Convert between units when needed (unit conversion).
Convert units before calculating area or volume, or square or cube the conversion factor if you convert after.
Core Idea
When converting between units, linear dimensions multiply by the conversion factor once, areas by the factor squared, and volumes by the factor cubed.
Understanding
A common SAT setup: dimensions in one unit, answer expected in another. For length, the conversion is direct — 1 foot = 12 inches, so multiply or divide by 12. But for area, you need to square the factor: 1 square foot =
The safest approach is to convert every measurement to the target unit before computing area or volume. That way you never have to remember whether to square or cube the conversion factor — the formula handles it for you.
Dimensional analysis helps: write each conversion as a fraction (e.g.,
Step by Step
- Identify the unit the answer requires.
- Convert each given measurement to that unit before doing any area or volume calculation.
- If you've already computed in the original unit, multiply the result by the conversion factor raised to the appropriate power (squared for area, cubed for volume).
Misconceptions
- Converting the final area or volume by the linear factor instead of squaring or cubing it.
- Dividing when you should multiply (or vice versa) — always check whether you're going to a larger or smaller unit.
- Forgetting to convert all dimensions, leaving a mix of units in the formula.
Worked Example
A rectangular patio measures 4 yards by 3 yards. What is the area of the patio, in square feet? (1 yard = 3 feet)
Select an answer to see the explanation