Temperature Conversion Calculator
Convert temperature between Celsius, Fahrenheit, Kelvin, Rankine, and Réaumur at once. See the from-Celsius formulas and a full step-by-step breakdown.
Why temperature conversion is different
Converting length, weight, or volume is a single multiplication: new value = old value × factor, because every unit in those families shares the same zero point (an empty length is 0 no matter which ruler you use). Temperature scales do not share a zero point — 0°C is the freezing point of water, 0°F is a much colder point, and 0 K is absolute zero itself. So converting temperature needs both a multiply (the degree sizes differ) and an add or subtract (the zero points differ).
Freezing point, boiling point, and absolute zero by scale
| Scale | Water freezes | Water boils | Absolute zero |
|---|---|---|---|
| Celsius (°C) | 0 | 100 | −273.15 |
| Fahrenheit (°F) | 32 | 212 | −459.67 |
| Kelvin (K) | 273.15 | 373.15 | 0 |
| Rankine (°R) | 491.67 | 671.67 | 0 |
| Réaumur (°Ré) | 0 | 80 | −218.52 |
The formulas, starting from Celsius
This calculator converts your input to Celsius first, then derives every other scale from that one Celsius value — five formulas instead of twenty:
Worked example: 50°C
- Already in Celsius, so °C = 50.
- Fahrenheit: 50 × 9/5 + 32 = 90 + 32 = 122°F.
- Kelvin: 50 + 273.15 = 323.15 K.
- Rankine: 90 + 491.67 = 581.67°R.
- Réaumur: 50 × 4/5 = 40°Ré.
Worked example: 100°C (boiling point of water)
Following the same steps: 100°C converts to 212°F, 373.15 K, 671.67°R, and 80°Ré — the values in the boiling-point row of the table above.
Worked example: converting from Fahrenheit
Starting from a Fahrenheit value instead flips the first step: °C = (°F − 32) × 5/9. For 98.6°F (average human body temperature): (98.6 − 32) × 5/9 = 66.6 × 5/9 = 37°C = 310.15 K.
The −40 crossover
Celsius and Fahrenheit are the only pair of common scales that intersect at a negative number: −40°C equals exactly −40°F. Setting °F = °C in the Celsius-to-Fahrenheit formula and solving confirms −40 is the unique solution — every other temperature reads differently on the two scales.
Which scale is used where
Celsius is the everyday scale across most of the world and in scientific reporting. Fahrenheit remains the everyday scale in the United States. Kelvin is the standard unit in physics and chemistry whenever an equation needs an absolute (never-negative) temperature, such as gas laws or blackbody radiation formulas. Rankine appears occasionally in US engineering thermodynamics as the Fahrenheit-sized absolute scale, and Réaumur survives mostly in older European (especially French and Russian) recipes and historical scientific texts.
Common mistakes
- Multiplying only, forgetting the add/subtract step. Unlike length or weight, temperature needs both.
- Swapping 9/5 and 5/9. Celsius-to-Fahrenheit multiplies by 9/5; Fahrenheit-to-Celsius multiplies by 5/9 (after subtracting 32).
- Using Celsius directly in physics formulas that require an absolute scale, like the ideal gas law, which needs Kelvin.
- Entering a value below absolute zero. Nothing can be colder than −273.15°C / 0 K / −459.67°F — a result on this side of that boundary describes a temperature that cannot physically exist.
Related calculators
Physics formulas that require an absolute temperature scale, such as the ideal gas law, always expect Kelvin, not Celsius — convert to Kelvin here first. Temperature conversion is itself a form of percentage-style scaling combined with an offset, unlike a plain multiply-only unit conversion.
Frequently asked questions
- Why is converting temperature different from converting length or weight?
- Most units only differ in scale, so converting is a single multiplication by a factor. Temperature scales differ in BOTH the size of one degree and where zero sits, so converting needs a multiply-and-add (or subtract) step, not just a multiply.
- What is the formula to convert Celsius to Fahrenheit?
- Fahrenheit equals Celsius times nine-fifths, plus 32. For example, 50°C times 9/5 is 90, plus 32 gives 122°F.
- What is the formula to convert Fahrenheit to Celsius?
- Celsius equals Fahrenheit minus 32, times five-ninths. For example, 122°F minus 32 is 90, times 5/9 gives 50°C.
- Why do Celsius and Fahrenheit meet at -40 degrees?
- -40°C and -40°F represent the same temperature because that is the single point where the two linear scales cross. Solving °C = (°C × 9/5) + 32 for °C gives exactly -40.
- What is absolute zero and why does it matter here?
- Absolute zero (0 Kelvin, -273.15°C, -459.67°F) is the coldest temperature physically possible, where molecular motion stops. This calculator rejects any input that would compute to a Kelvin value below zero, since it describes a temperature that cannot exist.
- What are Rankine and Réaumur scales used for?
- Rankine is an absolute scale (like Kelvin) but sized in Fahrenheit-sized degrees, occasionally used in older US engineering and thermodynamics contexts. Réaumur is a historical European scale, now rarely used outside some older French and Russian culinary and scientific texts.
- How does Kelvin relate to Celsius?
- Kelvin equals Celsius plus 273.15 — the degree size is identical to Celsius, only the zero point shifts to absolute zero instead of the freezing point of water.
- Do I need to convert to Celsius first before converting to another scale?
- This calculator does exactly that internally: it converts your input to Celsius first, then derives all five scales from that single Celsius value, which needs far fewer formulas than converting directly between every possible pair.