Celsius, Fahrenheit and Kelvin: Formulas and Oven Marks

The exact formulas

°F = °C × 9/5 + 32

°C = (°F − 32) × 5/9

K = °C + 273.15Kelvin is written without a degree sign.

The factor 9/5 (or 1.8) appears because a Celsius degree is larger than a Fahrenheit degree. At standard pressure there are 100 Celsius degrees between freezing and boiling water (0 to 100), but 180 Fahrenheit degrees (32 to 212).

Worked example, Celsius to Fahrenheit: 25 °C × 1.8 = 45, and 45 + 32 = 77 °F. Fahrenheit to Celsius: 72 °F − 32 = 40, and 40 × 5/9 = 22.2 °C. When starting from Fahrenheit, always subtract 32 before you multiply.

A mental shortcut and how accurate it is

To estimate Fahrenheit from Celsius, double the number and add 30. The shortcut is exact at 10 °C and drifts as you move away from it:

That is fine for deciding what to wear, but not for ovens, cooking thermometers or anything where the exact value matters. The reverse shortcut, subtract 30 and halve, is off by a similar margin.

A few anchor points make it easier to judge a forecast quickly, and they show the pattern that every 5 °C step is a 9 °F step:

Temperature differences convert without the 32. A rise of 10 °C is a rise of 18 °F, because only the size of the degree matters when you are measuring a change.

Where the scales meet, and Kelvin

The two scales read the same at −40: (−40 × 9/5) + 32 = −72 + 32 = −40. It is the only temperature where they agree.

Kelvin is the absolute scale used in science. A kelvin is the same size as a Celsius degree, and zero is absolute zero: 0 K is −273.15 °C, or about −459.67 °F. Some formulas only work with absolute temperature. In the ideal gas law, pV = nRT, a temperature of 20 °C has to be written as 293.15 K. See the ideal gas law calculator for that formula in use.

• Water freezes at 0 °C (32 °F, 273.15 K) and boils at 100 °C (212 °F, 373.15 K) at standard sea-level pressure.
• A body temperature of 37 °C is 98.6 °F, the commonly quoted typical value.

Oven temperatures and gas marks

Recipes round oven temperatures to convenient numbers, so a published Fahrenheit value is often not the exact conversion. Gas marks, used on many British ovens, are a third scale layered on top.

Worked example: a US recipe says to bake at 375 °F. Subtract 32 to get 343, then multiply by 5/9 to get 190.6 °C. Set an oven that works in Celsius to 190 °C. For 350 °F the exact answer is 176.7 °C, which recipes and ovens treat as 180 °C, and 425 °F is 218.3 °C, which becomes 220 °C. Rounding to the nearest setting your oven offers is normal and rarely changes the result by much.

Charts for the lower gas marks differ slightly between sources, so follow the numbers printed in your recipe or on your oven dial when they are given.

A fan (convection) oven circulates hot air and cooks faster, so recipes usually ask for a lower setting. A common rule is about 20 °C lower, but check the recipe and your oven's manual. If the ingredient quantities need converting too, the recipe converter handles cups, grams and ounces.

Common mistakes

• Dropping the brackets. In °C = (°F − 32) × 5/9 the subtraction comes first. Computing 212 − 32 × 5/9 instead gives 194.2 rather than the correct 100.
• Adding 32 to a difference. A warming of 10 °C is 18 °F of change, not 50 °F.
• Using 273 where precision matters. Rounding to 273 is fine for everyday estimates, but scientific work uses 273.15.
• Writing a degree sign on kelvin. The unit is simply K, as in 293.15 K.
• Using the double-and-add-30 trick for baking. At oven temperatures the shortcut is off by 30 degrees or more, which is enough to burn or undercook.