Convert Units of Measurement
To convert units, multiply by a conversion factor arranged so the old unit cancels. For example, 5 ft × (12 in / 1 ft) = 60 in. Use the lesson for the method, the converter to check a result, and the practice tool to try numerical questions.
Unit conversion: choose the factor that cancels
Write the unit you have and the unit you need. Put the unwanted unit in the denominator of the conversion factor so it cancels. The remaining unit tells you what your answer measures.
Why the direction matters
To convert 5 ft to inches, use 5 ft × (12 in / 1 ft) = 60 in. Feet cancel, leaving inches. Using 1 ft / 12 in instead would leave ft²/in, so that factor is upside down for this problem.
A multi-step example: yards to millimeters
2 yd × (3 ft / 1 yd) × (12 in / 1 ft) × (25.4 mm / 1 in) = 1,828.8 mm. Yards, feet, and inches cancel in turn. Keep the factors together and round only at the end if the problem asks you to.
Area and volume need powered factors
Because 1 m = 100 cm, a square meter contains 100 × 100 = 10,000 square centimeters. Thus 2 m² × (100 cm / 1 m)² = 20,000 cm². For volume, cube the length factor: 1 m³ = 1,000,000 cm³.
Check yourself: convert 750 mL to liters
750 mL × (1 L / 1,000 mL) = 0.75 L. A liter is larger than a milliliter, so the number of liters should be smaller.
The pop-up below checks general study habits. For numerical unit-conversion questions, use the Unit Conversion Practice tool above.
Convert Units of Measurement: pop-up practice
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, for length, mass, capacity, and time conversions, the method is: 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 express the same quantity in another unit. Temperature scales such as Celsius and Fahrenheit also require an offset; a single multiplication factor is not enough.
Since 12 inches = 1 foot, either 12 in / 1 ft or 1 ft / 12 in is a conversion factor. The numerator and denominator describe the same length, so each ratio equals 1. Choose the direction 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:
Original measurement × (equivalent amount in desired units / equivalent amount in original units) = measurement in desired units.
U.S. Customary Conversion Facts
- Length: 12 in = 1 ft; 3 ft = 1 yd; 5,280 ft = 1 mi
- Weight: 16 oz = 1 lb; 2,000 lb = 1 U.S. short ton
- U.S. liquid capacity: 8 fl oz = 1 cup; 2 cups = 1 pt; 2 pt = 1 qt; 4 qt = 1 gal
- Time: 60 s = 1 min; 60 min = 1 h; 24 h = 1 day
Metric Conversion Facts
- Length: 10 mm = 1 cm; 100 cm = 1 m; 1,000 m = 1 km
- Mass: 1,000 mg = 1 g; 1,000 g = 1 kg
- Capacity: 1,000 mL = 1 L
Step-by-Step Summary
- Identify the original unit and the target unit.
- Find the conversion factor that relates the two units.
- Set up the fraction so the original unit cancels (it appears in the denominator of the conversion factor).
- Multiply and simplify. Attach the new unit label.
- 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.
5 ft × (12 in / 1 ft) = 60 in
Example 2: Convert 3 yards to feet.
3 yd × (3 ft / 1 yd) = 9 ft
Example 3: Convert 2.5 hours to minutes.
2.5 h × (60 min / 1 h) = 150 min
Example 4: Convert 500 centimeters to meters.
500 cm × (1 m / 100 cm) = 5 m
Example 5: Convert 3 kilograms to grams.
3 kg × (1,000 g / 1 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
- Convert 8 feet to inches.
- Convert 4.5 pounds to ounces.
- Convert 3 hours 30 minutes to minutes.
- Convert 250 centimeters to meters.
- Convert 4 kilometers to meters.
- Convert 2 gallons to quarts.
Answers
- 96 in
- 72 oz
- 210 min
- 2.5 m
- 4,000 m
- 8 qt
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:
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 the appropriate factor for the specific unit. One inch equals exactly 2.54 cm. For rounded calculations, 1 mile ≈ 1.609 km, 1 pound ≈ 0.454 kg, and 1 U.S. liquid gallon ≈ 3.785 L. An Imperial gallon has a different value. Multiply by the factor in the direction that cancels your starting unit.
Can I chain multiple conversions together?
Yes. For example, 60 mi/h × (5,280 ft / 1 mi) × (1 h / 3,600 s) = 88 ft/s. Miles and hours cancel, leaving feet per second.
For broader algebra review, use the Algebra 1 worksheet collection and choose the skill you need. The optional books on this page offer a separate paid study path; check each product preview and contents before buying.
Conversion reference: NIST conversion-factor tables, including exact inch and foot relationships and distinct U.S. and Imperial volume units.
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