How this calculator works
Dimensional analysis rests on one rule: quantities can be added, compared or converted only when they have the same physical dimension. A length cannot be compared with a mass, but 1 mile and 1 kilometre can be compared after both are expressed in metres. This calculator first checks that both units belong to the chosen quantity, then converts each value to the category base unit before dividing. For temperature, the base unit is kelvin, so a comparison is a ratio of absolute temperatures rather than of Celsius readings.
Formula
For a comparison, ratio = value 1 converted to base / value 2 converted to base. The comparison statement reports the larger value. For a conversion, converted = value 1 x F(unit 1) / F(unit 2), with temperature using its offset conversion. F is the size of the unit in base units.
Worked example
2 km compared with 500 m: 2,000 m / 500 m = 4, so value 1 is four times larger. 60 mph converted to km/h is 96.561 km/h. 1 kg compared with 1 lb is 2.20462, because 1 lb is 0.453592 kg.
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Frequently asked questions
What does matching dimensions mean?
Each quantity has a dimension such as length, mass or time. A unit is valid only within its own dimension. The calculator checks the chosen units against the chosen quantity and refuses a mismatch rather than producing a meaningless number.
Why compare temperatures in kelvin?
A ratio of Celsius temperatures depends on where zero was placed, while a ratio of kelvin temperatures is absolute. The calculator converts both readings to kelvin for a comparison and says so.
Can this check a physics equation?
It can check that the two sides of an equation share a dimension, but it does not symbolically simplify units. Use it for numerical comparisons and unit conversions, and check the algebra separately.