Unit Conversions Quick Reference

SI Base Units

| Quantity | Unit | Symbol | |----------|------|--------| | Length | meter | m | | Mass | kilogram | kg | | Time | second | s | | Electric current | ampere | A | | Temperature | kelvin | K | | Amount of substance | mole | mol | | Luminous intensity | candela | cd |

Length Conversions

Metric System

• 1 kilometer (km) = 1,000 meters
• 1 meter (m) = 100 centimeters = 1,000 millimeters
• 1 centimeter (cm) = 10 millimeters

Imperial System

• 1 mile = 5,280 feet = 1,760 yards
• 1 yard = 3 feet = 36 inches
• 1 foot = 12 inches

Metric ↔ Imperial

• 1 meter = 3.28084 feet = 39.3701 inches
• 1 kilometer = 0.621371 miles
• 1 inch = 2.54 centimeters
• 1 foot = 0.3048 meters
• 1 mile = 1.60934 kilometers

Example: Convert 5 miles to kilometers $5 \text{ miles} \times 1.60934 = 8.0467 \text{ km}$

Mass/Weight Conversions

Metric System

• 1 kilogram (kg) = 1,000 grams
• 1 gram (g) = 1,000 milligrams
• 1 metric ton = 1,000 kilograms

Imperial System

• 1 pound (lb) = 16 ounces
• 1 ton (US) = 2,000 pounds

Metric ↔ Imperial

• 1 kilogram = 2.20462 pounds
• 1 pound = 0.453592 kilograms
• 1 ounce = 28.3495 grams

Example: Convert 150 pounds to kilograms $150 \text{ lbs} \times 0.453592 = 68.04 \text{ kg}$

Temperature Conversions

Formulas

• Celsius to Fahrenheit: $F = \frac{9}{5}C + 32$
• Fahrenheit to Celsius: $C = \frac{5}{9}(F - 32)$
• Celsius to Kelvin: $K = C + 273.15$
• Kelvin to Celsius: $C = K - 273.15$

Reference Points

| Description | Celsius | Fahrenheit | Kelvin | |-------------|---------|------------|--------| | Absolute Zero | -273.15°C | -459.67°F | 0 K | | Water Freezing | 0°C | 32°F | 273.15 K | | Room Temperature | ~20°C | ~68°F | ~293 K | | Body Temperature | 37°C | 98.6°F | 310.15 K | | Water Boiling | 100°C | 212°F | 373.15 K |

Example: Convert 25°C to Fahrenheit $F = \frac{9}{5} \times 25 + 32 = 45 + 32 = 77°F$

Volume Conversions

Metric System

• 1 liter (L) = 1,000 milliliters (mL)
• 1 cubic meter (m³) = 1,000 liters

Imperial System

• 1 gallon (US) = 4 quarts = 8 pints = 16 cups
• 1 quart = 2 pints = 4 cups
• 1 pint = 2 cups = 16 fluid ounces

Metric ↔ Imperial

• 1 liter = 0.264172 gallons (US) = 1.05669 quarts
• 1 gallon (US) = 3.78541 liters
• 1 fluid ounce = 29.5735 milliliters

Example: Convert 2 gallons to liters $2 \text{ gallons} \times 3.78541 = 7.57 \text{ L}$

Area Conversions

Metric System

• 1 square kilometer (km²) = 1,000,000 m² = 100 hectares
• 1 hectare = 10,000 m²
• 1 square meter (m²) = 10,000 cm²

Imperial System

• 1 square mile = 640 acres
• 1 acre = 43,560 square feet
• 1 square yard = 9 square feet

Metric ↔ Imperial

• 1 square meter = 10.7639 square feet
• 1 square kilometer = 0.386102 square miles
• 1 hectare = 2.47105 acres

Speed Conversions

Common Conversions

• 1 m/s = 3.6 km/h = 2.237 mph
• 1 km/h = 0.277778 m/s = 0.621371 mph
• 1 mph = 1.60934 km/h = 0.44704 m/s

Example: Convert 60 mph to km/h $60 \text{ mph} \times 1.60934 = 96.56 \text{ km/h}$

Energy Conversions

Common Units

• 1 joule (J) = 1 N⋅m = 1 W⋅s
• 1 calorie = 4.184 joules
• 1 kilowatt-hour (kWh) = 3.6 × 10⁶ joules
• 1 BTU = 1,055 joules

Pressure Conversions

Common Units

• 1 pascal (Pa) = 1 N/m²
• 1 atmosphere (atm) = 101,325 Pa = 760 mmHg
• 1 bar = 100,000 Pa = 0.987 atm
• 1 psi = 6,895 Pa

Energy Conversions

Common Energy Units

• 1 joule (J) = 1 N⋅m = 1 W⋅s (SI base unit)
• 1 kilojoule (kJ) = 1,000 joules
• 1 calorie (cal) = 4.184 joules
• 1 kilocalorie (kcal) = 4,184 joules = 1.163 Wh
• 1 watt-hour (Wh) = 3,600 joules
• 1 kilowatt-hour (kWh) = 3.6 × 10⁶ joules
• 1 BTU = 1,055 joules
• 1 electron volt (eV) = 1.602 × 10⁻¹⁹ joules

Energy Scale Examples

• Chemical bond energy: ~1-10 eV
• Food calorie: 1 kcal = 4,184 J
• Household electricity: measured in kWh
• Gasoline energy density: ~44 MJ/kg

Example: Convert 1 kWh to calories $1 \text{ kWh} = 3.6 \times 10^6 \text{ J} \div 4.184 = 860,421 \text{ cal}$

Space-Time Distance Conversions

Astronomical Units

• 1 Astronomical Unit (AU) = 149,597,870.7 km (Earth-Sun distance)
• 1 light-year (ly) = 9.461 × 10¹⁵ m = 63,241 AU
• 1 parsec (pc) = 3.086 × 10¹⁶ m = 3.26 ly = 206,265 AU
• 1 light-second = 299,792,458 m
• 1 light-minute = 17,987,547,480 m

Cosmic Scale Examples

• Earth to Moon: ~1.3 light-seconds
• Earth to Sun: 1 AU = 8.3 light-minutes
• Solar System diameter: ~100 AU
• Nearest star: 4.24 light-years
• Milky Way diameter: ~100,000 light-years
• Nearest galaxy: 2.5 million light-years

Example: Convert 1 parsec to light-years $1 \text{ pc} = 3.26 \text{ ly}$

Quick Conversion Tips

1. Temperature: Remember 0°C = 32°F and 100°C = 212°F
2. Length: 1 inch ≈ 2.5 cm, 1 foot ≈ 30 cm, 1 meter ≈ 3.3 feet
3. Mass: 1 kg ≈ 2.2 lbs, 1 lb ≈ 450 g
4. Volume: 1 liter ≈ 1 quart, 1 gallon ≈ 4 liters
5. Speed: 100 km/h ≈ 60 mph
6. Energy: 1 kWh ≈ 860,000 cal, 1 BTU ≈ 1,055 J
7. Astronomy: 1 ly ≈ 63,000 AU, 1 pc ≈ 3.26 ly