Unit converters · Temperature
Convert Celsius, Fahrenheit, and kelvin
Celsius and Fahrenheit are offset; you do not multiply a “degree” like a meter. Every conversion goes through kelvin. Below 0 K there is no thermodynamic temperature.
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How the calculator works
The input is first expressed in kelvin, the SI unit of thermodynamic temperature. It is then converted to °C or °F. The formulas are affine (offset + slope), not a simple factor. That is why 20 °C is not “20 times hotter” than 1 °C, and why a 1 °C gap equals a 1 K gap, while 1 °F is smaller (5/9 K).
Formula and method
T(K) = t(°C) + 273,15
SI relation between Celsius and kelvin (same unit gap).
t(°C) = (t(°F) − 32) × 5/9
Offset 32 and slope 5/9 (water: 32 °F ↔ 0 °C, 212 °F ↔ 100 °C).
t(°F) = T(K) × 9/5 − 459,67
Equivalent via kelvin; the implementation goes through an intermediate °C.
The kelvin is defined by BIPM (Boltzmann constant in the current SI; the practical scale remains T/K = t/°C + 273.15 for everyday conversion). Fahrenheit is not an SI unit; the 5/9 and 32 factors are the usual scale relations. Any arrival temperature corresponding to T < 0 K is rejected: that is not a forgotten “deep freeze,” it is absolute zero.
Worked example
20 °C to Fahrenheit
x = 20, from °C to °F.
- Kelvin: 20 + 273.15 = 293.15 K.
- Celsius unchanged: 20.
- Fahrenheit: 20 × 9/5 + 32 = 36 + 32 = 68 °F.
68 °F (293.15 K). Water’s historical boiling point at 1 atm is 100 °C = 212 °F.
−300 °C
Below −273.15 °C.
- Kelvin = −300 + 273.15 = −26.85 K < 0 → reject.
Input refused (under 0 K).
Input notes
- Value
- A number, possibly negative in °C or °F. −40 is accepted (the point where °C and °F coincide). −300 °C is not.
- From
- C = Celsius, F = Fahrenheit, K = kelvin (no degree sign).
- To
- Display scale of the result. Intermediate kelvin is also returned.
Assumptions and limits
Assumptions
- The 273.15 and 5/9 relations are those of the usual international scales.
- We convert a temperature, not a gap: for a Δt, 1 °C = 1 K and 1 °F = 5/9 K, without the +32.
- 0 K is the lower accepted bound.
Limits
- No Rankine or Réaumur scale.
- No ITS-90 correction for a metrology lab.
- A gap (“the temperature rose 10 °F”) does not convert with the same form as 10 °F “on the scale.”
How to read the result
20 °C = 68 °F is a cool-ish US indoor reading. For an oven, 180 °C ≈ 356 °F: convert the setpoint; do not multiply 180 by 1.8 without adding 32. For a gap (“+2 °C”), do not add 32: +2 °C = +2 K = +3.6 °F.
Common mistakes
Multiplying by 1.8 without adding 32 (or the reverse).
t(°F) = t(°C) × 9/5 + 32. Both terms are needed for a temperature, not for a gap.
Writing “°K.”
The SI symbol is K, without a degree. You say “293 kelvins.”
Converting a 10 °C gap as if it were 10 °C on the scale (with +32).
A gap: multiply by 9/5 to get °F. No 32.
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Frequently asked questions
Why go through kelvin?
For one thermodynamic scale, and to refuse what is under absolute zero.
Celsius and Fahrenheit are translations (and, for F, a scale change). Kelvin anchors zero. Implementing C ↔ F directly would give the same numeric result, but K makes the 0 K bound obvious and stays faithful to SI (BIPM).
−40 °C is how many °F?
−40 °F. That is where the two scales cross.
(−40) × 9/5 + 32 = −72 + 32 = −40. Not a bug. In kelvin: −40 + 273.15 = 233.15 K, well above 0.
0 K is how many °C?
−273.15 °C.
That is the usual conversion definition. Typing −273.15 °C toward K gives 0. Below, the math stops. That does not stop a badly calibrated thermometer from displaying anything: the tool refuses thermodynamic inconsistency, not a sensor error.
Do 100 °C always make 212 °F?
On the historical Celsius and Fahrenheit water scales at 1 atm, yes. That is a scale identity, not a measurement of your pot.
Real boiling depends on pressure. The 100 ↔ 212 conversion is a scale identity, useful for notices. A kitchen thermometer converts the same way, without knowing your altitude.
Author and update
Written by Rédaction HexaCalc (editorial team). Content last updated: August 25, 2026. No third-party medical or financial review is claimed.
- NIST Guide to the SI, Appendix B: Conversion Factors — National Institute of Standards and Technology
- The International System of Units (SI) — Bureau international des poids et mesures (BIPM)
Other units, linear
Length, mass, area, and volume convert by a factor, without an offset. Temperature is the odd case.
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