Celsius, Fahrenheit and Kelvin: Conversion and Mental Math

How the three scales are built

The Celsius scale places the freezing point of water at about 0 degrees and its boiling point at about 100 degrees at standard atmospheric pressure. Modern definitions tie it to the kelvin, but for everyday purposes the water-based picture is all you need.

The Fahrenheit scale puts the same two points at 32 and 212 degrees. Because 180 Fahrenheit degrees span the same range as 100 Celsius degrees, one Fahrenheit degree is only 5/9 the size of one Celsius degree. The zero points differ as well, which is why converting needs both a multiplication and an offset.

The kelvin is the SI unit of temperature. Its zero is absolute zero, the lowest temperature possible in thermodynamics, and its degree is the same size as a Celsius degree. Zero degrees Celsius is 273.15 K. Kelvin is written without a degree sign and is used in physics, chemistry, engineering and for the color temperature of light bulbs.

The exact formulas, with examples

To convert Celsius to Fahrenheit, multiply by 9/5 (1.8) and add 32. To convert Fahrenheit to Celsius, subtract 32 and then multiply by 5/9 (or divide by 1.8). To get kelvin, add 273.15 to the Celsius value.

Some worked examples: 25 C is 25 x 1.8 + 32 = 77 F. Normal body temperature of 37 C is 98.6 F. A weather forecast of 72 F is (72 - 32) x 5/9, about 22.2 C. An oven setting of 350 F is (350 - 32) x 5/9, about 176.7 C. Boiling water at 100 C is 373.15 K.

Keep temperature readings and temperature differences apart. If the temperature rises by 10 C, the change in Fahrenheit is 10 x 1.8 = 18 F, with no 32 added, because the offset cancels out when you subtract two readings. A change of 10 C is also a change of exactly 10 K.

• F = C x 1.8 + 32
• C = (F - 32) / 1.8
• K = C + 273.15
• A difference of 1 C equals a difference of 1.8 F and of 1 K

The point where Celsius and Fahrenheit agree

There is exactly one temperature where both scales show the same number. Setting x = 1.8x + 32 gives -0.8x = 32, so x = -40. In other words, -40 C is -40 F.

This fact makes a neat check on any conversion, and it also gives a symmetric method that is hard to get backwards. Add 40, multiply or divide by 1.8, then subtract 40. Celsius to Fahrenheit is (C + 40) x 1.8 - 40, and Fahrenheit to Celsius is (F + 40) / 1.8 - 40. Try it with 100 C: 140 x 1.8 = 252, minus 40 is 212 F.

How accurate is double it and add 30?

The best-known mental shortcut for Celsius to Fahrenheit is to double the number and add 30. It replaces 1.8 with 2 and 32 with 30, which is easy to do in your head. The error it introduces follows a simple pattern: the shortcut minus the true value equals 0.2 x C - 2.

That means the shortcut is exact at 10 C, two degrees low at 0 C, two degrees high at 20 C and four degrees high at 30 C. Across the range of everyday weather, being a few degrees off rarely matters when you are deciding whether to take a jacket.

The error grows as temperatures rise, and that is where the shortcut becomes risky. At 37 C it gives 104 F, which is 5.4 degrees above the true 98.6 F and would suggest a high fever when there is none. In the kitchen the gap is larger still: 180 C becomes 390 F with the shortcut but is really 356 F, an error of 34 degrees, enough to burn a cake.

A slightly longer method is exact: double the Celsius value, subtract a tenth of the result, then add 32. For 25 C, double to 50, subtract 5 to get 45, and add 32 to get 77 F. Going the other way, subtract 32, halve it, and add a tenth of the half. This is within about one percent; for 350 F, 318 halved is 159, plus 15.9 gives about 174.9 C against the exact 176.7 C.

• 0 C: shortcut 30 F, exact 32 F (2 low)
• 10 C: shortcut 50 F, exact 50 F (no error)
• 20 C: shortcut 70 F, exact 68 F (2 high)
• 37 C: shortcut 104 F, exact 98.6 F (5.4 high)
• 180 C: shortcut 390 F, exact 356 F (34 high)

Handy reference points

For weather, memorize a few anchors at 10-degree Celsius steps: 0 C is 32 F, 10 C is 50 F, 20 C is 68 F and 30 C is 86 F. At the extremes, 0 F is about -17.8 C and 100 F is about 37.8 C.

For body temperature, 36 to 37 C corresponds to about 96.8 to 98.6 F, and 38 C is 100.4 F. Many guidelines treat a reading of around 100.4 F (38 C) or above as a fever, but always follow local medical advice and use exact conversions when health decisions depend on the number.

For cooking, common oven settings in recipes written in Fahrenheit are 350 F (about 177 C), 400 F (about 204 C) and 450 F (about 232 C). Oven dials often move in steps of 5 or 10 degrees, so choose the nearest setting. Real oven temperatures vary between appliances, so watch the food as it cooks.

Using the temperature converter

The temperature converter on this site converts a value from Celsius, Fahrenheit, Kelvin, Rankine or Reaumur into all the other units at once. Every conversion passes through Celsius internally, so you get consistent results whichever unit you start from. A practical habit is to estimate in your head first, then confirm the exact number with the tool whenever accuracy matters, such as for a fever reading, a recipe or a lab calculation.