How to convert Celsius, Fahrenheit, and Kelvin

Why temperature is not a simple multiplication

Most unit conversions are one multiplication. Inches to centimeters, pounds to kilograms, and miles to kilometers all work by multiplying by a fixed number, because both units start counting from the same zero. Zero inches is zero centimeters.

Temperature scales do not share a zero. On the Celsius scale, 0 is the ice point of water. On the Fahrenheit scale, zero was originally set from a brine mixture, which puts it about 32 Fahrenheit degrees below the freezing point of water. So a Celsius-to-Fahrenheit conversion needs two steps: a scale factor that accounts for the different degree sizes, and an offset that accounts for the different zeros.

That distinction, offset versus ratio, is the key idea in this whole guide. Celsius and Fahrenheit differ in both. Celsius and kelvin differ only in the offset, because a degree Celsius and a kelvin are the same size.

The formulas

Between Celsius and Fahrenheit, a Celsius degree is 1.8 times as large as a Fahrenheit degree: there are 180 Fahrenheit degrees between water freezing and boiling, but only 100 Celsius degrees. Combine that with the 32 degree offset:

Fahrenheit = Celsius x 9/5 + 32. Celsius = (Fahrenheit - 32) x 5/9.

Between Celsius and kelvin there is only the offset: Kelvin = Celsius + 273.15, and Celsius = Kelvin - 273.15. NIST describes the degree Celsius as equal in magnitude to the kelvin, with Celsius temperature defined as the thermodynamic temperature minus 273.15 K.

To go between Fahrenheit and kelvin, convert through Celsius: subtract 32, multiply by 5/9, then add 273.15. The order of operations matters. On the way from Fahrenheit, you subtract the 32 before multiplying. On the way to Fahrenheit, you multiply before adding the 32.

• Celsius to Fahrenheit: multiply by 9/5, then add 32
• Fahrenheit to Celsius: subtract 32, then multiply by 5/9
• Celsius to kelvin: add 273.15
• Kelvin to Celsius: subtract 273.15
• Fahrenheit to kelvin: (F - 32) x 5/9 + 273.15

Worked examples: body, kitchen, and weather

Body temperature: 37°C x 9/5 = 66.6, and 66.6 + 32 = 98.6°F. In kelvin, 37 + 273.15 = 310.15 K. Going the other way, 98.6°F gives (98.6 - 32) x 5/9 = 37°C. A reading of 100.4°F comes out to 38°C.

Oven temperatures are where most people reach for a converter. 350°F is (350 - 32) x 5/9 = 176.7°C. 400°F is 204.4°C and 425°F is 218.3°C. In the other direction, a recipe that says 180°C is 180 x 9/5 + 32 = 356°F, 200°C is 392°F, and 220°C is 428°F. Ovens vary and most dials move in steps, so a result like 176.7°C is normally rounded to a setting you can actually dial in.

Weather: 35°C is 95°F, 25°C is 77°F, 20°C is 68°F, 15°C is 59°F, and -10°C is 14°F. Room temperature, 72°F, is (72 - 32) x 5/9 = 22.2°C.

The EveryFix Temperature Converter does these steps for you and rejects any value below absolute zero, but knowing the formula lets you sanity-check a result quickly.

• 37°C = 98.6°F = 310.15 K
• 350°F = 176.7°C; 400°F = 204.4°C; 425°F = 218.3°C
• 180°C = 356°F; 200°C = 392°F; 220°C = 428°F
• 35°C = 95°F; 25°C = 77°F; 20°C = 68°F; 15°C = 59°F; -10°C = 14°F
• 72°F = 22.2°C

The -40 crossover

There is exactly one temperature where the Celsius and Fahrenheit numbers are identical, and it is -40. You can find it by setting the two equal. If F = C, then C = C x 9/5 + 32. Subtract C x 9/5 from both sides: C - C x 9/5 = 32, so C x (1 - 9/5) = 32, so C x (-4/5) = 32, and C = 32 x (-5/4) = -40.

Check it: -40 x 9/5 = -72, and -72 + 32 = -40. In the other direction, (-40 - 32) x 5/9 = -72 x 5/9 = -40. The two scales cross there because Fahrenheit starts 32 degrees higher at the freezing point, but its degrees are smaller, so the gap shrinks as you go colder and closes at -40.

It is a handy anchor for checking your arithmetic. If a conversion of something near -40 does not come out near -40 on both scales, you have made a slip, usually forgetting the 32 or applying it in the wrong order.

Kelvin and absolute zero

Kelvin is the SI base unit of thermodynamic temperature. Since the 2019 redefinition, NIST states that its size is set by fixing the Boltzmann constant at exactly 1.380649 x 10^-23 joules per kelvin, instead of by the triple point of water as before. For everyday conversion this changes nothing: the offset from Celsius is still 273.15, and a kelvin is the same size as a Celsius degree.

Kelvin has no degree symbol and is written as K, not degrees K. Its zero is absolute zero, the lower limit of the thermodynamic temperature scale, so there are no negative kelvin temperatures on the ordinary scale. Absolute zero is 0 K, which is -273.15°C and about -459.67°F. That is why the converter refuses to accept anything colder.

Some conversions in kelvin: water freezes at 273.15 K (0°C) and boils at 373.15 K (100°C) at standard pressure. Room temperature of 20°C is 293.15 K. A scientific reading of 300 K is 26.85°C. Fahrenheit 0°F is 255.37 K.

• 0 K = -273.15°C = about -459.67°F (absolute zero)
• 273.15 K = 0°C = 32°F (water freezes)
• 293.15 K = 20°C = 68°F
• 310.15 K = 37°C = 98.6°F
• 373.15 K = 100°C = 212°F (water boils at standard pressure)

Offset versus ratio: temperatures and temperature differences

The offset-versus-ratio idea has a practical consequence. A temperature (a point on the scale) and a temperature difference (a gap between two points) convert differently. The 32 and 273.15 offsets belong only to points. A difference ignores the offset because it cancels out.

A rise of 10 degrees Celsius is the same size as a rise of 10 kelvins, and as a rise of 18 degrees Fahrenheit (10 x 9/5). You only apply the 9/5 and skip the 32. If a heater warms a room by 5°C, that is a 9°F rise, not 41°F.

Ratios are also not meaningful on Celsius or Fahrenheit. Is 40°C twice as hot as 20°C? In kelvin, 20°C is 293.15 K and 40°C is 313.15 K, a ratio of only about 1.07. Only kelvin, whose zero is real absolute zero, supports statements like twice as much thermal energy per particle. That is why physics formulas such as the gas law use kelvin instead of Celsius.

Mental shortcuts and where they fail

For a rough Celsius to Fahrenheit estimate, double the Celsius value and add 30. It gives 80 for 25°C when the true value is 77, and 70 for 20°C against a true 68. For Fahrenheit to Celsius, subtract 30 and halve: 86°F gives 28 against a true 30. The shortcut is fine for weather chat, since the error stays small near everyday temperatures.

It breaks down at extremes, and it is never right for cooking, lab work, or anything safety-related, where you should use the exact formula or the converter. The shortcut is also wrong at -40, where the correct answer is itself -40.

Common mistakes

Most wrong conversions come from a few slips.

• Adding 32 before multiplying by 9/5 when converting Celsius to Fahrenheit.
• Forgetting to subtract 32 first when converting Fahrenheit to Celsius.
• Using 273 as a rounded kelvin offset for work that needs the exact 273.15.
• Applying the 32 or 273.15 offsets to a temperature difference.
• Writing degrees kelvin, or entering a value below absolute zero.
• Treating Celsius or Fahrenheit values as ratios, such as calling 40°C twice as hot as 20°C.