Celsius to Fahrenheit in your head, with the exact formulas

To turn Celsius into Fahrenheit exactly, multiply by 9/5 and add 32: °F = °C × 9/5 + 32. To turn Fahrenheit into Celsius, subtract 32 and multiply by 5/9. For a quick mental estimate, double the Celsius figure and add 30. That shortcut is exact at 10 °C and drifts further from the true figure as the temperature moves away from 10, so it suits mild weather and fails badly for an oven.

The exact formulas

Fahrenheit and Celsius divide the same stretch of temperature differently. On the Fahrenheit scale, water freezes at 32 degrees and boils at 212, a span of 180 degrees. On the Celsius scale the same span runs from 0 to 100, a span of 100 degrees. Each Celsius degree is therefore 9/5 of a Fahrenheit degree, and the 32 is the offset that lines up the zeros.

Take 37 °C, a common body temperature reference. 37 × 9/5 = 66.6, and 66.6 + 32 = 98.6 °F. Going the other way, 68 °F minus 32 is 36, and 36 × 5/9 is 20 °C.

If the multiplication by 9/5 is awkward, multiply by 9 and divide by 5 instead. For 23 °C, 23 × 9 = 207, and 207 ÷ 5 = 41.4. Add 32 and the answer is 73.4 °F.

The two scales meet at −40. Check it: −40 × 9/5 = −72, and −72 + 32 = −40. Above −40 the Fahrenheit figure is the larger of the two, and below −40 the Celsius figure is the larger. At −50 °C the Fahrenheit reading is −58 °F.

To go the other way by hand, subtract 32, multiply by 5, then divide by 9. For 350 °F, 350 − 32 = 318, 318 × 5 = 1,590, and 1,590 ÷ 9 = 176.7 °C.

The double-and-add-30 shortcut

The shortcut is °F ≈ 2 × °C + 30. It is easy to do in your head, but it is an approximation. Compared with the exact formula, 1.8 × °C + 32, the shortcut is larger by 0.2 × (°C − 10). That means it is exact at 10 °C, where both give 50 °F, and it is off by 0.2 °F for each degree away from 10. The error is symmetric around 10 °C. At 0 °C the shortcut is 2 °F low, and at 20 °C it is 2 °F high. The further the temperature moves from 10 °C in either direction, the larger the error grows.

Between about 0 and 30 °C the shortcut stays within 4 °F, which is close enough for weather and clothing. A forecast of 25 °C gives 2 × 25 + 30 = 80 °F by the shortcut, against an exact 77 °F. Three degrees out is fine for choosing a jacket. At 37 °C the shortcut is about 5 °F high, and at boiling it is 18 °F high. For those cases use the exact formula.

Turned round, the shortcut gives a rough Fahrenheit-to-Celsius rule: subtract 30 and halve. At 68 °F that gives 19 °C, one degree under the exact 20. The exact version is to subtract 32 and multiply by 5/9.

Reference temperatures

Recipes often give oven temperatures in Fahrenheit. 350 °F is 176.7 °C, and conversion charts usually pair it with 180 °C. The difference is small, but it is a difference, so use the exact figure if you are converting a setting that matters.

Three pairs are worth memorising: 0 °C and 32 °F for freezing, 20 °C and 68 °F for a comfortable room, and 100 °C and 212 °F for boiling at sea level. With those three pairs, a value can be placed quickly between them.

Using the unit converter

The unit converter handles these conversions. Choose Temperature, type the value, then pick the unit it is in and the unit you want. Temperature has three units: Celsius, Fahrenheit and kelvin. It gives the exact figure, not the shortcut. The metric and imperial guide covers the same habit for length, weight and volume. The result panel also lists the other units in the category, so 20 °C appears as 293.15 K as well.

Kelvin starts at absolute zero. To convert a Celsius value to kelvin, add 273.15. The converter also refuses a temperature below absolute zero, which is −273.15 °C, and says so instead of showing a figure.

Edge cases

• Differences are not offsets. A change of 10 °C is a change of 18 °F, not 10 °F. Differences scale by 9/5 with no 32 added. A rise of 5 °C is a rise of 9 °F, and mixing the two up is a common slip with weather reports and heating settings. A single degree is 1.8 °F, so a forecast moving from 20 °C to 21 °C is a rise of about 2 °F.
• Negative values. The same formulas work below zero. The freezer example gives −0.4 °F at −18 °C, and the scales only cross at −40. A forecast of −5 °C is 23 °F. The shortcut would give 20 °F, three degrees too low.
• Rounding. A reading of 98.6 °F is exactly 37 °C. Thermometers and displays round their figures, so the last decimal place can differ between devices.
• Ranges. Convert both ends of a forecast range. A range of 15 to 20 °C is 59 to 68 °F.
• Rough estimates. For weather and everyday talk, the shortcut is usually enough. For recipes or any figure that must be exact, use the formula or the converter.