Percentage Calculator

Percentages appear everywhere in daily life — from calculating a sale discount to understanding a raise, figuring out a test score, or tracking investment returns. Our percentage calculator provides four distinct modes to handle any scenario, with instant results and a clear explanation of the formula used.

Find what X percent of a number equals. Example: What is 20% of 85?

Percentage (%)

Of Number

—

Four Percentage Modes Explained

Mode 1: What is X% of Y?

This is the most common percentage question. Use it to calculate discounts, tips, tax amounts, and more. The formula is straightforward: multiply the percentage by the total value, then divide by 100.

Formula: Result = (X ÷ 100) × Y

Example: A jacket is $120 and is 30% off. The discount is (30 ÷ 100) × 120 = $36. So you pay $84.

Mode 2: X is What Percent of Y?

Use this when you have both values and want to express the relationship as a percentage. Common uses: calculating a test score percentage, finding what share one number is of a total, or determining what fraction of a budget you've spent.

Formula: Result = (X ÷ Y) × 100

Example: You scored 42 out of 50 on an exam. Your percentage is (42 ÷ 50) × 100 = 84%.

Mode 3: Percentage Change

Percentage change tells you how much a value has increased or decreased relative to its original value. A positive result is an increase; a negative result is a decrease. Useful for tracking price changes, portfolio returns, weight loss, and business metrics.

Formula: Change = ((New Value − Old Value) ÷ Old Value) × 100

Example: Your salary went from $65,000 to $72,000. The increase is ((72,000 − 65,000) ÷ 65,000) × 100 = 10.77%.

Mode 4: Reverse Percentage (X is Y% of What?)

Sometimes you know the final value and the percentage, but need to work backward to find the original. This is especially useful in retail (if an item is $60 after a 25% discount, what was the original price?) or in tax calculations.

Formula: Original = X ÷ (Y ÷ 100)

Example: After a 25% discount, a shirt costs $45. The original price was $45 ÷ 0.25... wait, that gives the discount amount. Actually: $45 = 75% of original, so original = $45 ÷ 0.75 = $60.

Common Percentage Mistakes to Avoid

Adding percentages directly: If a price increases by 10% then decreases by 10%, the result is NOT the same as the original. A $100 item that goes up 10% is $110. Down 10% from $110 is $99 — not $100. Percentages are multiplicative, not additive.
Confusing percentage and percentage points: If an interest rate goes from 3% to 4%, it increased by 1 percentage point — but by 33.3% in percentage terms. These are different things.
Tipping on the wrong base: Always tip on the pre-tax subtotal, not the post-tax total (unless you prefer to). The difference is small but proper to know.

Frequently Asked Questions

How do I calculate a percentage in my head?

Here are quick mental math tricks: For 10%, move the decimal one place left ($85 → $8.50). For 20%, double the 10% amount. For 5%, halve the 10% amount. For 15% tip, find 10% then add half of that. For 25%, divide by 4. These shortcuts handle most real-world scenarios without a calculator.

What's the difference between percent increase and percentage points?

A percentage point is an absolute difference between two percentages. If an interest rate goes from 2% to 5%, that's a 3 percentage point increase but a 150% increase in rate. Always clarify which is being discussed, as the two are often confused in financial reporting and news.

How do I calculate tax on a purchase?

Multiply the price by the tax rate expressed as a decimal. For a $50 item with 8.5% sales tax: $50 × 0.085 = $4.25 tax, totaling $54.25. Or use our Mode 1 — enter 8.5% and 50 to get the tax amount instantly.

📊 Percentage Calculator