Kelvin to Fahrenheit Converter, K ⇄ °F (and °C, °R)

What this converter does

This page converts any temperature between kelvin (K), the SI base unit of thermodynamic temperature, and degrees Fahrenheit (°F), with Celsius (°C) and Rankine (°R) shown alongside as bonus read-outs. The math rests on two international definitions: the 9/5 (1.8) ratio for the different size of one degree between the metric and imperial families, and the 459.67-degree offset that aligns the bottom of the Fahrenheit scale with absolute zero. Both constants are exact by NIST SP 811 and the BIPM SI Brochure (9th ed., 2019).

The kelvin matters wherever physics, chemistry, or engineering meets temperature. The ideal gas law is written PV = nRT with T in kelvin because the temperature must appear linearly. Blackbody radiation (the four-power dependence in the Stefan-Boltzmann law, the Planck spectrum, and astronomical colour-temperature work) is also defined in kelvin. Cryogenic physics lives in the dozens-of-kelvin range, and surface temperatures of stars are quoted in thousands of kelvin. This converter is the bridge between those absolute, scientific readings and the everyday °F values that HVAC thermostats, oven dials, and US weather forecasts use.

How to use this converter

1. Pick which side to enter. Type a value into either the Kelvin (K) field or the Fahrenheit (°F) field. The other field, plus the Celsius and Rankine read-outs, update instantly to match.
2. Check the sign of absolute zero. A negative Kelvin value would be physically impossible, the calculator accepts it and shows the math for documentation, but the absolute-zero note reminds you that 0 K is the theoretical floor.
3. Use a preset if you are starting from a reference point. The Quick Kelvin presets row covers absolute zero, the cosmic microwave background, liquid nitrogen, the water triple point, room temperature, body temperature, the water boiling point, an industrial oven, a hot exhaust, and the surface of the Sun.
4. Read all four cards. The output area shows K, °C, °F, and °R side by side; the K and °F cards are boxed solid (those are the two you control), the °C and °R cards are dashed (those are derived read-outs).
5. Copy the result. The Copy button between the two inputs writes all four numbers plus the forward and inverse formulas to your clipboard in one line, useful for lab notes or problem sets.
6. Sanity-check with the test table. The "Hand-verified test cases" table at the bottom of the tool lists eight anchor points that have been independently checked against NIST SP 811 and the BIPM SI Brochure.

Formulas

The kelvin was adopted as the SI base unit of thermodynamic temperature at the 13th General Conference on Weights and Measures (CGPM, 1967-1968) and re-anchored in 2019 to the Boltzmann constant k_B = 1.380649 × 10⁻²³ J/K exactly. The 273.15 offset between the Celsius and Kelvin scales, and the 459.67 offset between the Fahrenheit and Rankine scales, are likewise defined exactly by international agreement.

K → °F (forward)

The Fahrenheit scale begins at the temperature of a freezing brine solution in the original 1724 design by Daniel Gabriel Fahrenheit, with the boiling point of water at +212 °F and the freezing point at +32 °F. The scale's absolute zero, the temperature at which a perfect, idealised gas would exert zero pressure, sits at −459.67 °F. Converting from kelvin to Fahrenheit therefore requires a 9/5 ratio (180 Fahrenheit degrees span the same temperature interval as 100 kelvin) and the 459.67 offset:

°F = K × 9/5 − 459.67       (exact)

Example: 293.15 K (room temperature) × 9/5 − 459.67 = 527.67 − 459.67 = 68 °F.

°F → K (inverse)

To convert back, add the 459.67 offset and then multiply by 5/9:

K = (°F + 459.67) × 5/9     (exact)

Example: 100 °F = (100 + 459.67) × 5/9 = 559.67 × 5/9 = 310.927… K.

K → °C (bonus read-out)

The Celsius scale shifts the kelvin scale by exactly 273.15, because the zero of the Celsius scale is defined to be 273.15 K below the water triple point (0.01 °C = 273.16 K exactly, CIPM 1954):

°C = K − 273.15             (exact)

This is the same conversion our sibling Celsius-to-Kelvin calculator is built around, just with the subtraction on the other side of the equation.

K → °R (bonus read-out, Rankine)

The Rankine scale is the absolute Fahrenheit scale, with one degree the same size as one Fahrenheit degree but with zero at absolute zero:

°R = K × 9/5                (exact)
°R = °F + 459.67            (exact)

Rankine is rarely used outside some US engineering texts and certain thermodynamic textbooks, but it is the right scale for any equation that needs absolute temperature in an imperial-units context (steam tables for US power plants, for example).

Why the 9/5 and 273.15 are exact

The Celsius scale and the Kelvin scale share the same degree (a 1 °C temperature change is exactly equal to a 1 K change) but offset by 273.15. The Fahrenheit scale and the Rankine scale share the same degree (a 1 °F change is exactly equal to a 1 °R change) but offset by 459.67. The 9/5 ratio connecting the two families is also exact: the Celsius scale's 100 degrees between the freezing and boiling points of water at 1 atm equals 180 Fahrenheit degrees over the same interval, so 180 / 100 = 9/5. There is no measurement; the constants are defined, not measured.

Worked examples

Example 1, room temperature. Typical lab temperature is 20 °C. What is that in Kelvin and Fahrenheit?

K = 20 + 273.15 = 293.15 K. °F = 293.15 × 9/5 − 459.67 = 527.67 − 459.67 = 68 °F.

Verify: 20 °C × 9/5 + 32 = 68 °F. Both routes agree.

Example 2, boiling water. Fresh water boils at 100 °C at standard atmospheric pressure (101 325 Pa). What is that in kelvin and Fahrenheit?

K = 100 + 273.15 = 373.15 K. °F = 373.15 × 9/5 − 459.67 = 671.67 − 459.67 = 212 °F.

This is the same anchor the original Fahrenheit scale was built around (212 °F at the boiling point, 32 °F at the freezing point, 180 °F spread).

Example 3, liquid nitrogen. The boiling point of liquid nitrogen at 1 atm is 77.36 K. What is that in °F?

°F = 77.36 × 9/5 − 459.67 = 139.248 − 459.67 = −320.422 °F.

Cryogenic storage tanks and lab dewar flasks are routinely labelled with this value, because it is the temperature the liquid will settle at when vented to atmospheric pressure.

Example 4, jet-engine inlet. Modern high-bypass turbofan engines draw in air at roughly 1000 K at full thrust. What is that in °F?

°F = 1000 × 9/5 − 459.67 = 1800 − 459.67 = 1340.33 °F.

This is well above the melting point of aluminium (933 K ≈ 1220 °F) and below the surface temperature of the Sun (5778 K ≈ 9940 °F). Most high-temperature alloys in the hot section of the engine sit in the 1000 to 1500 K range.

Example 5, cosmic microwave background. The leftover blackbody radiation from the Big Bang is at 2.725 K. What is that in °F?

°F = 2.725 × 9/5 − 459.67 = 4.905 − 459.67 = −454.765 °F.

This is about 4.9 °F above absolute zero, close to the lower limit of what the Universe can ever reach in any region of macroscopic size.

Where kelvin shows up in real work

Physics laboratories. The kelvin is the unit of every thermodynamic quantity from 0 K to 10³² K (the Planck temperature). Calorimetry uses K to keep heat capacity and entropy tables consistent; cryogenics uses K because liquid helium (4.2 K), liquid nitrogen (77.36 K), and dry ice (194.65 K) all sit in the same decade; radiation thermometry uses K to calibrate pyrometers against blackbody cavities.

Astronomy. Stellar surface temperatures are quoted in kelvin. The Sun is 5778 K; cool red dwarfs are 2 500 to 3 500 K; the hottest O-stars exceed 30 000 K; the cosmic microwave background is 2.725 K. Colour-temperature ratios for incandescent lamps and LED fixtures are also in kelvin, a "warm white 2700K" LED bulb is the same colour as a 2 700 K blackbody.

Chemistry and reaction kinetics. The Arrhenius equation k = A·exp(−E_a/RT) uses T in kelvin. Plug in °C, and reaction rates appear to drop violently anywhere water freezes, even though the chemistry is unchanged. Osmotic pressure π = iMRT, gas densities ρ = PM/RT, and vapour-pressure relations all need absolute temperature.

Climate and atmospheric science. The lapse rate of the atmosphere is roughly 6.5 K per kilometer through the troposphere. IPCC climate projections report global-mean surface temperature in °C, but every atmospheric model runs internally in kelvin to keep solar and terrestrial radiation terms consistent in the energy-balance equations.

HVAC and refrigeration. The coefficient of performance (COP) of a refrigerator depends on the temperature of the cold reservoir and the ambient temperature, both must be in kelvin (or Rankine) for the Carnot limit to come out right. A freezer at 255 K in a 293 K kitchen has a Carnot COP of 293 / (293 − 255) = 7.7; real-world compressor cycles are typically 30 to 40% of that.

Industrial process control. Furnace temperature controllers often display in °C but use thermocouple tables in K. Calibration labs compare their reference standards (273.16 K for the water triple point, 692.677 K for the tin freezing point, 1 234.93 K for the copper point) to ITS-90 (International Temperature Scale of 1990).

Common mistakes

Confusing °R and K. A Rankine degree is the same size as a Fahrenheit degree (1 °R = 1 °F), but the zero is at absolute zero. A Kelvin degree is the same size as a Celsius degree (1 K = 1 °C), and the zero is also at absolute zero. The numerical value of a temperature in K is not the same as the numerical value in °R, multiplying by 9/5 converts. Substituting kelvin for Rankine in an imperial-units formula (or vice versa) is the single most common error in US-engineering thermodynamics.

Forgetting the 459.67 offset. The formula °F = K × 9/5 − 273.15 is wrong, it uses the Celsius offset where the Fahrenheit offset is required. The correct formula is °F = K × 9/5 − 459.67. The difference (459.67 − 273.15 = 186.52) will not catch itself.

Mixing signs on the inverse. The inverse formula is K = (°F + 459.67) × 5/9, not K = (°F − 459.67) × 5/9. Adding 459.67 cancels the offset between °F and °R; subtracting it would partly preserve it. This is the same kind of error as writing °C = (°F − 32) × 5/9 instead of °C = (°F − 32); everyone catches the second one in two seconds, but the first one slips past.

Rounding at 459.67. Some sources write 459.4, 459.5, or 460. The exact value, traceable to the Rankine scale definition (0 °F = 459.67 °R exactly), is 459.67. Using 459.4 introduces roughly 0.075 K of drift per calculation, which compounds across engineering tables.

Losing the degree on "kelvin". The SI symbol is K, never °K. The kelvin is an absolute scale, so the degree sign (which only makes sense for relative scales like °C and °F) is dropped. Many kitchen and weather sources still write "°K" by analogy with °C; the SI Brochure has been firm on this since 1967.

Treating 0 °F as "freezing". 0 °F is not the freezing point of water (that's 32 °F). 0 °F was originally the temperature of a saturated salt-water brine, and is now just a deeply cold winter reading, roughly −17.78 °C, or 255.37 K.

Frequently Asked Questions

What is the exact formula for Kelvin to Fahrenheit? The exact forward formula, defined by NIST SP 811 and the BIPM SI Brochure 9th ed. (2019), is °F = K × 9/5 − 459.67. The 9/5 (or 1.8) ratio converts the size of one degree between the metric and imperial families, and the 459.67 offset aligns the bottom of the Fahrenheit scale with absolute zero. Both constants are exact by international definition; no rounding or measurement uncertainty is involved. The inverse is K = (°F + 459.67) × 5/9.

Is 0 K really the coldest possible temperature? Yes. 0 K is the theoretical floor of thermodynamic temperature, the point at which a perfect, idealised gas would exert zero pressure and a perfect crystal would have zero entropy. The third law of thermodynamics states that 0 K can be approached but never fully reached. The coldest sustained temperature recorded in a laboratory is on the order of 100 picokelvin (10⁻¹⁰ K), achieved in laser-cooled rubidium Bose-Einstein condensates. 0 K corresponds to −273.15 °C exactly and −459.67 °F exactly.

Why is Kelvin the SI base unit instead of Celsius? The Celsius scale is defined relative to the freezing point of water and makes physical equations (the ideal gas law, the Stefan-Boltzmann law, the Planck spectrum, the Arrhenius equation) take their simplest form only when the temperature is offset to absolute zero. The kelvin is defined from absolute zero, so PV = nRT, P = σT⁴, and k = A·exp(−E_a/RT) all use T directly with no offset. The 2019 SI redefinition anchored the kelvin to k_B = 1.380649 × 10⁻²³ J/K exactly, replacing the previous definition based on the triple point of water (273.16 K).

Is Celsius-to-Kelvin the same as Fahrenheit-to-Kelvin? No, the offset is different. Celsius to Kelvin uses K = °C + 273.15 (the Celsius scale is 273.15 K below absolute zero). Fahrenheit to Kelvin uses K = (°F + 459.67) × 5/9 (the Fahrenheit scale is 459.67 °F below absolute zero, and one Fahrenheit degree is 5/9 of a kelvin degree). The Celsius offset 273.15 is not the same as the Fahrenheit offset 459.67; mixing them up is the most common cause of off-by-186.52 answers.

Where does 459.67 come from? The Fahrenheit scale's absolute zero is at −459.67 °F by definition, so 0 °F = 459.67 °R exactly. The 459.67 itself comes from the size of one Fahrenheit degree (5/9 of a kelvin degree) and the 273.15 K offset between Celsius and Kelvin: 273.15 K × 9/5 = 491.67 °R, then 491.67 °R − 32 °F (the freezing-point offset) = 459.67 °F. That is the origin of the magic number.

Why is the water triple point 273.16 K, not 273.15 K? The triple point of water, the unique temperature and pressure at which solid, liquid, and gaseous water can coexist in equilibrium, is exactly 0.01 °C by definition. The conversion °C = K − 273.15 gives 273.16 K, which is a different number from 273.15 K (the freezing point at 1 atm). The triple point sits 0.01 K above the freezing point because the freezing point is pressure-dependent (lower pressure raises it slightly) while the triple point is locked at 611.657 Pa. Modern metrology uses the triple point, not the freezing point, as the primary reference.

What is the Rankine scale used for? Rankine (°R) is the absolute Fahrenheit scale, with 0 °R = absolute zero and 1 °R = 1 °F. It is the imperial-units analogue of the kelvin. Rankine appears in some US steam tables, certain thermodynamics textbooks, and older engineering references that pair imperial units with absolute temperature. Modern SI practice has largely replaced Rankine with kelvin in international scientific literature, but the conversion °R = K × 9/5 (exact) is exact by definition.

What is the surface temperature of the Sun in Fahrenheit? The Sun's effective blackbody surface temperature is about 5778 K (the value used in the Stefan-Boltzmann law to reproduce the measured solar constant). Converting: °F ≈ 5778 × 9/5 − 459.67 ≈ 9940 °F. The Sun's core is much hotter (roughly 1.57 × 10⁷ K, ≈ 2.8 × 10⁷ °F) but that is not a surface temperature and is not visible from outside.

Can the Kelvin temperature ever be negative? Not in classical thermodynamics. The ground state of a quantum-mechanical system can have negative absolute temperature in a specific sense (inverted population, like in a laser), but that is a population-weighted definition rather than a "below absolute zero" reading. Physically, every system that exchanges heat with a thermal reservoir will move toward, not away from, 0 K. Asking for K < 0 in the converter is a useful sanity check that the inputs are sensible.

How accurate is the conversion? The conversion is exact. The 9/5 ratio, the 273.15 K offset, and the 459.67 °F offset are all defined by international agreement (NIST SP 811, BIPM SI Brochure, ITS-90). There is no measurement to propagate; the only floating-point arithmetic involved is the standard IEEE 754 round-off (which, for any reasonable input, is below 10⁻¹⁵ K). For any temperature that can be measured in a laboratory, the conversion error is many orders of magnitude smaller than the measurement error.

References

• NIST Special Publication 811 (2008, with updates). Guide for the Use of the SI Units. For the Kelvin to Fahrenheit Converter, K ⇄ °F (and °C, °R), National Institute of Standards and Technology. §B.8 (temperature), §B.9 (definitions of the kelvin), §B.6 (the 273.15 offset).
• BIPM SI Brochure (2019, 9th ed.). The International System of Units (SI). For the Kelvin to Fahrenheit Converter, K ⇄ °F (and °C, °R), Bureau International des Poids et Mesures, Sèvres. §2.3.1 (kelvin), §2.3.2 (Celsius), §2.3.3 (the 2019 redefinition).
• CGPM Resolution 3 (1967-1968). 13th General Conference on Weights and Measures. Original SI definition of the kelvin as 1/273.16 of the thermodynamic temperature of the triple point of water.
• Preston-Thomas, H. (1990). The International Temperature Scale of 1990 (ITS-90). Metrologia 27, 3 to 10. doi:10.1088/0026-1394/27/1/002.
• IUPAC (2007). Quantities, Units and Symbols in Physical Chemistry (Green Book), 3rd ed., RSC Publishing. §2.3 (temperature).
• CODATA 2018. Recommended Values of the Fundamental Physical Constants.