Unit converter

School-style problems with solutions

Speed conversion is the most common step in physics homework. To turn 90 km/h into metres per second, divide by 3.6: 90 ÷ 3.6 = 25 m/s. Going the other way, multiply: 10 m/s × 3.6 = 36 km/h. The 3.6 comes from 1 km being 1000 m and 1 hour being 3600 s.

In an area problem a field measures 2.5 ha. One hectare is 100 × 100 m, or 10,000 m², so 2.5 ha = 25,000 m². A square kilometre holds 100 hectares.

In a volume problem a can holds 330 ml. Since 1 l = 1000 ml, that is 0.33 l. A cubic metre is 1000 litres, so 1 m³ of water weighs about a tonne.

The square and cubic unit trap

The most common mistake is assuming that because 1 m = 100 cm, 1 m² must be 100 cm². The factor has to be squared: 100 × 100 = 10,000, so 1 m² = 10,000 cm². For cubic units it is cubed: 1 m³ = 1,000,000 cm³.

• 1 km² = 1,000,000 m² = 100 ha
• 1 ha = 10,000 m²
• 1 m² = 10,000 cm²
• 1 m³ = 1000 l
• 1 l = 1 dm³ = 1000 ml

Temperature: a reading and a change are different things

The converter converts a temperature reading. 10 °C is 50 °F because the formula adds 32. But if the temperature rises by 10 degrees Celsius, the rise on the Fahrenheit scale is 18 degrees: for a change you only multiply by 9/5 and leave out the 32. So a temperature difference cannot be run through the converter like an ordinary reading.

A kelvin and a degree Celsius are the same size; only the zero point differs. 20 °C = 293.15 K and absolute zero, 0 K, is -273.15 °C. A change of 5 °C is exactly 5 K.

Handy checkpoints: -40 °C is exactly -40 °F, and 37 °C is 98.6 °F. If your answer clearly disagrees with these, the formula was probably applied in the wrong direction.

Imperial and US units: what exactly is converted

English-language manuals and recipes often use one name for several units. The converter uses fixed definitions, so check that your source means the same thing.

• gal is the US gallon, 3.78541 l. The UK gallon is larger (about 4.546 l) and is not in the converter.
• oz is the weight ounce, 28.35 g. The fluid ounce (fl oz) is a volume unit and cannot be converted under mass.
• mi is the statute mile, 1609.344 m. The nautical mile is 1852 m and is built into the knot (kn): 20 kn = 37.04 km/h.
• 70 mph = 112.65 km/h, 6 ft = 1.83 m, 150 lb = 68.04 kg, and a 15.6 in screen has a 39.62 cm diagonal.
• 1 acre (ac) = 0.4047 ha, roughly 40 % of a hectare.

Precision and rounding

Results are shown with up to four decimals. Some conversion factors are rounded internally, such as the km/h to m/s ratio, so with very large numbers the last decimal may differ from a hand calculation.

In schoolwork, do not give an answer more precise than the input: if a length is given as 6 ft, 1.83 m is enough rather than 1.8288 m. Before converting, also check whether the task needs mass or weight, since the kilogram is a unit of mass and the newton a unit of force.