Converting Between US Customary and Metric

In everyday life, you will often need to move between US customary units and metric units. A European recipe might list ingredients in grams while your kitchen scale reads ounces. A running app might display your pace in kilometers while road signs show miles. Knowing a handful of key conversion factors and a reliable method for applying them will let you handle any of these situations confidently.

Common Conversion Factors

These approximate conversions are widely used and sufficient for most practical purposes:

Length

Weight / Mass

Volume / Capacity

Dimensional Analysis

Dimensional analysis is a method that uses conversion factors written as fractions to cancel unwanted units and produce the desired units. The key idea is that any conversion factor can be written as a fraction equal to 1:

$\frac{2.54 \text{ cm}}{1 \text{ in}} = 1 \qquad \text{and} \qquad \frac{1 \text{ in}}{2.54 \text{ cm}} = 1$

To convert, multiply by the fraction that places the unwanted unit in the denominator so it cancels out, leaving the desired unit in the numerator.

$\text{starting value} \times \frac{\text{desired unit}}{\text{starting unit}} = \text{converted value}$

Worked Examples

Example 1: Inches to Centimeters

Convert 18 inches to centimeters.

Set up the conversion factor with inches in the denominator:

$18 \text{ in} \times \frac{2.54 \text{ cm}}{1 \text{ in}}$

The inches cancel:

$= 18 \times 2.54 \text{ cm} = 45.72 \text{ cm}$

18 inches = 45.72 cm.

Example 2: Kilometers to Miles

A road sign in Canada says a city is 150 km away. How far is that in miles?

We need to go from km to miles. Since 1 mile = 1.609 km, place km in the denominator:

$150 \text{ km} \times \frac{1 \text{ mi}}{1.609 \text{ km}}$

$= \frac{150}{1.609} \text{ mi} \approx 93.2 \text{ mi}$

150 km is approximately 93.2 miles.

Example 3: Pounds to Kilograms

A suitcase weighs 52 pounds. What is that in kilograms?

$52 \text{ lb} \times \frac{0.454 \text{ kg}}{1 \text{ lb}} = 52 \times 0.454 \text{ kg} = 23.608 \text{ kg}$

Rounding to one decimal place:

52 pounds is approximately 23.6 kg.

Example 4: Liters to Gallons

A car’s fuel tank holds 60 liters. How many gallons is that?

Since 1 gallon = 3.785 liters, place liters in the denominator:

$60 \text{ L} \times \frac{1 \text{ gal}}{3.785 \text{ L}} = \frac{60}{3.785} \text{ gal} \approx 15.9 \text{ gal}$

60 liters is approximately 15.9 gallons.

Example 5: Multi-Step Conversion (Feet to Meters)

Convert 25 feet to meters.

You can use the direct factor (1 ft = 30.48 cm) and then convert cm to m, or chain the factors:

$25 \text{ ft} \times \frac{30.48 \text{ cm}}{1 \text{ ft}} \times \frac{1 \text{ m}}{100 \text{ cm}}$

First, feet cancel:

$= 25 \times 30.48 \text{ cm} \times \frac{1 \text{ m}}{100 \text{ cm}}$

Then centimeters cancel:

$= \frac{25 \times 30.48}{100} \text{ m} = \frac{762}{100} \text{ m} = 7.62 \text{ m}$

25 feet = 7.62 meters.

Quick Estimation Shortcuts

When you do not need exact values, these rough approximations are useful:

• 1 inch is about 2.5 cm (precisely 2.54 cm — this one is exact by definition)
• 1 meter is a little more than 3 feet (more precisely 3.281 ft)
• 1 kilometer is about 0.6 miles (more precisely 0.621 mi)
• 1 kilogram is about 2.2 pounds (more precisely 2.205 lb)
• 1 liter is a little more than 1 quart (more precisely 1.057 qt)

These shortcuts let you do a mental sanity check on your calculated answers.

Practice Problems

Try each conversion before revealing the answer.

Key Takeaways

• Keep a short list of key conversion factors memorized: 2.54 cm per inch, 1.609 km per mile, 0.454 kg per pound, 3.785 liters per gallon.
• Dimensional analysis is a systematic, reliable method: write conversion factors as fractions and cancel units.
• Always check that the unwanted unit appears in both the numerator and denominator so it cancels completely.
• For multi-step conversions, chain multiple conversion fractions together.
• Use rough estimates (1 kg is about 2.2 lb, 1 km is about 0.6 mi) to verify your answers make sense.

Return to Arithmetic for more foundational math topics.