Math & Conversion Calculators

Percentage increase formula: ((New Value - Old Value) / Old Value) × 100. Example: price increases from $50 to $65. Calculation: ((65 - 50) / 50) × 100 = 30% increase. Common uses: salary raises, price changes, sales growth. Remember: if the new value is smaller, you have a percentage decrease instead. Our percentage calculator handles both increases and decreases automatically, showing you the exact change and final amount.

Percentage is a proportion out of 100 (50% means 50 out of 100). Percentile is a position in a ranked dataset (50th percentile means you're above 50% of the group). Example: scoring 85% on a test means you got 85 out of 100 points. Being in the 85th percentile means you scored better than 85% of test-takers. Percentages measure performance; percentiles measure rank. Used differently in tests, statistics, and growth charts.

Divide the numerator (top number) by the denominator (bottom number). Examples: 1/4 = 1 ÷ 4 = 0.25, 3/8 = 3 ÷ 8 = 0.375, 2/3 = 2 ÷ 3 = 0.666... (repeating). For mixed numbers like 2 1/2, convert the fraction part (1/2 = 0.5) and add to the whole number (2 + 0.5 = 2.5). Our fraction calculator handles all types including complex fractions, and can convert to percentages too.

Essential conversions: Length: 1 inch = 2.54 cm, 1 foot = 30.48 cm, 1 mile = 1.609 km. Weight: 1 ounce = 28.35 g, 1 pound = 0.453 kg, 1 kg = 2.205 lbs. Volume: 1 cup = 237 ml, 1 pint = 473 ml, 1 gallon = 3.785 L. Temperature: °C = (°F - 32) × 5/9, °F = (°C × 9/5) + 32. Our conversion calculators handle all these plus specialty units for cooking, construction, and science.

Percentage change formula: ((New - Old) / |Old|) × 100. Positive result = increase, negative = decrease. Example 1: Stock goes from $100 to $120: ((120-100)/100) × 100 = +20%. Example 2: Price drops from $80 to $60: ((60-80)/80) × 100 = -25%. Used for tracking: stock performance, weight loss, sales trends, economic indicators. Use absolute value of old value in denominator to handle negative starting numbers correctly.

Quality conversion calculators are 99.99% accurate—they use exact conversion factors defined by international standards (NIST, SI units). Errors come from: rounding (we calculate to 6-10 decimal places), input mistakes, or outdated conversion factors. For critical applications (medical, engineering, legal), verify with multiple sources. Our calculators use official conversion factors updated annually and show full precision. For everyday use (cooking, DIY), accuracy is more than sufficient.

Key conversions: Distance: 1 inch = 2.54 cm (exact), 1 meter = 39.37 inches. Weight: 1 kg = 2.2046 lbs, 1 oz = 28.35 g. Volume: 1 L = 33.814 fl oz, 1 gallon = 3.785 L. Tip: Learn approximate mental math: 1 kg ≈ 2.2 lbs, 1 m ≈ 3.3 feet, 1 L ≈ 1 quart (close enough). For construction: 1 inch = 25mm (close enough). For precision work, use our conversion calculator with exact factors.

To find X% of a number: (X / 100) × Number. Examples: 20% of 150 = (20/100) × 150 = 30. 75% of 80 = (75/100) × 80 = 60. Shortcut: Move decimal two places left, then multiply. 15% = 0.15, so 15% of 200 = 0.15 × 200 = 30. For tips: 20% = divide by 5, 15% = divide by 10 then add half, 10% = move decimal left once. Our percentage calculator handles all variations instantly.

Ratio compares two quantities (3:2 means 3 units of A per 2 units of B). Proportion states two ratios are equal (3:2 = 9:6). To solve proportions: cross-multiply. Example: If 3 items cost $15, how much for 7 items? Set up: 3/15 = 7/x. Cross-multiply: 3x = 105, x = $35. Used in: recipe scaling, mixture problems, map scales, gear ratios. Our ratio calculator handles scaling up/down and finds missing values in proportions.

Choose units based on context: Tiny measurements: millimeters (screws, electronics). Small: centimeters/inches (books, phones). Medium: meters/feet (room dimensions, height). Large: kilometers/miles (travel distance). Weight: grams (food, jewelry), pounds (body weight, groceries), tons (vehicles, cargo). Volume: milliliters (medicine), cups (cooking), liters (beverages), gallons (fuel). Use same units in calculations—don't mix inches and centimeters. Convert everything to one system first for accuracy.