Percentage Calculator

How to use this calculator

Pick a mode at the top: X% of Y to find a percentage of a number, X is what % of Y to find a ratio as a percent, or % change to measure an increase or decrease between two values. Enter the two numbers and the answer appears instantly with a plain-English explanation.

How percentages work

The word "percent" comes from the Latin per centum, meaning "by the hundred." A percentage is simply a ratio expressed as a fraction of 100. This makes it easy to compare proportions that would otherwise involve different denominators — saying "37 out of 100" is less intuitive than saying "37%."

The key step in almost all percentage calculations is the same: convert the percentage to a decimal by dividing by 100. Once you have the decimal, the arithmetic becomes straightforward multiplication or division.

The three types of percentage problems

• Finding a percent of a number — "What is 30% of 250?" Multiply the number by the decimal form of the percentage: 250 × 0.30 = 75.
• Expressing one number as a percent of another — "45 is what percent of 180?" Divide the part by the whole and multiply by 100: (45 ÷ 180) × 100 = 25%.
• Calculating percentage change — "A price rose from $80 to $100. By what percent did it increase?" Subtract the old value from the new, divide by the old value, multiply by 100: ((100 − 80) ÷ 80) × 100 = 25%.

Worked examples

Example 1 — percent of a number

• Question: What is 20% of 80?
• Convert: 20% = 0.20
• Calculation: 0.20 × 80 = 16

Example 2 — what percent is one number of another?

• Question: 20 is what percent of 80?
• Calculation: (20 ÷ 80) × 100 = 25%

Example 3 — percentage increase

• Question: A stock rose from $80 to $100. What was the percentage increase?
• Difference: 100 − 80 = 20
• Calculation: (20 ÷ 80) × 100 = 25% increase

Example 4 — percentage decrease

• Question: A stock fell from $100 to $80. What was the percentage decrease?
• Difference: 80 − 100 = −20
• Calculation: (−20 ÷ 100) × 100 = −20% (a 20% decrease)
• Note: the base is the original value (100), not the new value — this is why a 25% rise is not reversed by a 25% fall.

Percentage points vs. percent

This distinction trips up many people. If an interest rate rises from 2% to 3%, that is a 1 percentage-point increase. But relative to the starting rate, 2%, it is a 50% increase(because 1 ÷ 2 = 0.5). Both statements are correct; they just describe different things. In financial and policy contexts, it matters enormously which one is used.

Common mistakes to avoid

• Reversing an increase with the same percentage decrease. If something increases by 25%, it does not return to the original after a 25% decrease. After a 25% rise from 100 to 125, a 25% fall takes you to 93.75, not 100. The base has changed.
• Confusing percentage points with percent. Going from a 4% tax rate to a 6% tax rate is a 2 percentage-point increase, but a 50% increase in the rate. Using the wrong term is a common source of misleading headlines.
• Using the new value as the base for percentage change. Always divide by the original (old) value, not the new one. (Old → New, so old is the denominator.)
• Forgetting to convert the percentage to a decimal. Multiplying 80 × 20 gives 1,600, not 16. Always divide by 100 first (or write 0.20 instead of 20).

The formulas

Percent of: (X ÷ 100) × Y  ·  Is what percent: (X ÷ Y) × 100  ·  Change: ((New − Old) ÷ Old) × 100