To convert a measurement, multiply it by a conversion factor written as a fraction equal to one, arranged so the unit you have cancels and the unit you want is left. For example, 5 feet × (0.3048 m ÷ 1 ft) = 1.524 m. The feet cancel, meters remain. That one method, sometimes called dimensional analysis or the unit-fraction method, handles almost every conversion. The exceptions are temperature, fuel economy and cooking conversions by ingredient, which each need an extra step.
What is a conversion factor? #
A conversion factor is a ratio between two equal amounts in different units. Since 1 inch is exactly 2.54 cm, both of these fractions equal one:
- 2.54 cm ÷ 1 in
- 1 in ÷ 2.54 cm
Multiplying by one doesn’t change a quantity’s size, only the units it’s written in. You choose whichever version puts the unit you’re getting rid of on the bottom.
Some factors are exact because they’re definitions: 1 in = 2.54 cm, 1 lb = 0.45359237 kg, 1 mile = 1,609.344 m, 1 US gallon = 3.785411784 L. Others are rounded because they’re reciprocals of those: 1 kg ≈ 2.20462 lb never terminates. The US reference for these values is NIST SP 811.
How do you convert units step by step? #
- Write the number with its unit. 70 in.
- Pick a factor with the old unit on the bottom. 2.54 cm ÷ 1 in.
- Multiply. 70 in × 2.54 cm ÷ 1 in.
- Cancel the units that appear on top and bottom. Inches cancel.
- Do the arithmetic and round sensibly. 177.8 cm.
If the unit you wanted doesn’t come out, the factor is upside down. That’s the whole safety net of the method: the units tell you when you’ve made a mistake.
Worked example: pounds to kilograms #
150 lb × (0.45359237 kg ÷ 1 lb) = 68.04 kg.
Dividing by 2.2 instead gives 68.18 kg. The 0.14 kg difference comes from rounding the factor, and it’s bigger than the error on most bathroom scales. Use the exact direction when you can.
How do you convert through several units at once? #
Chain factors so each unit cancels the one before it. To convert 60 mph to meters per second:
60 mi/h × (1,609.344 m ÷ 1 mi) × (1 h ÷ 3,600 s) = 26.8224 m/s
Miles cancel with miles, hours with hours, and meters per second remain. You can take a longer route through feet and get the same exact answer: 60 × 5,280 ft × 0.3048 m ÷ 3,600 s = 26.8224 m/s. When a chain of exact factors gives the same result both ways, you know the arithmetic is right.
How do you convert square and cubic units? #
Square or cube the factor as well. Forgetting to is the most common conversion mistake.
Since 1 ft = 0.3048 m:
- 1 ft² = 0.3048 × 0.3048 = 0.09290304 m², not 0.3048 m².
- 1 ft³ = 0.3048³ = 0.0283168 m³, or 28.3168 L.
Worked example: a room is 12 ft × 15 ft. That’s 180 ft². 180 × 0.09290304 = 16.72 m². Using the plain length factor would give 54.9, more than three times too big.
Another: a yard of mulch or concrete is a cubic yard. 0.9144³ = 0.7646 m³, so 3 cubic yards is 2.29 m³.
How do you convert compound units? #
Handle each part of the unit separately. Density in g/cm³ to lb/ft³ needs a mass factor and a volume factor:
1 g/cm³ = 1,000 kg/m³, and 1 lb/ft³ = 0.45359237 kg ÷ 0.0283168 m³ = 16.0185 kg/m³. So 1 g/cm³ = 1,000 ÷ 16.0185 = 62.43 lb/ft³. Water, at about 1 g/cm³, weighs about 62.4 lb per cubic foot.
Or volume in a pool: 20,000 US gallons × 3.785411784 L/gal = 75,708 L, or 75.7 m³.
Which conversions don’t work by multiplying? #
| Type | Why it’s different | What to do |
|---|---|---|
| Temperature (°C, °F) | The scales have different zero points | Use the formula: °F = °C × 1.8 + 32 |
| Temperature differences | A change has no zero point | Multiply by 1.8 only (a 5 °C rise is 9 °F) |
| Fuel economy (mpg, L/100km) | One is the reciprocal of the other | Divide: L/100km = 235.215 ÷ US mpg |
| Cups to grams | Volume to mass depends on the ingredient | Use the ingredient’s grams per cup |
| Feet and inches | Mixed units | Convert to one unit first (5'10" = 70 in) |
| US vs UK measures | Same names, different sizes | Check which gallon, pint or cup is meant |
Each of these has its own article: the Celsius to Fahrenheit formula, mpg to L/100km, and the cups to grams conversion chart.
How many digits should you keep? #
Your answer can’t be more precise than your starting measurement. If a board is “about 8 feet,” converting it to 2.4384 m suggests precision you don’t have. 2.4 m is honest.
Three rules cover most cases:
- Exact factors don’t limit precision. 2.54 is exactly 2.54000…, so the number of digits in your measurement sets the precision.
- Round once, at the end. Rounding in the middle of a chain adds error at each step.
- Keep a digit or two more than you need when a result feeds into another calculation.
How can you check a conversion? #
- Bigger unit, smaller number. Converting to a larger unit (cm to m, oz to lb) should make the number smaller. If it grows, the factor is upside down.
- Estimate first. 70 kg is “a bit over 140 lb” (double it). If you get 31.8, you divided instead of multiplying.
- Round-trip it. Convert the answer back. You should land on the number you started with.
Converting lots of numbers at once #
For a list, a spreadsheet is fastest. Excel’s CONVERT function takes a number and two unit codes, for example =CONVERT(68,“F”,“C”) returns 20, according to Microsoft’s documentation. Fill it down a column and every row converts.
For one-off conversions, Convert Units Calculator does the factor work for you with the exact definitions, and shows every unit in the category at once, so a chained question (miles, then feet, then nautical miles) is answered by a single entry. Version 1.0.5 adds a keypad that does arithmetic in the value field, so you can type 12*15 for a room’s square feet and read square meters directly. It works offline. The common factors are collected in our metric to imperial conversion chart.
Frequently asked questions #
What’s the easiest way to convert units? #
Multiply by a conversion factor arranged so the old unit cancels. Write the units in every step, and they’ll tell you if you’ve flipped the factor. For everyday conversions, a converter app or a printed chart is quicker.
What is dimensional analysis? #
It’s the method of treating units like numbers that multiply and cancel. You multiply by fractions equal to one (like 2.54 cm ÷ 1 in) until only the unit you want remains. Chemistry and physics classes teach it for multi-step conversions.
How do you convert square feet to square meters? #
Multiply by 0.09290304, which is 0.3048 squared. For example, 500 ft² is 46.45 m². Going the other way, multiply square meters by 10.7639.
Why do temperature conversions need +32? #
Because Fahrenheit and Celsius put zero in different places: water freezes at 0 °C but 32 °F. After scaling by 1.8 you shift by 32. Temperature differences don’t need the shift, since a difference has no starting point.
What’s the difference between exact and approximate conversion factors? #
An exact factor comes from a definition, such as 1 in = 2.54 cm, and has no rounding error. An approximate one, like 1 kg ≈ 2.2046 lb, is rounded because its decimals never end. Converting in the exact direction and rounding at the end gives the most accurate answer.