Percentage Calculator

Multiply the number by the percentage and divide by 100: Result = Number × Percentage ÷ 100. For example, 15% of 200 = 200 × 15 ÷ 100 = 30. Alternatively, convert the percentage to a decimal first (15% = 0.15) and multiply: 200 × 0.15 = 30. Both methods give identical results. Common real-world applications: sales tax (8.25% of $45.00 = $3.71), tips (20% of $72 = $14.40), discounts (30% off $89.99 = $26.997 savings = $62.99 final price), and tax withholding (22% federal bracket on income above $48,475). The formula works with any percentage, including those over 100% — for example, 150% of 60 = 90. For tax-specific percentage calculations, try the Income Tax Calculator.

Multiply the pre-tax bill by the tip percentage. For a $72 bill with an 18% tip: $72 × 0.18 = $12.96. The mental math shortcut: find 10% by moving the decimal ($72 → $7.20), then adjust — for 15%, add half of 10% ($7.20 + $3.60 = $10.80). For 20%, double 10% ($7.20 × 2 = $14.40). US tipping norms: 15–20% for sit-down restaurants, 15–18% for buffets, 10–15% for takeout, $1–2/drink at bars, 18–20% for delivery. Under OBBBA, tip income up to $25,000 is now federally tax-exempt for qualifying workers — meaning a server keeping $20,000/year in tips saves approximately $2,400 in federal tax. Always tip on the pre-tax subtotal, not the total after sales tax. Try our Tip Income Calculator for detailed tip tax analysis.

Divide the sale price by (1 − discount rate as decimal). If an item costs $63 after a 30% discount: $63 ÷ (1 − 0.30) = $63 ÷ 0.70 = $90.00 original price. The common mistake is adding 30% back to $63, which gives $81.90 — wrong, because 30% of $90 ($27) was removed, not 30% of $63 ($18.90). This reverse-percentage concept is critical in business: a retailer who buys at $63 and wants a 30% margin (not markup) must price at $63 ÷ 0.70 = $90. The same math applies to tax-inclusive pricing: if a $108 total includes 8% sales tax, the pre-tax price is $108 ÷ 1.08 = $100 (not $108 − 8% of $108 = $99.36). For financial discount calculations, see the Balance Transfer Calculator to compare interest savings.

Percent describes a ratio relative to a base. Percentage point (pp) describes the arithmetic difference between two percentages. If a tax rate rises from 5% to 8%, it increased by 3 percentage points — but the relative increase is 60% (because 3/5 = 0.60). This distinction matters enormously in finance: the Federal Reserve raising rates by "25 basis points" (0.25 pp) is precise — saying rates "increased 25%" would be wildly misleading if the rate went from 1.00% to 1.25%. Basis points (bps) are the smallest standard unit: 1 bp = 0.01 percentage points = 0.0001. A mortgage rate of 6.75% vs. 6.50% differs by 25 bps, which on a $400,000 30-year loan changes the monthly payment by approximately $67/month ($24,120 over the life of the loan). See how rate differences affect your tax brackets or retirement growth.

Because the base changes between the two operations. Starting at $100: a 50% increase gives $150 (new base). Then 50% of $150 is $75, so a 50% decrease leaves you at $75, not $100. You lost $25 — a net 25% decline. To return from $150 to $100, you need only a 33.3% decrease (because $50/$150 = 33.3%). This asymmetry is critical for investors: if a stock drops 50% (from $100 to $50), it needs a 100% gain to recover — not 50%. A 20% loss requires a 25% gain to break even. A 33% loss needs 50%. The S&P 500 dropped approximately 34% from February to March 2020 (COVID crash) and needed a 51% gain to recover, which took until August 2020. This math explains why avoiding large drawdowns matters more than chasing large gains. Track your portfolio with the 401(k) Calculator.

Use the formula: ((New − Old) ÷ |Old|) × 100. If a stock went from $40 to $52: ((52 − 40) ÷ 40) × 100 = +30%. If it dropped to $34: ((34 − 40) ÷ 40) × 100 = −15%. Use the absolute value of Old to handle cases where the starting value is negative (e.g., a company going from −$2M to +$1M in profit). For year-over-year salary growth: $65,000 to $71,500 = ((71,500 − 65,000) ÷ 65,000) × 100 = +10% raise. The average annual growth rate over multiple years uses a different formula: (Final/Initial)^(1/years) − 1. For example, $50,000 growing to $75,000 over 5 years: (75,000/50,000)^(1/5) − 1 = 8.45% average annual growth. Track salary changes with the Salary Calculator or model long-term growth with the 401(k) Calculator.

APR (Annual Percentage Rate) is the simple annual interest rate without compounding. APY (Annual Percentage Yield) includes the effect of compounding — interest earning interest. The formula: APY = (1 + APR/n)^n − 1, where n is the number of compounding periods per year. A credit card with 24% APR compounded monthly has an APY of 26.82%: (1 + 0.24/12)^12 − 1 = 0.2682. A savings account advertising 5.00% APY compounded daily has an APR of approximately 4.88%. The Truth in Lending Act (TILA) requires lenders to disclose APR, while the Truth in Savings Act requires banks to disclose APY — deliberately making loans look cheaper (lower APR) and deposits look more attractive (higher APY). Use our Balance Transfer Calculator to see how APR affects credit card debt.

Your marginal tax rate is the percentage applied to your last dollar of income — the highest bracket you reach. Your effective (average) tax rate is total tax paid ÷ total income × 100. For example, on $100,000 taxable income in 2026: you pay 10% on the first $11,925, 12% on $11,926–$48,475, and 22% on $48,476–$100,000. Your marginal rate is 22%, but total federal tax is approximately $15,664 — an effective rate of 15.7%. This distinction matters because many people overestimate their tax burden by confusing the two. Getting a raise into a "higher bracket" does NOT mean all your income is taxed at the new rate — only the income above the bracket threshold. See exactly how brackets work with our Income Tax Calculator or Tax Bracket Calculator.

Divide the numerator by the denominator, then multiply by 100. 3/8 = 3 ÷ 8 = 0.375 × 100 = 37.5%. Common fractions to know: 1/3 = 33.33%, 1/4 = 25%, 1/5 = 20%, 1/6 = 16.67%, 1/8 = 12.5%, 2/3 = 66.67%, 3/4 = 75%, 5/6 = 83.33%. To convert back: 37.5% ÷ 100 = 0.375 = 375/1000 = 3/8 (simplify by dividing both by 125). In financial contexts, fractions still appear in bond pricing (Treasury bonds quote in 32nds: 99-16 means 99 and 16/32 = 99.5% of face value) and real estate commissions ("six percent" = 6/100 of sale price). This calculator handles both decimal and fraction inputs.

Markup is the percentage added to cost: (Price − Cost) ÷ Cost × 100. Margin is profit as a percentage of selling price: (Price − Cost) ÷ Price × 100. Example: a product costs $60 and sells for $100. Markup = ($100 − $60) ÷ $60 × 100 = 66.7% markup. Margin = ($100 − $60) ÷ $100 × 100 = 40% margin. Same product, same profit, but very different percentages. This is one of the most common percentage confusions in business. A 50% markup always equals a 33.3% margin. A 100% markup equals a 50% margin. Conversion formula: Margin = Markup ÷ (1 + Markup). Retailers typically think in margin (target 40-60%), while wholesalers often use markup (target 15-25%). Know which your business uses — mixing them up can destroy profitability.

Multiply each value by its weight, sum the products, then divide by the total weight. Example: GPA calculation — Course A (4 credits, grade 3.5), Course B (3 credits, grade 4.0), Course C (3 credits, grade 3.0). Weighted sum = (4×3.5) + (3×4.0) + (3×3.0) = 14 + 12 + 9 = 35. Total credits = 10. Weighted GPA = 35 ÷ 10 = 3.50. Same principle applies to: investment portfolio returns (weight by allocation — 60% stocks at +12% and 40% bonds at +4% = 0.60×12 + 0.40×4 = 8.8% portfolio return), blended interest rates across multiple loans, and tax rate calculations across brackets. Simple averages ignore relative sizes and produce misleading results — a $500K account at 2% matters more than a $5K account at 10%.