Why units matter more than you think
In September 1999, the Mars Climate Orbiter, a $327 million NASA spacecraft, entered the Martian atmosphere and burned up. The cause was a unit conversion error. One engineering team had specified thrust in pound-seconds (an imperial unit), and the software that interpreted the value expected newton-seconds (a metric unit). The discrepancy of about a factor of 4.45 was enough to put the spacecraft on a fatal trajectory. The probe was lost, the mission was over, and the lesson was clear: units are not bookkeeping, they are part of the physical quantity.
Closer to the ground, unit errors cause medication overdoses, structural failures, and lost shipments. The aviation industry standardized on metric units in 1977 after an Air Canada flight ran out of fuel mid-flight because of a confusion between pounds and kilograms of fuel. Hospitals report unit errors as one of the leading causes of medication incidents, especially when converting between adult and pediatric dosing. The point of taking units seriously is not pedantry; it is that the difference between 5 mg and 5 g of a drug can be lethal.
The SI base units and how they fit together
The International System of Units, abbreviated SI from the French Système International, was formalized in 1960 and is maintained by the Bureau International des Poids et Mesures in Sèvres, France. As of the 2019 redefinition, the SI rests on seven base units, each defined in terms of a fundamental constant of nature rather than a physical artifact. The meter is defined by the distance light travels in a vacuum in 1/299,792,458 of a second. The kilogram is defined by the Planck constant. The second is defined by the hyperfine transition of cesium-133. The ampere is defined by the elementary charge. The kelvin is defined by the Boltzmann constant. The mole is defined by Avogadro's number. The candela is defined by luminous efficacy at a specific frequency.
Every other SI unit is derived from these seven. The newton (force) is a kilogram times a meter per second squared. The joule (energy) is a newton times a meter. The watt (power) is a joule per second. The pascal (pressure) is a newton per square meter. The hertz (frequency) is an inverse second. The coherent structure means that if you use only SI base units and SI derived units in a calculation, no conversion factors are needed at all. The constants are 1.
The SI prefixes scale units by powers of ten. Kilo means a thousand (10³), mega a million (10⁶), giga a billion (10⁹), tera a trillion (10¹²), and so on through peta, exa, zetta, and yotta. Going down: milli is a thousandth (10⁻³), micro a millionth (10⁻⁶, with the prefix symbol µ), nano a billionth (10⁻⁹), pico (10⁻¹²), femto (10⁻¹⁵), atto (10⁻¹⁸), zepto (10⁻²¹), and yocto (10⁻²⁴). A new pair of prefixes, ronna (10²⁷) and quetta (10³⁰), ronto (10⁻²⁷) and quecto (10⁻³⁰), were added in 2022 to handle the scale of modern data and physics.
Length, mass, and temperature in detail
Length is the most straightforward conversion. One inch is exactly 25.4 millimeters, by international agreement since 1959. One foot is 12 inches (0.3048 m), one yard is 3 feet (0.9144 m), one mile is 5,280 feet (1,609.344 m). The nautical mile is different, defined as exactly 1,852 meters, originally chosen because it approximates one minute of latitude. Speeds in aviation and shipping use knots, where one knot is one nautical mile per hour.
Mass is more subtle because of the distinction between mass and weight. Mass is the amount of matter, measured in kilograms. Weight is the force exerted by gravity on that mass, measured in newtons. In everyday language the two are conflated, which is mostly harmless until you start moving between planets or accelerating. One pound (avoirdupois) is exactly 0.45359237 kilograms. One ounce is one sixteenth of a pound, so 28.349523125 grams. The troy ounce, used for precious metals, is 31.1034768 grams — different from the avoirdupois ounce, which catches people out when they buy gold.
Temperature is the trickiest because the conversion is multiplicative plus additive, not just multiplicative. Celsius and Kelvin share the same size of degree; only the zero point differs. Zero degrees Celsius is 273.15 kelvin, so adding 273.15 converts between them. Fahrenheit uses a smaller degree (5/9 the size of a Celsius degree) and a different zero point. To convert Celsius to Fahrenheit, multiply by 9/5 and add 32. To convert Fahrenheit to Celsius, subtract 32 and multiply by 5/9. The rankine scale, rarely used outside some engineering contexts, is to Fahrenheit what Kelvin is to Celsius.
The imperial holdouts and how to translate
Three countries have not adopted the metric system as their official standard: the United States, Liberia, and Myanmar. Liberia has largely metricated in practice, and Myanmar is in the middle of a transition. The United States is the significant holdout, with the metric system legal for trade since 1866 and preferred for government contracts since the 1970s but never mandated for civilian use. The result is a mixed system where scientists use SI, engineers use a mix, construction uses imperial, and consumers see both.
Translation requires care because imperial units are not always consistent. A US gallon is 3.785411784 liters. An imperial (UK) gallon is 4.54609 liters, about 20 percent larger. The US fluid ounce is 29.5735295625 milliliters; the imperial fluid ounce is 28.4130625 milliliters. The US hundredweight is 100 pounds; the imperial hundredweight is 112 pounds. The US ton (also called a short ton) is 2,000 pounds; the imperial ton (long ton) is 2,240 pounds; the metric ton (tonne) is 1,000 kilograms, or 2,204.6226 pounds. When a recipe or shipping document says ton, check which one.
Significant figures and rounding
A conversion factor is only as good as the precision of the input. If you weigh yourself on a bathroom scale that reads to the nearest kilogram, the number is good to about plus or minus 0.5 kg. Converting that to pounds using a six-decimal conversion factor does not add precision; it just adds false confidence. The rule of significant figures is that the result of a calculation should be reported to the same precision as the least precise input. A weight of 70 kg converts to 154.324 pounds, but only 154 pounds carries real information.
Rounding should be done last. Every intermediate rounding introduces a small error that compounds through subsequent calculations. Keep all digits in your calculator until the final step, then round to the appropriate number of significant figures. For financial calculations involving money, the convention is to keep at least four decimal places through the calculation and round to two places only at the final display. For scientific work, the convention is to keep one extra guard digit through intermediate steps and round at the end.
The rounding mode matters in some contexts. The default in most programming languages is round half to even (also called banker's rounding), which rounds 0.5 to the nearest even number rather than always up. This avoids the systematic upward bias that round half up introduces over many calculations. For most engineering and scientific work, banker's rounding is correct. For tax calculations, the rules vary by jurisdiction; the European Union specifies round-half-up for VAT, while the United States has no single rule. Most spreadsheets and calculators use round-half-up by default, which is fine for casual use but produces small upward biases in large datasets. For scientific work where you are averaging many rounded values, switch to banker's rounding in your tool of choice (the ROUND function in Excel has a mode argument, and Python's round() uses banker's rounding by default). The bias is small per measurement but compounds across millions of data points.
Common conversion mistakes and how to avoid them
The first mistake is mixing unit systems within a single calculation. A formula that expects meters will give a wrong answer if you feed it feet, even if the feet value is correct in isolation. Write the units next to every number in your working, and cancel them like algebraic terms. If the units do not cancel to the expected result, the calculation is wrong before you even check the arithmetic. This technique, called dimensional analysis, catches errors that no other check will.
The second mistake is trusting floating-point arithmetic to be exact. Most decimal fractions cannot be represented exactly in binary floating-point, so 0.1 plus 0.2 equals 0.30000000000000004 in JavaScript, Python, and most other languages. For unit conversions involving money or precision measurements, use a decimal type or an integer with an explicit scale factor. For engineering work, the floating-point error is usually small enough to ignore, but be aware of it when comparing two results for equality.
The third mistake is forgetting temperature's offset. Converting 100°C to Fahrenheit gives 212°F, but converting a 100°C temperature difference to Fahrenheit gives a 180°F difference, not 212°F. The first case uses the full formula with the plus-32 offset; the second case uses only the 9/5 multiplier, because differences do not have an offset. This catches people out in heat transfer calculations and weather forecasts of temperature changes. When in doubt, write the formula explicitly and check whether the constant appears.