Math · Ratios & measurement
Measurement Systems and Unit Conversions
Estimated time includes reading and one quiz. Take the time you need.
Start here: key ideas
- A conversion factor equals one, so it changes units without changing the amount.
- Arrange conversion factors so unwanted units cancel.
- Metric prefixes follow powers of ten.
- Between systems, use the supplied factor and keep US liquid units distinct from Imperial units.
- Area and volume require squaring or cubing the entire length conversion.
What you’ll be able to do
- Convert within metric and customary systems.
- Use conversion factors so unwanted units cancel.
- Apply conversion factors correctly to squared and cubed units.
- Convert length, mass and capacity between customary and metric units using supplied factors.
A conversion factor equals one, so it changes units without changing the amount. Arrange conversion factors so unwanted units cancel.
Optional review
If you’d like to review the basics, visit Ratios and Proportions. You can start this lesson without completing those first.
Know the relationships
A conversion factor can be written in either direction because its numerator and denominator are equal amounts.
Scroll the table sideways if needed.
| Quantity | Metric relationships | Customary relationships |
|---|---|---|
| Length | 1 km = 1,000 m; 1 m = 100 cm | 1 ft = 12 in; 1 yd = 3 ft; 1 mi = 5,280 ft |
| Mass/weight | 1 kg = 1,000 g; 1 g = 1,000 mg | 1 lb = 16 oz |
| Capacity | 1 L = 1,000 mL | 1 gal = 4 qt; 1 qt = 2 pt; 1 pt = 2 cups |
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