Percentage Calculator

The Percentage Calculator is a versatile mathematical tool that handles the three most common types of percentage calculations encountered in everyday life, business, and academic work. Percentages are one of the most frequently used mathematical concepts, appearing in contexts ranging from shopping discounts and restaurant tips to investment returns, tax rates, statistical analysis, and scientific measurements. Despite their ubiquity, percentage calculations are a common source of errors — studies show that a significant portion of adults struggle with percentage problems, particularly percentage change calculations where the direction of comparison matters. This calculator eliminates errors by providing three dedicated modes: finding a percentage of a value (e.g., what is 15% of 200?), determining what percentage one value is of another (e.g., 30 is what percent of 200?), and calculating the percentage change between two values (e.g., from 100 to 130 is what percentage increase?). Each mode handles the arithmetic automatically, including proper treatment of negative values, zero values, and decimal results. Whether you are calculating a sale discount, figuring out a tip, analyzing year-over-year revenue growth, computing a grade percentage, or determining the markup on a product, this calculator provides instant, accurate results.

The calculator offers three tabs, each designed for a specific type of percentage problem: Tab 1 — Percent of Value: Use this when you know a percentage and a base value and need to find the result. Enter the percentage in the first field and the value in the second field. For example, to find 20% of 350, enter 20 and 350. Common uses: calculating discounts (what is 30% off 89,000 KRW?), tips (what is 18% of the bill?), tax amounts (what is 10% VAT on this price?), and commission (what is 5% of the sale price?). Tab 2 — What Percent: Use this when you have two values and need to determine what percentage the first is of the second. Enter the part in the first field and the whole in the second field. For example, if you scored 42 out of 50 on a test, enter 42 and 50 to find that your score is 84%. Common uses: calculating exam scores, determining what portion of a budget was spent, finding the ratio of two quantities, and computing market share. Tab 3 — Percent Change: Use this when you have an original value and a new value and want to know the percentage increase or decrease. Enter the original (from) value first and the new (to) value second. For example, if a stock went from 50,000 to 65,000, enter 50000 and 65000 to find a 30% increase. Common uses: investment returns, price changes, population growth, and year-over-year comparisons. All calculations are performed automatically as you type, with results displayed instantly below the input fields.

Each mode uses a specific formula: Mode 1 — Percent of Value: Result = Value x (Percentage / 100) Example: 15% of 200 = 200 x (15/100) = 200 x 0.15 = 30 Example: 7.5% of 1,200 = 1,200 x 0.075 = 90 Example: 120% of 50 = 50 x 1.20 = 60 (percentages over 100% are valid) Mode 2 — What Percent: Percentage = (Part / Whole) x 100 Example: 30 is what % of 200? = (30/200) x 100 = 15% Example: 75 is what % of 60? = (75/60) x 100 = 125% (the part can exceed the whole) Example: 3 is what % of 8? = (3/8) x 100 = 37.5% Mode 3 — Percent Change: Percentage Change = ((New Value - Original Value) / |Original Value|) x 100 Example: From 100 to 130 = ((130-100)/100) x 100 = 30% increase Example: From 200 to 150 = ((150-200)/200) x 100 = -25% decrease Example: From 80 to 100 = ((100-80)/80) x 100 = 25% increase Important notes on Percent Change: - The denominator uses the absolute value of the original value - A positive result indicates an increase; a negative result indicates a decrease - The calculation is undefined when the original value is zero (division by zero) - Percent change is NOT symmetric: going from 100 to 200 is +100%, but going from 200 to 100 is -50% - This asymmetry is a common source of confusion and errors in business reporting

The Commutative Property of Percentages: A useful mental math trick is that x% of y equals y% of x. So 8% of 50 is the same as 50% of 8, which is obviously 4. This can make many calculations much easier in your head: 4% of 75 = 75% of 4 = 3. Use this trick when one arrangement is easier to compute mentally than the other. Percentage Change Direction Matters: One of the most common percentage mistakes is assuming that a 50% increase followed by a 50% decrease returns to the original value. It does not: 100 increased by 50% = 150, then 150 decreased by 50% = 75 (not 100). The correct reverse is always a different percentage. A 50% increase requires a 33.3% decrease to return to the original value. Similarly, a 20% decrease requires a 25% increase to recover. Always be mindful of which value is the base (denominator) in your calculation. Percentage Points vs. Percentages: In media and business reporting, there is a critical distinction between percentage points and percentages. If an interest rate goes from 5% to 7%, it increased by 2 percentage points but by 40 percent (a 40% relative increase). Confusing these two can lead to dramatically wrong conclusions. This calculator computes percent change (relative change). For percentage point changes, simply subtract the two percentages directly. Chaining Percentages: When applying multiple percentage changes sequentially, you cannot simply add or subtract the percentages. A 10% increase followed by a 20% increase is not a 30% increase — it is a 32% increase (1.10 x 1.20 = 1.32). Conversely, a 10% discount followed by a 20% discount gives a total discount of 28%, not 30% (1 - 0.90 x 0.80 = 0.28). Decimal Precision: For financial calculations, be careful about how many decimal places you use. Rounding percentages prematurely can compound errors, especially in multi-step calculations. This calculator shows results to two decimal places, which is sufficient for most practical purposes. Common Business Applications: Gross margin = ((Revenue - Cost) / Revenue) x 100. Markup = ((Selling Price - Cost) / Cost) x 100. Note that margin and markup are different even though they are related — a 50% markup corresponds to a 33.3% margin.