by 100. The same two colors track part and whole across all three:

$$\text{Percent of a Number: } \vA{\text{Part}} = \left(\frac{\vC{\text{Percent}}}{100}\right) \times \vB{\text{Whole}}$$ $$\text{What Percent One Number Is of Another: } \vC{\text{Percent}} = \left(\frac{\vA{\text{Part}}}{\vB{\text{Whole}}}\right) \times 100$$ $$\text{Reverse Percentage (Find the Whole): } \vB{\text{Whole}} = \frac{\vA{\text{Part}}}{\vC{\text{Percent}} \div 100}$$

Percent change and percent difference each compare two independent values rather than a part and a whole, so they use their own variable names instead of reusing part/whole/percent above:

$$\text{Percent change} = \left(\frac{\text{new} - \text{original}}{\text{original}}\right) \times 100$$ $$\text{Percent difference} = \left(\frac{|a - b|}{(|a| + |b|) \div 2}\right) \times 100$$

The percent change formula is signed on purpose: a positive result means the value went up, and a negative result means it went down. That’s why “the price dropped 25%” shows up as $-25$, not $25$, in the change calculation.

Percent difference is a different question from percent change: change is directional and measured against the first (original) value, while difference is symmetric — it measures how far apart two values are relative to their average, so swapping the two numbers gives the same answer and the result is never negative. Use change when one value came before the other; use difference when you’re just comparing two independent measurements.

Worked Example

Say a jacket’s price increases from $80 to $92, and you want to know the percent increase.

1. Subtract the original from the new value: $92 - 80 = 12$.
2. Divide that difference by the original value: $12 \div 80 = 0.15$.
3. Multiply by 100 to express it as a percentage: $0.15 \times 100 = 15$.

The price went up by 15%. If the jacket had instead dropped from $80 to $68, the same three steps give $((68 - 80) \div 80) \times 100 = -15$, a 15% decrease — the negative sign is the calculator’s way of telling you which direction the value moved.

Common Mistakes

• Confusing percentage change with a percentage point difference. Going from a 10% interest rate to a 12% rate is a “2 percentage point” increase, but a “20% increase” in the rate itself (2 ÷ 10 × 100) — the two numbers are both correct, but answer different questions.
• Using the wrong base value for a decrease. A value that drops by 20% and then rises by 20% does NOT return to the original number, since the second 20% is calculated on the smaller, already-reduced value — the two percentages apply to different base amounts.
• Mixing up “percent of” and “percent change.” “What is 15% of 80?” (a direct multiplication) and “What percent did 80 change to reach 92?” (a change calculation) use different modes above — picking the wrong one for the question being asked gives a technically-correct but irrelevant answer.