How to Convert Units Accurately

Unit conversion feels like simple multiplication, and most of the time it is. But the mistakes people make, a recipe that fails, a room that won’t fit the furniture, or famously a spacecraft lost in orbit, almost always come from the same few traps. This guide covers the method that works for any conversion, the definitions that make it exact, and the special cases that need extra care.

Why there are so many units

Most of the world uses the metric system, formally the International System of Units (SI). Its units scale by powers of ten, with the same prefixes everywhere:

Prefix	Symbol	Factor	Example
kilo	k	1,000	1 km = 1,000 m
hecto	h	100	1 hPa = 100 Pa
centi	c	0.01	1 cm = 0.01 m
milli	m	0.001	1 mL = 0.001 L
micro	µ	0.000001	1 µm = 0.000001 m

The United States uses US customary units (feet, pounds, gallons), and the UK uses a mix of metric and imperial units. Since the 1959 international yard and pound agreement, these are all defined in terms of metric units. That is why conversions between them are exact:

• 1 inch = 2.54 cm exactly
• 1 foot = 0.3048 m exactly
• 1 pound = 0.45359237 kg exactly
• 1 US gallon = 3.785411784 L exactly

The factor-label method

The most reliable way to convert anything is to multiply by fractions that equal 1, arranged so the unwanted units cancel. This is called the factor-label method, or dimensional analysis.

Worked example: 65 mph in meters per second

65 mi/h × 1,609.344 m/mi × 1 h/3,600 s = 29.0576 m/s

1. Start with 65 mi/h.
2. Multiply by 1,609.344 m per mile. The mi cancels, leaving m/h.
3. Multiply by 1 hour per 3,600 seconds. The h cancels, leaving m/s.
4. Result: 29.06 m/s.

If the units don’t cancel to what you want, a fraction is upside down. That self-check is what makes the method so dependable, especially across several steps. The speed converter does the same calculation in one step.

Area and volume: square and cube the factor

A common trap is using a length factor on an area or a volume. Because area has two dimensions and volume three, the factor must be squared or cubed:

• Area: 1 ft² = 0.3048² = 0.09290304 m². A 10 ft × 12 ft room is 120 ft², or 11.15 m².
• Volume: 1 ft³ = 0.3048³ = 0.0283168 m³, or 28.32 liters.

Worked example: the air in a room

A room is 10 ft × 12 ft × 8 ft.

1. Volume in cubic feet: 10 × 12 × 8 = 960 ft³.
2. Convert with the cubed factor: 960 × 0.0283168 = 27.18 m³.

Multiplying 960 by the length factor 0.3048 gives 292.6, which is wildly wrong. The area converter and volume converter build these squared and cubed factors in.

Temperature: the one that needs an offset

Celsius, Fahrenheit and Kelvin don’t share a zero point, so a temperature conversion needs both a multiplication and an addition:

°F = °C × 9/5 + 32
°C = (°F − 32) × 5/9
K  = °C + 273.15

There is one important exception. A temperature difference converts without the offset. A rise of 10°C is a rise of 18°F, not 50°F. Weather forecasts, cooking temperatures and lab work each use both kinds of number, so check which one you have. The temperature converter handles absolute temperatures on all four scales.

Same name, different size

Several units share a name but not a size, depending on the country or the field:

Unit	US	UK / other
Gallon	3.785 L	4.546 L (imperial)
Pint	473 mL	568 mL
Ton	907 kg (short ton)	1,016 kg (long ton); 1,000 kg (metric tonne)
Cup	236.6 mL	250 mL (metric cup)
Mile	1,609 m	1,852 m (nautical mile)

Fuel economy is a good example. 30 mpg in the US equals 7.84 L/100 km, but 30 mpg in a UK review means a more efficient car, because the UK gallon is bigger. Use the weight converter and volume converter, which label US and UK units separately.

Compound units: convert each part

Units such as speed, density and fuel economy combine two or more base units. Convert each part separately, using the factor-label method above.

• Density: water is 1,000 kg/m³. In pounds per cubic foot: 1,000 kg/m³ × 0.0283168 m³/ft³ ÷ 0.45359237 kg/lb = 62.43 lb/ft³.
• Fuel economy: mpg and L/100 km are inverses. One measures distance per fuel and the other fuel per distance, so you divide rather than multiply: L/100 km = 235.215 ÷ mpg (US).
• Prices per unit: $4.50 per pound is 4.50 ÷ 0.45359 = $9.92 per kilogram. Here the unit is in the denominator, so you divide by the factor that you would multiply by for the weight itself.

When a unit sits in the denominator, the conversion runs the “opposite” way. Writing the units out makes this obvious.

Rounding and precision

A converted number should never look more precise than the original measurement:

• 5.5 ft converts to exactly 1.6764 m. Since the original was given to one decimal place, report it as 1.68 m.
• Keep full precision in intermediate steps and round once, at the end.
• For money, round to cents. For engineering, follow the tolerance on the drawing. For recipes, round to what your measuring tools can measure.

When conversion mistakes get expensive

• Mars Climate Orbiter (1999). One team’s software produced thruster data in pound-force seconds, while the navigation team expected newton-seconds. The spacecraft approached Mars far too low and was lost.
• The “Gimli Glider” (1983). An Air Canada Boeing 767’s fuel load was calculated with a pounds factor instead of kilograms, so it took off with less than half the fuel it needed. It ran dry mid-flight, and the crew glided it to a safe landing at a former air base in Gimli, Manitoba.

Both mistakes came down to a unit that wasn’t written down or checked. Writing units next to every number, as the factor-label method does, prevents exactly this kind of error.

A checklist for any conversion

1. Write the starting value with its unit.
2. Find the exact factor, and square or cube it for area or volume.
3. Arrange the factor so the old unit cancels.
4. For temperature, decide whether you have an absolute value or a difference.
5. Check for US vs. UK units of the same name.
6. Round once, at the end, to a sensible precision.
7. Sanity-check: a kilogram is about two pounds, a meter is a little over three feet, a liter is about a quart. If the answer is far off from that, something went wrong.

The length converter and the other converters linked here show every unit side by side, so you can confirm a result at a glance.

Frequently asked questions

Are metric to imperial conversions exact?

Most are. Since 1959 the inch has been defined as exactly 2.54 cm and the pound as exactly 0.45359237 kg, so length, area, volume and weight conversions between the systems are exact. Only the rounding of the result introduces error.

Why can't I convert Celsius to Fahrenheit by multiplying?

The two scales have different zero points. You need to multiply by 9/5 and add 32. Only temperature differences (such as "10 degrees warmer") convert with a plain multiplication by 1.8.

How do I convert square or cubic units?

Square or cube the length factor. 1 ft = 0.3048 m, so 1 ft² = 0.3048² = 0.0929 m² and 1 ft³ = 0.3048³ = 0.0283 m³, or 28.32 liters.

How many decimal places should I keep?

No more than the precision of the original measurement. A height of 5.5 ft is about 1.68 m. Writing 1.6764 m suggests a precision the original measurement never had.

Is a US gallon the same as a UK gallon?

No. A US gallon is 3.785 liters and a UK (imperial) gallon is 4.546 liters, about 20% larger. US and UK pints and fluid ounces differ too.