Unit Converter — Length, Mass, Volume, Area, Time, Speed

The core idea: multiply by a factor equal to 1

Most units — length, mass, volume, area, time, speed — share the same zero point, so converting between them is a single multiplication:

$\text{new value} = \text{old value} \times \text{conversion factor}$

The trick behind this is dimensional analysis: the conversion factor is really a fraction that equals 1 (like 1.609344 km / 1 mi), constructed so the old unit cancels out and only the new unit remains.

Worked example: 5 miles to kilometers

Using the factor 1 mi = 1.609344 km:

$5 \text{ mi} \times \frac{1.609344 \text{ km}}{1 \text{ mi}} = 8.04672 \text{ km}$

The "mi" in the numerator and denominator cancel, leaving only km.

Worked example: 10 kilograms to pounds

Using the factor 1 kg ≈ 2.20462262 lb:

$10 \text{ kg} \times 2.20462262 \approx 22.046226 \text{ lb}$

Reverse conversions: divide instead of multiply

If 1 mile equals 1.609344 km, converting the other way means dividing by that same factor rather than multiplying by a new one: 1 km ÷ 1.609344 ≈ 0.621 mi. Dividing and multiplying by the reciprocal give the same result — pick whichever is easier to compute by hand.

Area and volume need a squared or cubed factor

Area and volume conversions are the one place a plain linear factor gives the wrong answer, because both (or all three) dimensions scale together:

• Area: 1 m = 100 cm, so 1 m² = 100² = 10,000 cm² — not 100.
• Volume: 1 m = 100 cm, so 1 m³ = 100³ = 1,000,000 cm³ — not 100, and not 10,000.

Worked example: 1 square meter to square centimeters

$1 \text{ m}^2 \times (100)^2 = 1 \times 10{,}000 = 10{,}000 \text{ cm}^2$

Worked example: 2 hours to seconds

Time conversions often chain two factors together: 1 hour = 60 minutes, and 1 minute = 60 seconds, so 1 hour = 60 × 60 = 3,600 seconds.

$2 \text{ h} \times 3{,}600 = 7{,}200 \text{ s}$

Worked example: speed (km/h to m/s)

Speed combines a length factor and a time factor into one: converting km/h to m/s multiplies by the length factor (1 km = 1,000 m) and divides by the time factor (1 h = 3,600 s), giving an overall factor of 1,000/3,600 ≈ 0.277778.

$1 \text{ km/h} \times \frac{1000}{3600} \approx 0.277778 \text{ m/s}$

How precise is the result?

This calculator carries the conversion at high internal precision (decimal.js, not floating-point Number math) and displays up to 8 significant digits, trimming trailing zeros — so 10,000 cm² displays as 10000, not 10000.0000, while 10 kg → lb keeps all 8 meaningful digits (22.046226) instead of rounding early and compounding error in a later step.

Common conversion factors

Common mistakes

• Multiplying instead of dividing when converting in the reverse direction.
• Forgetting to square or cube the factor for area or volume conversions.
• Mixing up US and UK (imperial) gallons or other unit variants, which use different factors for the same unit name.
• Applying a plain multiply-by-factor approach to temperature, which needs an additional add/subtract step since temperature scales don't share a zero point.

Related calculators

For temperature, the same multiply-by-factor approach does not work on its own — the temperature converter needs an extra add/subtract step because Celsius, Fahrenheit, and Kelvin don't share a zero point. This converter is also a direct application of the unit rate idea (a ratio of one quantity per unit of another) and of ratio scaling covered in percentage.