Temperature Conversion Formulas: Celsius, Fahrenheit, and Kelvin

Published 2026-10-01

Temperature conversion is one of the few places where a formula is genuinely easier than memorization. There are only three scales in everyday use: Celsius, Fahrenheit, and Kelvin. This guide gives you the formulas, shows the arithmetic step by step, and lists the anchor points worth remembering.

The three scales in one paragraph

Celsius sets 0 degrees at the freezing point of water and 100 degrees at boiling. Fahrenheit sets 32 at freezing and 212 at boiling, so there are 180 Fahrenheit degrees where Celsius has 100, a ratio of 9 to 5. Kelvin uses the same size degree as Celsius but starts at absolute zero, so 0 K is minus 273.15 degrees Celsius. Kelvin has no negative values and no degree symbol.

The formulas

Celsius to Fahrenheit: F = C times 9/5, plus 32. Equivalently, F = C times 1.8, plus 32.

Fahrenheit to Celsius: C = (F minus 32) times 5/9.

Celsius to Kelvin: K = C plus 273.15.

Kelvin to Celsius: C = K minus 273.15.

To go from Fahrenheit to Kelvin, convert to Celsius first, then add 273.15. Two steps, no special formula needed.

Worked examples with exact arithmetic

Example 1: 25 C to Fahrenheit. Multiply 25 by 1.8 to get 45, then add 32 to get 77. So 25 C is exactly 77 F, a pleasant warm day.

Example 2: 37 C to Fahrenheit. Multiply 37 by 1.8 to get 66.6, then add 32 to get 98.6. So normal body temperature, 37 C, is 98.6 F.

Example 3: 350 F to Celsius. Subtract 32 from 350 to get 318, then multiply by 5/9. That is 318 times 5 divided by 9, which is 176.666…, so a 350 F oven is about 176.7 C.

Example 4: 100 C to Kelvin. Add 273.15 to get 373.15 K. Boiling water at sea level is 373.15 K.

Example 5: 0 C to both scales. Fahrenheit: 0 times 1.8 plus 32 equals 32 F. Kelvin: 0 plus 273.15 equals 273.15 K. Freezing is the one anchor everyone should know cold, so to speak.

The famous equal point: minus 40

There is exactly one temperature where Celsius and Fahrenheit agree: minus 40. Check it with the formula. Take minus 40 C, multiply by 1.8 to get minus 72, add 32, and you get minus 40. The two scales cross because the Fahrenheit offset of 32 exactly cancels the different degree size at that point. It is a useful party fact and a genuinely handy check: if your conversion of a very cold temperature does not pass through minus 40 correctly, you made an arithmetic error.

Anchors worth memorizing

• Water freezes: 0 C, 32 F, 273.15 K
• Water boils at sea level: 100 C, 212 F, 373.15 K
• Body temperature: 37 C, 98.6 F, 310.15 K
• The crossover: minus 40 C equals minus 40 F

Oven temperatures

Cooking is where most people meet this conversion. Common settings:

• 160 C equals 320 F (160 times 1.8 is 288, plus 32 is 320). A slow oven.
• 180 C equals 356 F (180 times 1.8 is 324, plus 32 is 356). The standard moderate oven in metric recipes.
• 200 C equals 392 F (200 times 1.8 is 360, plus 32 is 392). A hot oven for roasting.

Notice the pattern: every 10 degrees Celsius is exactly 18 degrees Fahrenheit, since 10 times 1.8 is 18. Once you know 180 C is 356 F, you can walk to 190 C by adding 18 to get 374 F.

Common mistakes

• Forgetting the offset. Multiplying by 1.8 and skipping the plus 32 is the most frequent error.
• Applying the offset in the wrong direction. Going Fahrenheit to Celsius, subtract 32 first, then multiply by 5/9. Order matters.
• Writing K with a degree symbol. Kelvin is written as 300 K, not 300 degrees K.

For instant results, the temperature converter on our homepage handles all three scales in both directions, no mental arithmetic required. If your recipe also mixes US and metric cups, our cooking measurement conversions guide pairs well with this one.