Convert Units of Measurement

The ability to convert units of measurement is a fundamental skill in Algebra 1, science, and everyday life. Whether you are converting miles to kilometers, hours to minutes, or pounds to kilograms, the method is always the same: multiply by a conversion factor — a fraction equal to 1 that switches the units without changing the value. This guide teaches the technique step by step with worked examples, two video lessons, and practice problems.

What Is a Conversion Factor?

A conversion factor is a fraction that expresses the relationship between two units and equals 1. Because multiplying by 1 does not change a value, you can use it to switch units freely.

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Example: since 12 \(\color{blue}{\text{ inches } = 1}\) foot, the conversion factor is \(\color{blue}{12 \frac{\text{ in }}{1} \text{ ft }}\) or \(\color{blue}{1 \frac{\text{ ft }}{12} \text{ in }}\). Choose the one that cancels the unit you want to remove.

How to Convert Units

The Dimensional Analysis Method

Write the original measurement as a fraction, then multiply by the conversion factor so the unwanted unit cancels:

\(\color{blue}{\text{ original measurement } \times (\text{ desired } \frac{\text{ unit }}{\text{ current }} \text{ unit }) = \text{ answer in desired units }}\)

U.S. Customary Conversion Facts

• Length: 12 \(\color{blue}{\text{ in } = 1}\) ft; 3 \(\color{blue}{\text{ ft } = 1}\) yd; 5,280 \(\color{blue}{\text{ ft } = 1}\) mi
• Weight: 16 \(\color{blue}{\text{ oz } = 1}\) lb; 2,000 \(\color{blue}{\text{ lb } = 1}\) ton
• Capacity: 8 fl \(\color{blue}{\text{ oz } = 1}\) cup; 2 \(\color{blue}{\text{ cups } = 1}\) pt; 2 \(\color{blue}{\text{ pt } = 1}\) qt; 4 \(\color{blue}{\text{ qt } = 1}\) gal
• Time: 60 \(\color{blue}{s = 1}\) min; 60 \(\color{blue}{\text{ min } = 1}\) h; 24 \(\color{blue}{h = 1}\) day

Metric Conversion Facts

• Length: 10 \(\color{blue}{\text{ mm } = 1}\) cm; 100 \(\color{blue}{\text{ cm } = 1}\) m; 1,000 \(\color{blue}{m = 1}\) km
• Mass: 1,000 \(\color{blue}{\text{ mg } = 1}\) g; 1,000 \(\color{blue}{g = 1}\) kg
• Capacity: 1,000 \(\color{blue}{\text{ mL } = 1}\) L

Step-by-Step Summary

1. Identify the original unit and the target unit.
2. Find the conversion factor that relates the two units.
3. Set up the fraction so the original unit cancels (it appears in the denominator of the conversion factor).
4. Multiply and simplify. Attach the new unit label.
5. For multi-step conversions, chain multiple conversion factors together.

Watch: Multi-Step Unit Conversion (Video Lesson)

Khan Academy works through a multi-step unit conversion word problem using dimensional analysis:

Convert Units of Measurement – Worked Examples

Example 1: Convert 5 feet to inches.

\(\color{blue}{5 \text{ ft } \times (12 \frac{\text{ in }}{1} \text{ ft }) = 60 \text{ in }}\)

Example 2: Convert 3 yards to feet.

\(\color{blue}{3 \text{ yd } \times (3 \frac{\text{ ft }}{1} \text{ yd }) = 9 \text{ ft }}\)

Example 3: Convert 2.5 hours to minutes.

\(\color{blue}{2.5 h \times (60 \frac{\text{ min }}{1} h) = 150 \text{ min }}\)

Example 4: Convert 500 centimeters to meters.

\(\color{blue}{500 \text{ cm } \times (1 \frac{m}{100} \text{ cm }) = 5 m}\)

Example 5: Convert 3 kilograms to grams.

\(\color{blue}{3 \text{ kg } \times (1,000 \frac{g}{1} \text{ kg }) = 3,000 g}\)

More Practice: Converting Measures (Video)

Anywhere Math demonstrates multiple unit conversions using conversion factors with clear step-by-step work:

Exercises for Converting Units of Measurement

1. Convert 8 feet to inches.
2. Convert 4.5 pounds to ounces.
3. Convert 3 hours 30 minutes to minutes.
4. Convert 250 centimeters to meters.
5. Convert 4 kilometers to meters.
6. Convert 2 gallons to quarts.

Answers

1. \(\color{blue}{96 \text{ in }}\)
2. \(\color{blue}{72 \text{ oz }}\)
3. \(\color{blue}{210 \text{ min }}\)
4. \(\color{blue}{2.5 m}\)
5. \(\color{blue}{4,000 m}\)
6. \(\color{blue}{8 \text{ qt }}\)

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Want More Practice?

We haven’t published a worksheet built specifically for Convert Units of Measurement just yet. In the meantime, the free worksheets below cover closely related skills and concepts. If you’d like extra practice, download any that look helpful, complete the problems, and check your work — they’re a great way to reinforce what you learned on this page and strengthen the foundations this topic builds on:

• Download Direct Variation Worksheet
• Download Personal Financial Literacy Worksheet

Frequently Asked Questions

What is dimensional analysis?

Dimensional analysis is the process of using conversion factors — fractions equal to 1 — to change units. By writing units as part of the calculation and canceling them like variables, you ensure the answer comes out in the correct unit.

How do I convert between U.S. customary and metric units?

Use an approximate conversion factor. Common ones: 1 inch ≈ 2.54 cm; 1 mile ≈ 1.609 km; 1 pound ≈ 0.454 kg; 1 gallon ≈ 3.785 L. Multiply by the factor and cancel units as usual.

Can I chain multiple conversions together?

Yes. Multiply by as many conversion factors as needed in one step. For example, to convert miles per hour to feet per second, multiply by \(\color{blue}{5,280 \frac{\text{ ft }}{1} \text{ mi }}\) and then by \(\color{blue}{1 \frac{h}{3},600 s}\) in the same calculation.

Related Topics

• Metric Units
• Unit Rates and Rates
• Arithmetic Sequences
• Writing Linear Equations