Temperature tells you how hot or cold something is, but the number you read depends on the scale. Water freezes at 0 on the Celsius scale, at 32 on the Fahrenheit scale and at 273.15 on the Kelvin scale. All three describe the same physical state, and converting between them takes one multiplication and one addition.
This page explains where each scale comes from, the fixed points that anchor them, the conversion formulas, and how to avoid the classic mistake of mixing up a temperature reading with a temperature change.
Contents
- The three scales and how they were born
- Reference points
- Conversion formulas
- Temperature readings and temperature changes
- Worked examples
- Quick mental estimates
- Other scales you may meet
- Common mistakes
- Practice problems
- Frequently asked questions
- Related calculators
- See also
The three scales and how they were born
Fahrenheit (°F). The German physicist Daniel Gabriel Fahrenheit built reliable mercury thermometers and published his scale in 1724. He set 0 °F at the temperature of a freezing mixture of ice, water and salt, and used the temperature of the human body as a second anchor. The scale was later adjusted so that water freezes at 32 °F and boils at 212 °F, exactly 180 degrees apart.
Celsius (°C). In 1742 the Swedish astronomer Anders Celsius proposed a scale divided into 100 degrees between the freezing and boiling points of water. His original version was upside down, with 0 at boiling and 100 at freezing. It was reversed soon after, giving the scale we use today: 0 °C for freezing and 100 °C for boiling at normal sea level pressure. Its degree is also called a centigrade degree.
Kelvin (K). In 1848 William Thomson, later Lord Kelvin, proposed an absolute scale. It starts at absolute zero, the lowest possible temperature, where particles have the least thermal motion that physics allows. The kelvin has the same size as the Celsius degree, so the two scales differ only by a shift. Since 2019 the kelvin is defined by fixing the Boltzmann constant, $latex k = 1.380649\times 10^{-23}$ J/K. Note that we write 300 K, not 300 °K: the kelvin is a unit, not a "degree".
Reference points
| Event | °C | °F | K |
|---|---|---|---|
| Absolute zero | -273.15 | -459.67 | 0 |
| The two scales agree | -40 | -40 | 233.15 |
| Water freezes (normal pressure) | 0 | 32 | 273.15 |
| Triple point of water | 0.01 | 32.018 | 273.16 |
| Comfortable room | 20 | 68 | 293.15 |
| Human body (typical) | 37 | 98.6 | 310.15 |
| Water boils (normal pressure) | 100 | 212 | 373.15 |
Water boils at just under 100 °C (about 99.97 °C) at standard sea level pressure, and much lower at altitude, so treat 100 °C as a handy anchor and not as a universal law.
Conversion formulas
The size of the degrees is what matters. Between freezing and boiling, Celsius has 100 steps and Fahrenheit has 180, so one Celsius degree equals 1.8 Fahrenheit degrees, which is $latex \frac{9}{5}$. Fahrenheit also starts 32 degrees higher.
$$°F = \frac{9}{5}\,°C + 32$$
$$°C = \frac{5}{9}\,(°F - 32)$$
$$K = °C + 273.15$$
$$°C = K - 273.15$$
Joining them gives $latex K = \frac{5}{9}(°F + 459.67)$. In the first formula you multiply first and add after. In the second you subtract first and multiply after. Doing it in a different order is the most common source of wrong answers.
Three thermometers, one temperature
Move the slider, type in any of the three boxes, or tap a landmark. The mercury rises to the same height on every scale.
Temperature readings and temperature changes
Adding 32 only applies to a reading. A change in temperature has no fixed point, so only the size of the degree matters:
$$\Delta T_{°F} = 1.8\,\Delta T_{°C}$$
$$\Delta T_{K} = \Delta T_{°C}$$
Heating water from 20 °C to 80 °C is a change of 60 °C, which is 60 K or 108 °F. It is not 140 °F.
Physics also cares about ratios. The ideal gas law and the laws of radiation use Kelvin because only that scale has a true zero. Going from 20 °C to 40 °C looks like doubling, but in kelvin it is 293.15 K to 313.15 K, an increase of about 6.8%.
Worked examples
Example 1: Celsius to Fahrenheit
Convert 25 °C to Fahrenheit.
$$°F = \frac{9}{5}(25) + 32 = 45 + 32 = 77\ °F$$
Example 2: Fahrenheit to Celsius
Convert 104 °F to Celsius.
$$°C = \frac{5}{9}(104 - 32) = \frac{5}{9}(72) = 40\ °C$$
Example 3: Kelvin to both
Convert 300 K to Celsius and Fahrenheit.
$$°C = 300 - 273.15 = 26.85\ °C$$
$$°F = \frac{9}{5}(26.85) + 32 = 80.33\ °F$$
Example 4: where the scales meet
At which temperature do Celsius and Fahrenheit show the same number? Set $latex °F = °C = x$.
$$x = \frac{9}{5}x + 32 \;\Rightarrow\; -\frac{4}{5}x = 32 \;\Rightarrow\; x = -40$$
So -40 °C equals -40 °F.
Example 5: a fever
A thermometer reads 100.4 °F. In Celsius:
$$\frac{5}{9}(100.4 - 32) = \frac{5}{9}(68.4) = 38\ °C$$
Doctors often use 38 °C (100.4 °F) as the fever threshold.
Example 6: a hot day
A weather app in Miami shows 95 °F. In Celsius:
$$\frac{5}{9}(95 - 32) = \frac{5}{9}(63) = 35\ °C$$
Quick mental estimates
For a rough Celsius to Fahrenheit conversion, double the Celsius value and add 30. For Fahrenheit to Celsius, subtract 30 and halve. These shortcuts are close in everyday weather and drift away at extremes.
| Reading | Mental shortcut | Exact value | Error |
|---|---|---|---|
| 25 °C | 2 × 25 + 30 = 80 °F | 77 °F | 3 °F |
| 10 °C | 2 × 10 + 30 = 50 °F | 50 °F | 0 °F |
| 68 °F | (68 - 30) ÷ 2 = 19 °C | 20 °C | 1 °C |
| 95 °F | (95 - 30) ÷ 2 = 32.5 °C | 35 °C | 2.5 °C |
Use the exact formulas for homework, lab reports and anything that needs a number you can trust.
Other scales you may meet
The Rankine scale (°R) is the Fahrenheit version of the Kelvin scale. Its degree has the size of a Fahrenheit degree and its zero is absolute zero, so $latex °R = °F + 459.67$. Water freezes at 491.67 °R. Some American engineering fields still use it. The Réaumur scale, which put water's freezing point at 0 and its boiling point at 80, is obsolete.
Common mistakes
- Adding 32 before multiplying. In °C to °F, multiply by 9/5 first and add 32 last.
- Swapping 5/9 and 9/5. Fahrenheit degrees are smaller, so the Fahrenheit number is the larger one (above -40). If your answer goes the wrong way, flip the fraction.
- Adding 32 to a temperature change. Differences use only the 1.8 factor.
- Writing °K. The correct symbol is K, with no degree sign.
- Using Celsius or Fahrenheit in gas laws. Convert to kelvin first.
- Rounding 273.15 to 273 too early. It is fine for rough work, but keep the full value in formulas where the difference matters.
Practice problems
1. Convert 68 °F to Celsius.
$latex \frac{5}{9}(68-32) = \frac{5}{9}(36) = $ 20 °C.
2. Convert -10 °C to Fahrenheit.
$latex \frac{9}{5}(-10)+32 = -18+32 = $ 14 °F.
3. Express absolute zero (0 K) in Celsius and Fahrenheit.
$latex 0-273.15 = $ -273.15 °C, and $latex \frac{9}{5}(-273.15)+32 = $ -459.67 °F.
4. Convert 350 K to Celsius.
$latex 350-273.15 = $ 76.85 °C.
5. Convert 212 °F to kelvin.
First $latex \frac{5}{9}(212-32) = 100$ °C, then $latex 100+273.15 = $ 373.15 K.
6. A sample cools by 15 K. By how many degrees Fahrenheit does it cool?
A change in kelvin equals a change in Celsius, and $latex 15\times 1.8 = $ 27 °F.
Frequently asked questions
Why does the United States use Fahrenheit?
The Fahrenheit scale was already established in the English-speaking world when the Celsius scale became popular, and the United States never made the switch for everyday weather, cooking and body temperature. American laboratories and physics classes use Celsius and kelvin.
Can the temperature drop below 0 K?
No. Absolute zero is the lower limit, and it cannot be reached exactly in a real experiment. Physicists have cooled matter to within a tiny fraction of a kelvin above it.
Is it "degrees Kelvin"?
No. Since 1967 the unit is simply the kelvin, with the symbol K. Celsius and Fahrenheit use degrees: °C and °F.
Why is 37 °C the normal body temperature?
It is an average. Healthy people vary by a few tenths of a degree depending on the person, the time of day and where the measurement is taken.
Which scale has the smallest degree?
The Fahrenheit degree is the smallest of the three. One Fahrenheit degree is $latex \frac{5}{9}$ of a Celsius degree or of a kelvin, which is why weather reports in Fahrenheit can describe the air in finer whole-number steps. For science, the size of the degree matters less than having a zero that means something, and that is the advantage of the Kelvin scale.
Do I need Kelvin outside a physics class?
Mostly in chemistry and physics, wherever a formula multiplies or divides by temperature: gas laws, heat engines, radiation, and reaction rates. For weather, cooking and medicine, Celsius or Fahrenheit is enough.