Convert °F to K

Fahrenheit puts freezing at 32 and boiling at 212, so a Fahrenheit degree is five ninths the size of a Celsius one. Converting therefore takes two steps, not one: a multiplication for the difference in degree size, and a shift for the different zero points.

Kelvin starts at absolute zero, the point where there is no thermal energy left to remove, and its degrees are the same size as Celsius ones. It takes no degree sign — it is 300 K, not 300 °K.

Fahrenheit and Kelvin do not start counting from the same place, so no single number converts between them. Multiplying is the mistake this page exists to prevent: it is right at exactly one temperature and wrong everywhere else, and the error grows the further you get from that point.

The two ends of this page's own scale show it. 0 °F is 255.37 K and 100 °F is 310.93 K — a hundred steps on one side, 55.56 on the other, and the two zeros in different places. That is why the formula above has two parts, something to multiply by and something to add; drop the addition and the answer stops being wrong slowly and starts being wrong badly.

Kelvin starts at absolute zero, the point where there is no thermal energy left to remove, and nothing below it exists to measure. That is what makes it a scale you can multiply on: 200 K really is twice 100 K, in a way that 200 °C is not twice 100 °C.

Neither Celsius nor Fahrenheit can say that. Their zeros were chosen, not found, which is why doubling a Celsius reading means nothing at all.

The two-step route works — take 32 off, multiply by 5/9, add 273.15 — but it carries a rounding hazard in the middle and an extra opportunity to misremember the order. Folding the constants together gives K = (°F + 459.67) × 5/9, which is one addition and one multiplication. 68 °F becomes (68 + 459.67) × 5/9, or 293.15 K.

The two forms are algebraically identical: 273.15 K is 491.67 Fahrenheit degrees above absolute zero, and moving that constant across the multiplication turns the 32 into 459.67. The single-step version is the one worth committing to memory, because its constant means something — it is absolute zero in Fahrenheit with the sign flipped — where the 32 and the 273.15 of the long route are two unrelated facts held in the same head.

Absolute zero is −459.67 °F. It is defined rather than measured, following directly from the exact 273.15 offset between Celsius and kelvin and the exact 9/5 ratio between the two degree sizes, so it is not a figure that will be refined by better instruments. It is also the reason no Fahrenheit number below −459.67 describes any physical state.

The constant is worth carrying because it turns every Fahrenheit reading into a distance. A room at 68 °F is 527.67 Fahrenheit degrees above absolute zero; multiply those degrees by 5/9 to restate them as kelvins and 293.15 K falls out. Thinking of the conversion as "how far above absolute zero, then rescale the degrees" is what makes the one-step formula memorable instead of arbitrary.

There is an absolute scale with Fahrenheit-sized degrees, and it is called Rankine. Degrees Rankine are Fahrenheit plus 459.67: 0 °R is absolute zero, water freezes at 491.67 °R and boils at 671.67 °R. That means the first half of the formula on this page is a Fahrenheit-to-Rankine conversion wearing a different name, and the second half is the 5/9 that turns Rankine degrees into kelvins.

It survives in US mechanical and aerospace engineering, in thermodynamics texts written for that audience, and in parts of combustion and air-conditioning work, for the same reason Fahrenheit survives in weather forecasts: the surrounding numbers are already in Fahrenheit-sized units, and changing scale would mean restating all of them. If a calculation you are feeding is written in °R, that is a legitimate destination and no kelvin conversion is needed at all.

The demand for this conversion is narrow and specific. Physics and chemistry are set in SI, so a Fahrenheit reading taken from a US instrument has to be restated before it enters a gas law, a radiation term or an efficiency limit — all of which are ratios of absolute temperatures and return wrong answers on any relative scale. A notebook kept in Fahrenheit is a notebook that has to be converted twice.

Beyond that, the usual routes are lighting and imaging, where colour temperature is quoted in kelvin worldwide including in the United States, and international documentation, where a US-manufactured component’s operating range has to be restated for a customer working in SI. Weather and cooking never need it, and a forecast converted to kelvin is a sign the conversion was reached for before the question was read.

One Fahrenheit degree is exactly 5/9 of a kelvin, or 0.5556 K, and that ratio governs every difference. A component that warms by 40 °F has warmed by 22.2 K. A tolerance of ±2 °F is ±1.1 K. A specification holding a chamber within 5 °F holds it within 2.8 K. Nothing is added in any of these, because 459.67 is the gap between two zeros and a difference does not have one.

It bites hardest in the direction people rarely check. A coefficient quoted per °F is a smaller number than the same coefficient per kelvin, by a factor of 9/5: a material expanding 10 ppm/°F expands 18 ppm/K. Dropping a US-sourced per-°F figure into an SI calculation without that 1.8 is an eighty per cent error that will not announce itself, because the result stays entirely plausible.

Four points will test any implementation. 32 °F is 273.15 K, 212 °F is 373.15 K, −459.67 °F is 0 K, and 98.6 °F is 310.15 K. The first two must differ by exactly 100, because 180 Fahrenheit degrees span the same range as 100 kelvins, and if they do not then the 5/9 was applied to the wrong quantity.

The sharpest single check is 0 °F, which is 255.372 K. It is round in neither scale, so a wrong order of operations tends to produce something suspiciously tidy instead. Room temperature is the other one worth holding: 68 °F is exactly 293.15 K, because 68 °F is exactly 20 °C, which is why so many American standards and physics problems specify that particular number.

Every kelvin result from a real Fahrenheit reading is positive, because the scale has a floor and no thermometer reads below it. A conversion that returns a negative kelvin figure is arithmetically wrong, and the cause is almost always one of two things: the 459.67 was subtracted rather than added, or the multiplication was done before the addition.

The answers are also rarely round, and that is expected. Round Fahrenheit numbers were chosen by people, and nothing in the conversion preserves them: 70 °F is 294.261 K, 100 °F is 310.928 K, 350 °F is 449.817 K. The exceptions are the Fahrenheit figures that happen to be round in Celsius — 68 °F, 104 °F, 212 °F — and everything else carries a decimal tail that is not a defect.

459.67 and 5/9 are both exact by definition, so the conversion introduces no error of its own. What limits the answer is the reading. A whole-degree Fahrenheit measurement carries about ±0.28 K of implied uncertainty, so reporting 73 °F as 295.9278 K claims six digits from a figure that offered two.

The practice that survives review is to convert at full precision and round at the end, to the digits the instrument earned: 73 °F becomes 295.9 K, or 296 K if the source was a wall dial. Where the Fahrenheit figure was itself a converted round Celsius number — as 98.6 °F was from 37 °C — the kelvin answer should land exactly on 310.15, and a result that does not means something upstream was rounded twice.