What Is a Percentage?
A percentage is a dimensionless ratio expressing a fraction of 100. The word comes from Latin 'per centum', meaning 'by the hundred'. 25% represents 25 parts out of 100, or the decimal fraction 0.25.
Quickly calculate percentages, percentage change, discounts, increases, decreases and reverse percentages with accurate results.
X ÷ 100 × Y25% of 200 = 25 ÷ 100 × 200 = 50(Part ÷ Whole) × 10025 of 200 = (25 ÷ 200) × 100 = 12.5%((New − Original) ÷ Original) × 100100 to 125 = ((125 − 100) ÷ 100) × 100 = +25%|A − B| ÷ ((A + B) ÷ 2) × 100|100 − 120| ÷ 110 × 100 = 18.18%Original × (1 + Percentage ÷ 100)100 + 20% = 100 × 1.20 = 120Original × (1 − Percentage ÷ 100)100 − 20% = 100 × 0.80 = 80Final ÷ (1 − Discount ÷ 100)$80 with 20% off = 80 ÷ 0.80 = $100Final ÷ (1 + Increase ÷ 100)$120 with 20% inc = 120 ÷ 1.20 = $100(Selling − Cost) ÷ Cost × 100Cost $100, Sell $125 = (25 ÷ 100) × 100 = 25%Bill × (Tip % ÷ 100)$100 bill with 15% tip = $15 tip ($115 total)Learn how to calculate percentages, percentage increases, percentage decreases, discounts, percentage changes and other common percentage problems.
A percentage is a dimensionless ratio expressing a fraction of 100. The word comes from Latin 'per centum', meaning 'by the hundred'. 25% represents 25 parts out of 100, or the decimal fraction 0.25.
To calculate what percentage one number is of another, divide the part by the total whole and multiply by 100: (Part ÷ Whole) × 100. For example, 15 out of 60 is (15 ÷ 60) × 100 = 25%.
Multiply the total number by the percentage converted to decimal: X ÷ 100 × Y. To find 20% of $450, calculate 0.20 × 450 = $90.
Treat the comparison as a fraction. If you scored 42 points out of 50 on an exam, divide 42 by 50 to get 0.84, then multiply by 100 to get 84%.
To calculate percentage increase, subtract the original value from the new value, divide by the original, and multiply by 100: ((New − Original) ÷ Original) × 100.
Calculate the reduction amount, divide it by the original starting value, and multiply by 100. If traffic drops from 1,000 visitors to 800, the decrease is ((800 − 1000) ÷ 1000) × 100 = −20%.
Percentage change conveys chronological growth or contraction. A positive result denotes an increase (+15%), whereas a negative result denotes a contraction (−10%).
Used when two values have no chronological order: divide the absolute difference by their arithmetic mean: |A − B| ÷ ((A + B) ÷ 2) × 100.
Multiply the sticker price by the discount decimal. A 30% discount on a $120 jacket saves $36 (120 × 0.30), leaving a final sale price of $84.
Divide the sale price by (1 − discount rate): Original = Sale ÷ (1 − Discount ÷ 100). If an item costs $60 after a 25% discount, original price was 60 ÷ 0.75 = $80.
Markup is the percentage added to wholesale cost to determine retail price: Cost × (1 + Markup ÷ 100). An item costing $50 with 40% markup sells for $70.
Profit percentage compares profit to cost: (Selling Price − Cost) ÷ Cost × 100. Buying at $80 and selling at $100 yields a 25% profit.
When selling below cost, calculate loss divided by cost: (Cost − Selling) ÷ Cost × 100. Buying at $100 and liquidating at $70 yields a 30% loss.
Multiply the pre-tax or post-tax meal bill by the desired gratuity percentage (15%, 18%, or 20%), then divide the total bill among diners to split costs.
Used in budgeting: divide an expenditure category by your total income and multiply by 100 to determine its percentage share of the total pie.
Subtract the used portion from the total: Remaining % = (Total − Used) ÷ Total × 100. If you used 45 GB of a 100 GB plan, 55% remains.
A jump from 10% to 15% is an increase of 5 percentage points, but a 50% relative increase. Confusing these two concepts is one of the most common statistical errors.
Divide total points earned across all questions by the total maximum possible score on the exam and multiply by 100.
Weighted course grades multiply each assignment category score by its syllabus weight percentage, summing the products to compute the final letter grade.
Subtract your old salary from your new salary, divide by the old salary, and multiply by 100. A raise from $60,000 to $66,000 represents a 10% salary increase.
Monitor inflation and supplier adjustments: calculate ((New Price − Old Price) ÷ Old Price) × 100 to track price volatility.
Determine effective tax rates: divide total tax paid by gross taxable income and multiply by 100 to evaluate your true tax bracket impact.
Reverse percentages invert forward arithmetic. If a final price already includes 8% sales tax, divide by 1.08 to find the original pre-tax price.
Compare baseline benchmarks directly: determine the quotient of the two numbers and format the resulting ratio as a standard percentage.
Common mistakes include confusing percentage points with percent change, adding successive discounts directly (20% off + 20% off is not 40% off), and dividing by the wrong denominator.
A percentage is a number or ratio expressed as a fraction of 100. It is denoted using the percent sign '%' and represents a portion of a whole.
Divide the part by the total whole and multiply by 100. For example, 25 out of 200 is (25 ÷ 200) × 100 = 12.5%.
To find 10% of any number, move the decimal point one position to the left, or multiply the number by 0.10. For example, 10% of 250 is 25.
Multiply the number by 0.20 or calculate 10% and double it. For example, 20% of 500 is 100.
Divide the smaller number (or part) by the total number and multiply by 100. Formula: (Value ÷ Total) × 100.
Subtract the original value from the new value, divide by the original value, and multiply by 100. Formula: ((New − Original) ÷ Original) × 100.
Subtract the new value from the original value, divide by the original value, and multiply by 100.
Percentage change compares an old value to a new value chronologically. Percentage difference compares two values without a chronological order by dividing the absolute difference by their average.
Multiply the original price by the discount percentage divided by 100 to find your savings, then subtract that amount from the original price.
Divide the discounted price by (1 − discount percentage ÷ 100). For example, $80 after a 20% discount is $80 ÷ 0.80 = $100.
Multiply the wholesale cost by (1 + markup percentage ÷ 100). For example, a $100 item marked up 25% has a selling price of $125.
Subtract cost price from selling price to get profit, then divide profit by the cost price and multiply by 100.
Subtract selling price from cost price to get loss, then divide loss by the cost price and multiply by 100.
Multiply the bill amount by the tip percentage (e.g., 0.15, 0.18, 0.20) and add the result to the bill to obtain the total amount.
Divide the total marks obtained by the maximum marks possible and multiply by 100. For example, 450 ÷ 500 × 100 = 90%.
Sum the earned points or weighted categories, divide by the total possible points, and multiply by 100.
Percentage points measure the absolute arithmetic difference between two percentages (e.g. 40% to 50% is 10 percentage points), whereas percent change measures relative growth (a 25% relative increase).
Yes. All formulas in this calculator handle decimal inputs and floating point fractions accurately.
Yes. Negative percentages represent reductions, decreases, or financial losses below the original benchmark.
All calculations use standard IEEE-754 double-precision floating-point arithmetic with configurable decimal rounding.
No. All calculations run strictly in your browser. Recent history and favorites are stored only on your device using local storage.
Yes. Once loaded, this page requires no active internet connection or external APIs to calculate.
Calculate percentages, discounts, increases, decreases and more instantly.