Length Conversions

Length conversions are the most frequently needed and form the foundation for area, volume, and speed calculations. The relationship between metric and imperial length units should be second nature to engineers working across systems.

  • 1 meter (m) = 3.28084 feet (ft) = 39.3701 inches (in)
  • 1 foot (ft) = 0.3048 meters (m) = 12 inches (in)
  • 1 inch (in) = 2.54 centimeters (cm) = 25.4 millimeters (mm)
  • 1 yard (yd) = 0.9144 meters (m) = 3 feet (ft)
  • 1 mile (mi) = 1.60934 kilometers (km) = 1,760 yards (yd)
  • 1 kilometer (km) = 0.621371 miles (mi) = 1,000 meters (m)
  • 1 centimeter (cm) = 10 millimeters (mm) = 0.393701 inches (in)
  • 1 millimeter (mm) = 0.0393701 inches (in)

For quick mental estimation: 1 meter is slightly longer than 3 feet (actually 3.28 ft). 1 inch is exactly 25.4 mm by definition. 1 mile is approximately 1.6 km. These approximate relationships are useful for field estimates, though precise work always requires exact values.

Engineering drawings frequently mix units. American manufacturers may dimension in inches while international collaborators use millimeters. Converting between them—particularly for fits and tolerances—requires careful attention to significant figures and rounding.

Area Conversions

Area conversions follow from length conversions but with squared factors. A square meter is (100 cm)² = 10,000 cm², not 100 times anything. Forgetting this squared relationship is a common source of errors.

  • 1 square meter (m²) = 10.7639 square feet (ft²) = 1,550.00 square inches (in²)
  • 1 square foot (ft²) = 0.092903 square meters (m²) = 144 square inches (in²)
  • 1 square inch (in²) = 6.4516 square centimeters (cm²) = 645.16 square millimeters (mm²)
  • 1 acre = 0.404686 hectares (ha) = 4,046.86 square meters (m²)
  • 1 hectare (ha) = 2.47105 acres = 10,000 square meters (m²)
  • 1 square kilometer (km²) = 0.386102 square miles (mi²) = 100 hectares (ha)
  • 1 square mile (mi²) = 2.58999 square kilometers (km²) = 640 acres

The hectare is particularly useful in engineering for moderately large land areas—easier to work with than acres or square kilometers. A soccer field is roughly a hectare in area, providing a useful visual reference.

Volume Conversions

Volume conversions require cubed factors, compounding the squared factor of area conversions. Additionally, volume units vary significantly between systems, with US and UK gallons differing substantially.

  • 1 liter (L) = 0.264172 US gallons (gal) = 0.219969 UK gallons (gal UK)
  • 1 US gallon (gal) = 3.78541 liters (L) = 231 cubic inches (in³)
  • 1 UK gallon (gal UK) = 4.54609 liters (L) = 1.20095 US gallons
  • 1 cubic meter (m³) = 264.172 US gallons = 35.3147 cubic feet (ft³)
  • 1 cubic foot (ft³) = 28.3168 liters (L) = 7.48052 US gallons
  • 1 cubic inch (in³) = 16.3871 milliliters (mL) = 0.0163871 liters (L)
  • 1 milliliter (mL) = 1 cubic centimeter (cm³) = 0.033814 fluid ounces (US)

Note the US/UK gallon distinction: UK gallons are approximately 20% larger than US gallons. When comparing fuel economy figures between the UK and US, remember that "miles per gallon" means significantly different things. The UK figure will always appear higher for equivalent fuel consumption.

Mass Conversions

Mass and weight are technically different—mass measures matter content while weight measures gravitational force—but in everyday Earth usage, the terms are used interchangeably for convenience. Engineering work involving non-Earth environments requires careful attention to this distinction.

  • 1 kilogram (kg) = 2.20462 pounds (lb) = 35.274 ounces (oz)
  • 1 pound (lb) = 0.453592 kilograms (kg) = 16 ounces (oz)
  • 1 ounce (oz) = 28.3495 grams (g)
  • 1 gram (g) = 0.035274 ounces (oz) = 1,000 milligrams (mg)
  • 1 metric ton (t) = 1,000 kilograms (kg) = 2,204.62 pounds (lb)
  • 1 short ton (US) = 2,000 pounds (lb) = 907.185 kilograms (kg)
  • 1 long ton (UK) = 2,240 pounds (lb) = 1,016.05 kilograms (kg)

The "ton" is ambiguous across contexts. In the US, "ton" typically means short ton (2,000 lb). In the UK, "ton" typically means long ton (2,240 lb). In international and scientific contexts, "ton" means metric ton (1,000 kg). Always clarify which ton is intended.

Temperature Conversions

Temperature conversions are unique among unit conversions because the different scales have different zero points, not just different scaling factors. This means you must add or subtract the offset between scales, not just multiply.

  • Celsius to Fahrenheit: °F = (°C × 9/5) + 32 or °F = (°C × 1.8) + 32
  • Fahrenheit to Celsius: °C = (°F - 32) × 5/9 or °C = (°F - 32) / 1.8
  • Celsius to Kelvin: K = °C + 273.15
  • Kelvin to Celsius: °C = K - 273.15
  • Fahrenheit to Kelvin: K = ((°F - 32) × 5/9) + 273.15
  • Kelvin to Fahrenheit: °F = ((K - 273.15) × 9/5) + 32

Key reference points to memorize: water freezes at 0°C (32°F), water boils at 100°C (212°F), normal human body temperature is 37°C (98.6°F), and absolute zero is -273.15°C (0 K).

For rough approximations, useful shortcuts include: every 5°C ≈ 9°F, every 10°C ≈ 18°F. Body temperature is approximately 37°C ≈ 100°F (useful for quick sanity checks).

Speed Conversions

Speed combines length and time units, making conversions require both factors. Common speed units include meters per second (m/s), kilometers per hour (km/h), miles per hour (mph), knots (nautical miles per hour), and feet per second (ft/s).

  • 1 m/s = 3.6 km/h = 3.28084 ft/s = 2.23694 mph
  • 1 km/h = 0.277778 m/s = 0.911344 ft/s = 0.621371 mph
  • 1 mph = 1.60934 km/h = 0.44704 m/s = 1.46667 ft/s
  • 1 knot = 1 nautical mile/hour = 1.852 km/h = 1.68781 ft/s = 1.15078 mph
  • 1 ft/s = 0.3048 m/s = 0.681818 mph = 1.09728 km/h

Speed conversion is particularly important in transportation engineering. Road design uses mph in the US and km/h elsewhere. Aircraft speed is often expressed in knots for navigation. Maritime navigation exclusively uses nautical miles and knots. Engineers in international projects must be fluent in all of these.

Pressure Conversions

Pressure (force per unit area) appears throughout mechanical, civil, and chemical engineering. Common units include Pascals (Pa), bars, pounds per square inch (psi), atmospheres (atm), and millimeters of mercury (mmHg).

  • 1 Pascal (Pa) = 1 N/m² = 0.000145038 psi
  • 1 bar = 100,000 Pa = 14.5038 psi = 0.986923 atm
  • 1 psi = 6,894.76 Pa = 0.0689476 bar = 0.068046 atm
  • 1 atm = 101,325 Pa = 1.01325 bar = 14.696 psi
  • 1 mmHg (Torr) = 133.322 Pa = 0.0193368 psi
  • 1 kPa = 1,000 Pa = 0.145038 psi = 0.01 bar
  • 1 MPa = 1,000,000 Pa = 145.038 psi = 10 bar

Atmospheric pressure at sea level is approximately 101.325 kPa (14.7 psi). This standard reference point is essential for barometric measurements, altimeter settings, and vacuum system design.

Energy Conversions

Energy appears in many forms—mechanical work, heat, electrical energy, chemical potential—and the conversion factors between these forms are fundamental to engineering analysis.

  • 1 Joule (J) = 0.239006 calories (cal) = 0.000277778 watt-hours (Wh)
  • 1 calorie (cal) = 4.184 J (thermochemical calorie; food calories = 1,000 cal = 4.184 kJ)
  • 1 kilowatt-hour (kWh) = 3,600,000 J = 860.421 kcal
  • 1 BTU (British Thermal Unit) = 1,055.06 J = 0.293071 Wh = 252 cal
  • 1 electronvolt (eV) = 1.60218 × 10⁻¹⁹ J
  • 1 foot-pound (ft·lbf) = 1.35582 J
  • 1 erg = 10⁻⁷ J (CGS unit, still seen in physics)

Electrical energy billing uses kilowatt-hours, making this a practical unit for energy economics. The conversion to joules—3.6 MJ per kWh—enables comparison with other energy forms. Fuel energy content is often expressed in BTU per unit mass or volume.

Heat transfer and thermodynamics frequently use calories and BTU, which are heat-specific energy units. The mechanical equivalent of heat—established by James Joule in the 19th century—connects mechanical work (foot-pounds) to heat energy (BTU or calories).

Tips for Memorizing and Using These Formulas

Rather than memorizing every formula, memorize the core relationships and derive the rest. For length: 1 in = 2.54 cm by definition (making metric-imperial conversions exact). From there, square for area and cube for volume. For speed, combine length and time conversions.

Build a personal reference card with the formulas you use most. As you repeatedly solve problems using specific conversions, those formulas become internalized naturally. Don't try to memorize everything at once—prioritize by your field and typical applications.

When precision matters, use exact definitions rather than approximations. The definition 1 in = 2.54 cm is exact by international agreement. Using 2.54 instead of 3.28 for meter-to-foot conversion makes a meaningful difference in precise engineering work.

Digital conversion tools like our conversion calculator eliminate memorization burden and reduce errors. These tools handle complex multi-step conversions, provide consistent precision, and can be referenced whenever you're unsure of a conversion factor.