Temperature conversion (°C °F K)
Use the formulas for any value; the table lists handy reference points.
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| Point | °C | °F | K |
|---|---|---|---|
| Absolute zero | -273.15 | -459.67 | 0 |
| Water freezes | 0 | 32 | 273.15 |
| Cool room | 15 | 59 | 288.15 |
| Room temperature | 20 | 68 | 293.15 |
| Body temperature | 37 | 98.6 | 310.15 |
| Water boils (1 atm) | 100 | 212 | 373.15 |
| Oven moderate | 180 | 356 | 453.15 |
| Formula C→F | — | °F = °C × 9/5 + 32 | — |
| Formula F→C | — | °C = (°F − 32) × 5/9 | — |
| Formula C→K | — | K = °C + 273.15 | — |
Notes
- Kelvin never uses a degree symbol in SI writing (write 300 K, not 300 °K).
- Boiling point shifts with altitude/pressure.
Formulas and why they work
Temperature conversion rests on two formulas: °F = °C × 9/5 + 32 and K = °C + 273.15. The Fahrenheit formula is affine rather than purely multiplicative because the scales disagree about zero: 0 °C, the freezing point of water, is 32 °F. The factor 9/5 reflects degree sizes — the 100 Celsius degrees between freezing and boiling span 180 Fahrenheit degrees, so each Celsius degree equals 1.8 Fahrenheit degrees. Kelvin keeps the Celsius degree size but moves the zero to absolute zero, which is why −273.15 °C = 0 K (row one of the table). Never convert with a bare ratio: unlike length, temperature scales have arbitrary zeros, so the offset is not optional — and route F→K through °C as an intermediate step.
Common mistakes
Most conversion errors come from a handful of habits. Forgetting the +32 (or −32) offset is the classic one: 20 °C is 68 °F, not 36 °F. Inverting the 9/5 factor is the second — multiplying by 5/9 when you should multiply by 9/5 turns 100 °C into 55.6 instead of 212 °F. A subtler trap is confusing a temperature with a temperature interval: a rise of 20 °C is a rise of 36 °F with no +32, because offsets cancel in differences. Rounding too early accumulates drift, so keep full precision until the final step. Finally, use −40 as a self-check: it is the unique point where both scales read the same, so any formula that fails there is wrong.
Practical reference points
The rows of the table double as a mental ruler. Water freezes at 0 °C / 32 °F; a cool room sits near 15 °C / 59 °F; typical room temperature is 20 °C / 68 °F; body temperature is 37 °C / 98.6 °F; and water boils at 100 °C / 212 °F at 1 atmosphere. For baking, a moderate oven is 180 °C / 356 °F. These anchors let you sanity-check any conversion instantly — if a result places a comfortable room below freezing, something went wrong. For quick mental math on the road, use the traveler's shortcut: double the Celsius value and add 30, which approximates Fahrenheit well around 10–30 °C (20 °C → 70, actual 68).
Regional and standard differences
Celsius is the everyday scale almost everywhere and the standard in all scientific publication; Fahrenheit survives mainly in daily life in the United States and a few other territories. Kelvin is different in kind: it is the SI base unit of temperature, used in physics and thermodynamics because its zero is true zero — no negative temperatures in the ordinary sense. Interval differences are quoted interchangeably in °C or K, since one kelvin equals one Celsius degree exactly. Note also that the boiling point depends on pressure: the 100 °C figure holds at 1 atmosphere, while at altitude water boils several degrees cooler, so recipes and lab instructions assume standard pressure unless stated otherwise.
Frequently asked questions
- How do I convert Celsius to Fahrenheit?
- Multiply by 9/5 and add 32: °F = °C × 9/5 + 32. For example, 20 °C = 68 °F.
- How do I convert Fahrenheit to Celsius?
- Subtract 32, then multiply by 5/9: °C = (°F − 32) × 5/9. So 98.6 °F = 37 °C.
- How do you convert Celsius to Kelvin?
- Add 273.15: K = °C + 273.15. Absolute zero is 0 K, equal to −273.15 °C.