Percentage Calculator

How to use this percentage calculator

This page includes six percentage tools. Each solves a different type of question. Enter the known values, leave the unknown field blank (where applicable), and click Calculate. The missing value is computed and shown with a step-by-step explanation.

1. Basic calculator: Fill any two of “X% of Y = result” to find the third.
2. Phrase tools: Use the word-problem layouts for “what is X% of Y,” “X is what % of Y,” and “X is Y% of what.”
3. Difference: Compare two values with the percentage-difference formula (relative to their average).
4. Change: Find a starting value, percent increase/decrease, or final value when you know two of the three.

For a full tutorial with more examples, read A Complete Guide to Percentages.

What is a percentage?

A percentage is a number or ratio expressed as a fraction of 100. The symbol % means “per hundred.” For example, 35% is the same as the decimal 0.35 or the fraction 35100 = 720.

Percentages are used everywhere — discounts, tax rates, exam scores, growth rates, and statistics. To find a percentage of a quantity, multiply the quantity by the percentage divided by 100.

Example: If 25 out of 50 students passed a test, the pass rate is (25 ÷ 50) × 100 = 50%.

Percentage formula

The basic relationship can be written as:

Where P is the percentage (as a decimal), V₁ is the original value, and V₂ is the result after applying the percentage. Our calculators work with whole-number percents (e.g. 20 for 20%) and show the steps in plain language.

Example: What percent is 1.5 of 30? P = 1.5 ÷ 30 = 0.05 → 5%

Percentage increase and decrease

To increase a value by X%: multiply by (1 + X/100). To decrease: multiply by (1 − X/100).

Example: A $200 item with a 15% discount costs 200 × (1 − 0.15) = $170.

Percentage difference

Percentage difference compares two values relative to their average (not relative to one of the values). This is useful when neither value is clearly a “before” or “after.”

Example: Compare 80 and 100: difference = |80 − 100| = 20, average = 90, so percentage difference = (20 ÷ 90) × 100 ≈ 22.22%. This is different from “25% increase from 80 to 100,” which uses the starting value as the base.

Percentage change vs. percentage difference

These terms are often confused but measure different things:

• Percentage change (or percent increase/decrease) compares the change to the original value: ((New − Old) ÷ Old) × 100. Going from $50 to $65 is a 30% increase.
• Percentage difference compares the gap to the average of the two values. It is symmetric — swapping the two numbers gives the same result.
• Percentage points: An absolute shift between two percentages. If a rate rises from 10% to 15%, that is a 5 percentage point increase (not a 50% increase unless stated relative to the base rate).

Converting between percentages, decimals, and fractions

Percentages, decimals, and fractions are three ways to express the same proportion:

• 25% = 0.25 = 14
• 12.5% = 0.125 = 18
• 33.3…% ≈ 0.333 = 13

To convert a percent to a decimal, divide by 100. To convert a decimal to a percent, multiply by 100. For fraction conversions, use our fraction calculator.

Real-world uses of percentages

Percentages are one of the most common math tools in daily life:

• Shopping & sales: A 30% discount on a $80 item saves $24 — try our discount calculator.
• Tax & tips: Adding 8.25% sales tax or calculating a 18% restaurant tip.
• Grades & tests: Scoring 42 out of 50 is 84%. Use “X is what % of Y” above.
• Finance: Interest rates, investment returns, and inflation are expressed as percentages — see compound interest.
• Health & fitness: Body fat percentage, daily calorie targets, and progress toward goals.
• Business: Profit margins, growth rates, market share, and conversion rates.

Common percentage mistakes to avoid

• Adding percentages incorrectly: A 20% discount plus 10% coupon is not always 30% off the original — the second discount may apply to the reduced price.
• Wrong base value: “Increased by 50% then decreased by 50%” does not return to the start (e.g. 100 → 150 → 75).
• Confusing “of” and “off”: 20% of 200 is 40; 20% off 200 means you pay 160.
• Mixing up difference and change: Use the correct tool above depending on whether you have a before/after or two independent values.

Frequently Asked Questions

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