How Unit Conversion Works: The Factor Method

The Factor Method (Dimensional Analysis)

Unit conversion is multiplication by a conversion factor — a fraction equal to 1, where the numerator and denominator are the same quantity expressed in different units. The original unit cancels, leaving the target unit.

Example: Convert 5 miles to kilometers. The exact conversion factor is 1 mile = 1.609344 km.

5 miles × (1.609344 km ÷ 1 mile) = 8.04672 km

Exact Conversion Factors

The following conversion factors are exact values as defined by international standards bodies (NIST, BIPM). They are not approximations.

Source: NIST Special Publication 811 (2008 Edition), Guide for the Use of the International System of Units.

Temperature: Why It Is Different

Temperature conversion is not simple multiplication because the Celsius and Fahrenheit scales have different zero points. Celsius 0° is the freezing point of water; Fahrenheit 32° is the same temperature. This offset must be accounted for before scaling.

• Body temperature: 37°C = (37 × 9/5) + 32 = 66.6 + 32 = 98.6°F
• Boiling point of water: 100°C = (100 × 9/5) + 32 = 180 + 32 = 212°F
• Room temperature: 72°F = (72 − 32) × 5/9 = 40 × 5/9 = 22.2°C

US vs. Imperial Units

The US customary system and the British imperial system are similar but not identical. The most significant difference is in volume:

• 1 US gallon = 3.785 liters
• 1 UK (imperial) gallon = 4.546 liters
• 1 US fluid ounce = 29.57 mL; 1 UK fluid ounce = 28.41 mL

This distinction matters for fuel economy comparisons: a car rated at 30 mpg in the US gets fewer miles per gallon than one rated 30 mpg in the UK, because the UK gallon is larger.