Temperature Unit Converter
Convert between Celsius, Fahrenheit, Kelvin, and Rankine using exact ITS-90 formulas. Unlike length or weight, temperature units are <em>affine</em> — each scale has both a multiplier and an offset — so this tool applies the proper formula automatically.
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What is temperature, and why are there four scales?
Temperature is a measure of the average kinetic energy of the particles in a substance — how vigorously molecules vibrate, rotate, and translate. The lowest possible temperature is absolute zero: the point at which all classical motion ceases and a quantum-mechanical zero-point remains. In SI units, absolute zero is exactly 0 K. The four scales in everyday and scientific use — Celsius (°C), Fahrenheit (°F), Kelvin (K) and Rankine (°R) — all measure the same physical quantity, but they differ in two design choices: where the zero point sits, and how big each degree is.
Because of those two choices, temperature conversion is fundamentally different from converting length or weight. You cannot simply multiply by a factor: 0 °C is not 0 °F, and doubling the Celsius value does not double the Fahrenheit value. Each conversion uses an affine formula of the form output = input × scale + offset. This page handles that arithmetic for you and shows the exact equation used.
The temperature scales, explained
Kelvin (K) — the SI base unit
The kelvin is the SI base unit of thermodynamic temperature. Since the 2019 redefinition, 1 K is fixed by setting the Boltzmann constant to exactly 1.380649 × 10⁻²³ J/K. The scale starts at absolute zero (0 K) and uses the same degree size as Celsius — 1 K = 1 °C — so the only difference between the two scales is the offset. Water freezes at 273.15 K and boils at 373.15 K (at 1 atm). Note: SI style writes "K", not "°K".
Celsius (°C) — the everyday metric scale
Celsius was originally defined by two reference points — 0 °C at the freezing point of water and 100 °C at the boiling point at standard atmospheric pressure. Today it is defined directly from the kelvin: T(°C) = T(K) − 273.15. It is the default civilian temperature scale almost everywhere outside the United States, used for weather forecasts, cooking, refrigeration, and clinical thermometers. Body temperature is roughly 37 °C, a refrigerator runs at about 4 °C, and a hot oven hits 220 °C.
Fahrenheit (°F) — the U.S. civilian scale
Daniel Gabriel Fahrenheit's 1724 scale fixed 32 °F at the freezing point of water and 212 °F at the boiling point, dividing the gap into 180 equal degrees — making each Fahrenheit degree only 5/9 the size of a Celsius degree. The conversion is °F = °C × 9/5 + 32 and reversed °C = (°F − 32) × 5/9. The United States, the Bahamas, the Cayman Islands, and a few territories still use Fahrenheit for daily weather and cooking. Body temperature is 98.6 °F, water freezes at 32 °F, and a typical summer afternoon hits the 80s or 90s °F.
Rankine (°R) — the imperial absolute scale
Rankine is to Fahrenheit what Kelvin is to Celsius: same degree size, but anchored at absolute zero. °R = °F + 459.67 and equivalently °R = K × 9/5. It survives in some U.S. thermodynamics and aerospace engineering texts where engineers prefer Fahrenheit-sized degrees but need an absolute scale for gas-law equations. Outside those niches it is rarely seen.
Real-world reference points across all four scales
- Absolute zero: 0 K = −273.15 °C = −459.67 °F = 0 °R. The lowest possible temperature; particle motion stops in the classical sense. Lab cryostats reach within nanokelvin of this limit.
- Water freezing point: 273.15 K = 0 °C = 32 °F = 491.67 °R, at standard atmospheric pressure. Roads ice over below this point; salt is added to lower it.
- Refrigerator interior: Most home fridges hold 1–4 °C (34–39 °F, 274–277 K) — cool enough to slow bacterial growth without freezing food.
- Comfortable room: 20–22 °C = 68–72 °F = 293–295 K. Most thermostats settle here. A swing of 1 °C is noticeable but mild; a swing of 1 °F is barely perceptible.
- Human body temperature: Normal core temperature is 37 °C = 98.6 °F = 310.15 K. A fever begins around 38 °C / 100.4 °F. Hypothermia sets in below 35 °C / 95 °F.
- Water boiling point: 373.15 K = 100 °C = 212 °F = 671.67 °R, at 1 atm. The boil point drops about 1 °C per 285 m of altitude — pasta cooks slower in Denver than in Los Angeles.
- Oven and cooking ranges: A moderate oven runs at 180 °C (350 °F, 453 K); a hot pizza oven 250–300 °C (480–570 °F).
- Industrial and scientific: Steel melts around 1,500 °C (2,730 °F, 1,773 K). The Sun's surface is roughly 5,800 K (5,500 °C, 9,930 °F). A liquid-nitrogen Dewar holds 77 K (−196 °C, −321 °F).
How much is 1 unit of each in Kelvin?
| Unit | Value in Kelvin (K) |
|---|---|
| 1 K (Kelvin) | 1 Pa |
| 1 °C (Celsius) | 1 Pa |
| 1 °F (Fahrenheit) | 0.5555555555555556 Pa |
| 1 °R (Rankine) | 0.5555555555555556 Pa |
Frequently asked questions about temperature units
Why does temperature need an offset, not just a multiplier?
Length, mass, and pressure all start at the same physical zero — 0 m = 0 ft = 0 km. Temperature scales were invented before absolute zero was understood, so each one chose a convenient zero point: water's freezing point (Celsius), an arbitrary brine mixture (Fahrenheit), or absolute zero itself (Kelvin, Rankine). Because the zero points differ, a temperature conversion needs both a scale factor and a shift. The general formula is T_target = (T_source × source_scale + source_offset − target_offset) ÷ target_scale, with all values referenced to a common base — Kelvin in this tool.
What is absolute zero, and why does it matter?
Absolute zero is the lower bound of thermodynamic temperature: 0 K, −273.15 °C, or −459.67 °F. At this limit, the entropy of a perfect crystal would be zero (the third law of thermodynamics) and classical particle motion would cease. The kelvin and Rankine scales start there, which makes ratios meaningful: 600 K is exactly twice as energetic as 300 K. Ratios of Celsius or Fahrenheit values have no such meaning — 20 °C is not "twice as hot" as 10 °C.
Why do scientists use Kelvin instead of Celsius?
Most physics equations — the ideal gas law (PV = nRT), Wien's displacement law, the Stefan–Boltzmann law, the Maxwell–Boltzmann distribution — require an absolute temperature, because they involve ratios or exponentials of T. Plug a Celsius value into PV = nRT and the math breaks at T below 0 °C, where pressure would supposedly become negative. Kelvin avoids that by starting at absolute zero. Engineers convert to kelvin for any equation that uses T as a multiplier or in an exponent.
How do I convert Celsius to Fahrenheit in my head?
Exact formula: °F = °C × 9/5 + 32. Quick mental approximation: double the Celsius value and add 30. Example: 20 °C → 2×20+30 = 70 °F (true value 68 °F). 30 °C → 90 °F (true 86 °F). The approximation is within 4 °F across normal weather range. For precise work, use the converter above.
What temperature is the same in Celsius and Fahrenheit?
−40 °C = −40 °F. It is the only point where the two scales meet, and it falls out of the algebra: setting x = x × 9/5 + 32 gives x = −40. Useful trivia for cold-weather engineers and a popular pub-quiz question.
Why does water freeze at 273.15 K and not 273 K exactly?
When the kelvin was redefined in 2019 around the Boltzmann constant, the freezing point of water (more precisely, the ice point at standard pressure) was no longer a defining reference. It became an experimentally measured quantity that happens to land at 273.15 K. The earlier triple-point definition fixed water's triple point at exactly 273.16 K — 0.01 K above the ice point — which is why both numbers appear in older textbooks.
Is body temperature really 98.6 °F?
Not exactly. The 98.6 °F figure is an 1851 average from German physician Carl Reinhold August Wunderlich. Modern studies put the average closer to 36.6 °C / 97.9 °F, with normal individual variation between 36.1–37.2 °C (97.0–99.0 °F) depending on time of day, sex, and measurement site. A clinical fever begins above 38 °C / 100.4 °F.
How does altitude affect the boiling point of water?
Boiling occurs when vapour pressure equals atmospheric pressure. As altitude rises, atmospheric pressure drops, so water boils at a lower temperature — roughly 1 °C lower per 285 m of elevation gain near sea level. In Mexico City (2,240 m) water boils around 92 °C; on Mount Everest's summit, near 70 °C. Cooking times must be lengthened accordingly, which is why high-altitude bakers tweak recipes.
What's the difference between Kelvin and degrees Kelvin?
There is no "degree Kelvin". The 13th General Conference on Weights and Measures (CGPM, 1967) dropped the degree sign: a temperature is written 300 K, not 300 °K, and a difference is 5 K, not 5 °K. Celsius, Fahrenheit, and Rankine still use the degree sign (°C, °F, °R) because they are scales, not absolute SI units. Style guides like NIST SP 811 are explicit about this.
Can I link to a specific temperature conversion?
Yes. The URL updates as you change units and values. Example: ?from=C&to=F&x=37 shares a body-temperature conversion. Copy the address bar after any conversion to share or bookmark.
References
Dedicated converter pages
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