📏 Length Formulas
Base Equation: 1 meter = 3.2808399 feet. 1 inch = exactly 25.4 millimeters (1959 International Yard Agreement). 1 kilometer = 0.6213712 miles.
Unit Conversion Formulas & Mathematical Derivations
Authoritative reference guide to the mathematical equations, thermal constants, and SI base factors powering Omega X.
▣ Area Formulas
Base Equation: 1 square meter = 10.7639 square feet. 1 acre = 0.404686 hectares. 1 hectare = 107,639 square feet.
🧪 Volume Formulas
Base Equation: 1 liter = 0.264172 gallons. 1 gallon = 3.78541 liters. 1 cubic meter = 35.3147 cubic feet.
⚖️ Mass Formulas
Base Equation: 1 kilogram = 2.20462 pounds. 1 pound = 453.592 grams. 1 stone = 6.35029 kilograms.
🌡️ Temperature Formulas
Base Equation: °F = (°C × 9/5) + 32. K = °C + 273.15. °C = (°F − 32) × 5/9.
⏱️ Time Formulas
Base Equation: 1 hour = 60 minutes = 3,600 seconds. 1 day = 24 hours. 1 year = 365.25 days (accounting for leap years).
🚀 Speed Formulas
Base Equation: 1 mph = 1.60934 km/h. 1 knot = 1.15078 mph = 1.852 km/h. Mach 1 ≈ 1,235 km/h at sea level.
🚀 Acceleration Formulas
Base Equation: 1 g = 9.80665 m/s². 1 m/s² ≈ 3.28084 ft/s².
💪 Force Formulas
Base Equation: 1 newton = 0.224809 pound-force. 1 N = 100,000 dynes. 1 kgf = 9.80665 N.
🔵 Pressure Formulas
Base Equation: 1 bar = 14.5038 PSI = 100,000 Pa. 1 atm = 14.696 PSI = 101,325 Pa. 1 mmHg = 133.322 Pa.
⚡ Energy Formulas
Base Equation: 1 calorie = 4.184 joules. 1 kWh = 3,412 BTU = 3.6 × 10⁶ J. 1 eV = 1.602 × 10⁻¹⁹ J.
💡 Power Formulas
Base Equation: 1 horsepower = 745.7 watts = 0.7457 kW. 1 kW = 1.341 horsepower. 1 W = 3.412 BTU/h.
⚡ Electricity Formulas
Base Equation: Ohm's Law: V = I × R. 1 kV = 1,000 V. 1 A = 1,000 mA. 1 kΩ = 1,000 Ω.
🧲 Magnetism Formulas
Base Equation: 1 Tesla (T) = 10,000 Gauss (G). 1 Gauss = 0.0001 Tesla.
〰️ Frequency Formulas
Base Equation: 1 kHz = 1,000 Hz. 1 MHz = 1,000 kHz = 1,000,000 Hz. 1 GHz = 1,000 MHz. 1 RPM = 1/60 Hz.
💾 Data Storage Formulas
Base Equation: 1 byte = 8 bits. 1 KB = 1,024 bytes. 1 MB = 1,024 KB. 1 GB = 1,024 MB. 1 TB = 1,024 GB.
🌐 Data Transfer Formulas
Base Equation: 1 Gbps = 1,000 Mbps = 1,000,000 Kbps. Note: 8 bits (b) = 1 Byte (B).
∡ Angle Formulas
Base Equation: π radians = 180°. 1 radian ≈ 57.2958°. 1° = 60 arcminutes = 3,600 arcseconds.
🔧 Torque Formulas
Base Equation: 1 N·m ≈ 0.737562 lb-ft. 1 lb-ft ≈ 1.355818 N·m.
⛽ Fuel Economy Formulas
Base Equation: L/100km = 235.215 / mpg (US). L/100km = 282.481 / mpg (UK). 1 km/L = 2.35215 mpg (US).
⬡ Density Formulas
Base Equation: 1 g/cm³ = 1,000 kg/m³. 1 kg/m³ ≈ 0.062428 lb/ft³. 1 lb/ft³ ≈ 16.0185 kg/m³.
🍳 Cooking Formulas
Base Equation: 1 US Cup = 16 tablespoons = 48 teaspoons = 240 mL = 8 fl oz. 1 tablespoon = 3 teaspoons = 15 mL.
🧵 Textile Formulas
Base Equation: GSM = weight in grams / area in square meters. Thread count = warp threads + weft threads per square inch.
🌌 Astronomy Formulas
Base Equation: 1 Light Year ≈ 9.461 × 10¹⁵ meters ≈ 63,241.1 AU. 1 Parsec ≈ 3.26156 Light Years ≈ 206,265 AU. 1 Solar Mass ≈ 333,000 Earth Masses.