Free percentage calculator with three modes — find what percent of a number is, calculate percent change between two values, or compute what percentage one number is of another. Instant discount calculator and percent change tool with no signup needed.
To find X percent of a number, multiply the number by X and divide by 100. To find what percent one number is of another, divide the first by the second and multiply by 100. A percentage simply expresses a value as a fraction of 100.
Three calculation modes in one tool
Percentages appear in nearly every financial and everyday context — retail discounts, sales tax, restaurant tips, investment returns, grade scores, interest rates, and statistical data. This percentage calculator handles all three core calculations in one place. Mode 1 ("What is X% of Y?") finds a percentage of any number — use it for discounts, tax amounts, and tips. Mode 2 ("X is what % of Y?") finds what percentage one number represents of another — useful for test scores, market share calculations, and budget analysis. Mode 3 ("% Change from X to Y") calculates the percentage increase or decrease between two values — critical for understanding price changes, investment returns, and business growth rates.
One of the most commonly confused percentage concepts is the asymmetry of gains and losses. If a stock price drops from $100 to $80, that is a 20% decrease. But to recover from $80 back to $100, you need a 25% increase — not 20%. This asymmetry is why financial advisors emphasize avoiding large losses: a 50% portfolio drop requires a 100% gain just to break even. Similarly, a store advertising "50% off then an additional 20% off" is not giving you 70% off — it's 50% off, then 20% off the reduced price, which equals a 60% total discount. Understanding how percent change and compound discounts work saves real money.
A 30% discount on a $150 item saves $45 — the sale price is $105. To find the discount amount: multiply the original price by the percentage (150 × 0.30 = 45). For stacked discounts, apply them sequentially: 20% off $100 = $80, then 10% off $80 = $72 total (not 70% of $100).
An 8.5% sales tax on a $200 purchase adds $17, bringing the total to $217. Use the percentage calculator to find the exact tax on any amount. Sales tax rates vary from 0% (Delaware, Oregon) to over 10% in some California cities — always verify the rate for your location.
Percent change = (New − Old) / Old × 100. A home value rising from $350,000 to $420,000 is a 20% increase. From $420,000 back to $350,000 is a 16.67% decrease — different percentages for the same dollar amount because the base changed. Direction matters in percent change calculations.
For a 20% tip on an $85 restaurant bill: 20% of $85 = $17 tip, total $102. For 15%, it's $12.75 tip, total $97.75. A quick mental shortcut: find 10% (move the decimal left one place), then double it for 20%, or add half for 15%. Works on any bill amount in seconds.
Percentages express a part relative to a whole of 100, and nearly every practical error with them comes from losing track of which number is the whole. Three distinct questions get muddled: what is X% of Y, X is what percent of Y, and what is the change from X to Y. The third is the trickiest because percentage change is not symmetric — a rise from 80 to 100 is +25%, but the fall back from 100 to 80 is −20%. The base changed, so the percentages cannot match, which is why a stock that drops 50% needs a 100% gain to recover.
Part = (Percent ÷ 100) × WholePercent = (Part ÷ Whole) × 100Change % = ((New − Old) ÷ Old) × 100where:
Assumptions: Percentage change always divides by the OLD value. Percentage-point differences are a separate idea: a rate moving from 4% to 6% has risen 2 percentage points but 50 percent.
A department's budget was $80,000 last year and is $92,000 this year, of which $23,000 is allocated to software.
Result+15% budget growth; software is 25% of the total
To reverse a percentage increase, divide rather than subtract: $92,000 ÷ 1.15 = $80,000. Subtracting 15% from $92,000 gives $78,200, which is wrong by $1,800.