Unit Conversion
Unit conversion problems test whether you can multiply by the right *fraction* — one that cancels the unit you don't want and leaves the unit you do.
Converting units = multiplying by a conversion fraction equal to 1.
1 hour = 60 minutes, so and . Multiplying by either doesn't change the value — but it does change the units.
| Have | Want | Right fraction | Why |
|---|---|---|---|
| miles | feet | $\times \frac{5280 \text{ ft}}{1 \text{ mi}}$ | miles cancels; feet remains |
| feet | miles | $\times \frac{1 \text{ mi}}{5280 \text{ ft}}$ | feet cancels; miles remains |
| hours | minutes | $\times \frac{60 \text{ min}}{1 \text{ hr}}$ | hr cancels; min remains |
| minutes | hours | $\times \frac{1 \text{ hr}}{60 \text{ min}}$ | min cancels; hr remains |
The dimensional analysis technique — write everything as a chain of fractions, cancel the units you don't want.
Convert 5 miles to feet (5,280 feet per mile):
The miles cancel; feet remain. The numerical answer is .
Multi-step conversions. Chain the fractions.
Convert 90 km/h to m/s:
The km cancels with km; hr cancels with hr. We're left with m/s.
SAT-typical setups:
- Time conversions: 1 hr = 60 min = 3,600 s. 1 day = 24 hr = 1,440 min.
- Length: 1 mile = 5,280 ft = 1,609 m. 1 km = 1,000 m. 1 m = 100 cm.
- Volume: 1 gallon ≈ 3.785 L. 1 L = 1,000 mL.
- Mass / weight: 1 kg = 1,000 g = 2.205 lb (often approximated).
The SAT often gives you the conversion factor in the problem — you don't need to memorize obscure ones. Read the problem carefully.
Square / cubic units. Converting square or cubic units requires squaring or cubing the linear factor.
- 1 m = 100 cm. So 1 m² = (100)² cm² = 10,000 cm². NOT 100 cm².
- 1 ft = 12 in. So 1 ft³ = 12³ in³ = 1,728 in³.
Word-problem unit traps:
- Speed × time = distance — make sure all in matching units. 60 mph × 30 min doesn't equal 1,800 miles; convert minutes to hours first: miles.
- Density × volume = mass — units must match.
Try this SPR. Set up your conversion fractions so the unwanted units cancel. Multiply through; the leftover units should match the answer.
There are 5,280 feet in one mile. How many feet are in 5 miles?
Worked examples
A bakery uses 24 cups of flour each day. How many gallons of flour does it use in 30 days, given that 16 cups = 1 gallon?
A rectangular field measures 20 m by 30 m. What is its area in square feet, given that 1 m ≈ 3.28 ft?
Common pitfalls
doesn't mean . It's . For volume: . Square the linear factor for square units; cube it for cubic units.
Going from a bigger unit to a smaller unit (miles → feet), multiply. From smaller to bigger (feet → miles), divide. Or just write the fraction and cancel — let the units guide you.
60 mph × 30 min doesn't directly give you a distance — the 60 is per hour, but you have minutes. Convert one to match: 30 min = 0.5 hr, so miles.
1 mile = 5,280 feet means there are 5,280 feet IN 1 mile. To convert miles to feet, multiply by 5,280. To convert feet to miles, divide. Don't mix it up.
Key takeaways
Multiply by a conversion fraction equal to 1 (e.g., ). Choose the orientation that cancels the unit you don't want.
Chain fractions for multi-step conversions. Cancel as you go.
Square units need the conversion factor SQUARED. Cubic units cubed.
Always check that your units cancel correctly — the result should leave the desired unit.
Match all units before doing arithmetic in word problems (e.g., convert minutes to hours if speed is in mph).
Watch & learn
Curated Khan Academy walkthroughs on Unit Conversion. They're complementary to this lesson — watch one if a written explanation isn't clicking, or after to reinforce.
Try it yourself
5 practice questions on Unit Conversion, drawn from the question bank. The tutor is one click away if you get stuck.