Unit Converter

Everything this converter knows is organized into eighteen families, each anchored to one base unit and holding its own roster of units. The table lists them as the engine defines them, with the base each family computes through and the count of units it contains — 146 definitions in all.

Seventeen of the eighteen run on the first kind of math: one stored factor per unit. A unit's factor says how many base units it is worth, so converting multiplies by the source factor to reach the base, then divides by the target factor to leave it. The detour is invisible and lossless when the factors are exact — a mile enters the base as 1,609.344 meters and leaves through the foot's 0.3048, and 1,609.344 ÷ 0.3048 comes out at exactly 5,280 feet. Data Storage is a linear family too, but it keeps two conventions side by side: decimal kilobytes at 1,000 bytes and binary kibibytes at 1,024, so the same file counted both ways reports two sizes.

The second kind of math belongs to Temperature, whose four units the engine marks as formula-based rather than linear — no single number can translate between scales with different zero points. One member of Fuel Economy needs the same treatment: liters per 100 kilometers is an inverse scale, so 5 km/L reads 20 L/100 km and 50 L/100 km reads 2. Families stay sealed off from one another — ask for kilograms in meters and the converter returns an error instead of inventing a bridge.

Some of the stored factors are definitions rather than measurements, which is why they carry no uncertainty. The inch holds 0.0254 meters because an international agreement of 1959 set the yard at exactly 0.9144 meters — and with it the foot at 0.3048 and the pound at 0.45359237 kilograms, ending the era when the US and UK units differed in the last places. The mile is 5,280 of those feet, so its 1,609.344 meters is settled arithmetic, not surveying.

Longer chains stay exact the same way. The pound-force factor of 4.4482216152605 newtons is the pound's mass multiplied by standard gravity, 9.80665 meters per second squared — both fixed values, and the product reproduces the stored factor digit for digit. The US gallon is defined as 231 cubic inches, which lands on precisely 3.785411784 liters; the acre is 43,560 square feet, or 4,046.8564224 square meters. Physical constants arrive exact as well: light travels 299,792,458 meters in a second by definition, and the electronvolt has been pinned at 1.602176634 × 10⁻¹⁹ joules since the 2019 revision of the SI.

A handful of practical units are stored rounded, and the difference is honest to know about. Mechanical horsepower is kept at 745.7 watts where the exact figure runs 745.69987; the knot is stored as 0.514444 meters per second against an exact 1,852 ÷ 3,600 = 0.5144444…, so a knot reads 1.851998 km/h here rather than 1.852. Display rounds once more, at six decimal places, which is why one kilogram shows 2.204623 pounds while the arithmetic carries 2.2046226218487757. The rounding sits at the edges — the factors and the printout — not in the middle of a calculation.

Multiply 100 °F by 5/9 and you get 55.6 — the true answer is 37.8 °C. The failure has two causes stacked: the scales put their zeros in different places (0 °F is not freezing), and their degrees are different sizes (a Fahrenheit degree spans 5/9 of a Celsius degree). Any scale with an arbitrary zero needs the offset handled before the size does: subtract first, then multiply. That structure — shift, then scale — is called affine rather than linear, and it is why the temperature family stores formulas instead of factors.

Negative values are where skipping the offset becomes expensive. Scale −40 °F by 5/9 alone and it lands at −22.2 °C, wrong by nearly eighteen degrees; done properly, (−40 − 32) × 5/9 = −40, the one reading where both scales agree. Offsets also guard absolute zero: Kelvin adds 273.15 without scaling, so 0 °C reads 273.15 K and nothing colder than −273.15 °C can be a physical temperature. The converter applies the formulas without policing physics — type −300 °C and it returns −26.85 K, a negative Kelvin figure that is the arithmetic's way of saying the input, not the formula, has left reality. The family's fourth unit, Rankine, puts Fahrenheit-sized degrees on Kelvin's footing: 0 °F reads 459.67 °R, and absolute zero sits at 0.

Eight factors cover most everyday translating, and every one below is derived from the converter's own stored factors — multiply into the base, divide out the other side. Where a ratio carries more precision than the display's six decimals can show, the fuller figure is quoted, so what gets memorized is the definition rather than a printout of it.

Notice the asymmetry between the first two rows: a mile is a terminating 1.609344 kilometers, but a kilometer is a never-ending 0.62137119… miles, because inverting a tidy fraction rarely stays tidy. Whichever direction you memorize decides how many decimals you must carry. Four or five places serve any mental arithmetic — 0.6214, 2.2046 — since the sixth decimal is far finer than a road sign or a recipe can express, and the display itself stops at six.

Two cautions keep the table honest. The gallon row is the US one: the converter also carries the UK gallon at 4.54609 liters, roughly twenty percent larger, and running a recipe through the wrong row is the classic gallon error. And there is no temperature row by design — no factor exists to memorize on those scales, only the offset-and-scale formulas covered in the previous section.