Celsius to Fahrenheit: Formula, Shortcut and Reference Tables

To convert Celsius to Fahrenheit, multiply by 1.8 (that is, 9/5) and add 32. To convert Fahrenheit to Celsius, subtract 32 and then divide by 1.8. So 37 °C is 37 × 1.8 + 32 = 98.6 °F, and 100 °F is (100 − 32) ÷ 1.8 = 37.78 °C.

The free temperature converter takes a value in Celsius, Fahrenheit or Kelvin and shows all three, rounded to two decimal places. The large number at the top is always the Celsius figure, so read Fahrenheit and Kelvin from the rows below it. This guide covers the formulas, the "double and add 30" shortcut and how far off it is, and tables for body temperature, weather and ovens.

The two formulas

• °F = °C × 9/5 + 32 (9/5 is 1.8)
• °C = (°F − 32) × 5/9 (or divide by 1.8)

Why these numbers? At sea level, water freezes at 0 °C (32 °F) and boils at 100 °C (212 °F). The same range is 100 Celsius degrees but 180 Fahrenheit degrees, so one Celsius degree is 1.8 Fahrenheit degrees. The 32 is there because the scales start at different points.

Order matters. Going from °F to °C, subtract 32 before dividing. Dividing first is the most common mistake.

Worked example 1: a 30 °C afternoon

1. 30 × 1.8 = 54.
2. 54 + 32 = 86 °F.

Worked example 2: a thermometer reading 102 °F

1. 102 − 32 = 70.
2. 70 ÷ 1.8 = 38.89 °C.

The converter gives the same answers: 86 °F for 30 °C, and 38.89 °C (312.04 K) for 102 °F.

The "double and add 30" shortcut, and its error

For a rough Celsius-to-Fahrenheit figure in your head, double the Celsius number and add 30. Going back, subtract 30 from the Fahrenheit number and halve it. The shortcut uses 2 instead of 1.8 and 30 instead of 32, so it is exact only at 10 °C and drifts the further you go from there.

The error is 0.2 × °C − 2 degrees Fahrenheit. Between −10 °C and 30 °C it stays within 4 °F, which is fine for deciding what to wear. It is no good for a fever (37 °C becomes 104 °F) or an oven, so use the full formula or the tables below for those.

For body temperatures there is a better trick: start from 37 °C = 98.6 °F and add 1.8 °F for every degree Celsius. 38 °C = 100.4 °F, 39 °C = 102.2 °F, 40 °C = 104 °F.

Body temperature and fever

The UK's NHS says normal body temperature differs between people and changes during the day, and that a high temperature is usually 38 °C or above. The US CDC counts a measured temperature of 100.4 °F (38 °C) or more as a fever, and notes that some guidance uses 100 °F (37.8 °C) instead. For young babies the NHS sets lower thresholds for getting urgent advice: 38 °C or higher under 3 months, and 39 °C or higher from 3 to 6 months.

A thermometer showing 99 °F (37.22 °C) is not a fever by either definition. If you feel unwell, or a child has a high temperature, speak to a doctor whatever the number. This is general information, not medical advice.

Weather

Indian forecasts are in Celsius, while American weather sites and some phone apps default to Fahrenheit. Exact conversions:

• 0 °C = 32 °F (freezing); 10 °C = 50 °F; 15 °C = 59 °F; 20 °C = 68 °F; 25 °C = 77 °F.
• 30 °C = 86 °F; 35 °C = 95 °F; 40 °C = 104 °F; 45 °C = 113 °F; 48 °C = 118.4 °F.
• −40 °C = −40 °F, the one point where the two scales agree.

Oven and cooking temperatures

American recipes give oven settings in Fahrenheit, and oven dials in India are usually in Celsius. Recipes round the converted figure to the nearest 5 or 10 °C, which is fine because ovens are not that precise.

Going the other way, 180 °C is 356 °F and 200 °C is 392 °F. Recipes that list ingredients in ounces or cups need converting too: the weight converter handles grams and ounces, and the volume converter handles cups and millilitres. The kg to lbs guide lists common recipe weights.

Kelvin, briefly

Kelvin is the scientific scale. It starts at absolute zero, the coldest possible temperature, and its steps are the same size as Celsius degrees.

• K = °C + 273.15, and °C = K − 273.15.
• 0 K = −273.15 °C = −459.67 °F.
• 300 K = 26.85 °C = 80.33 °F, a warm room.

Kelvin is written without a degree sign: 300 K, not 300 °K. You will also see it on LED bulb boxes as colour temperature, where it describes the colour of the light, not how hot the bulb gets. For other everyday units, see the unit conversion cheat sheet.

Frequently asked questions

Is 99 °F a fever?

No. 99 °F is 37.22 °C, below the 38 °C (100.4 °F) threshold that the NHS and CDC use.

What is 100 °F in Celsius?

37.78 °C. (100 − 32) ÷ 1.8 = 37.78.

What is 180 °C in Fahrenheit?

356 °F. 180 × 1.8 = 324, and 324 + 32 = 356. American recipes usually call this 350 °F.

What is 0 °F in Celsius?

−17.78 °C. (0 − 32) ÷ 1.8 = −17.78.

Is 37.5 °C a fever?

Not by the usual definition. 37.5 °C is 99.5 °F, below the 38 °C threshold, though it can be higher than normal for you.

Sources: NHS, "High temperature (fever) in adults" and "Fever in children"; US CDC, definitions of signs and symptoms of ill travellers; BIPM, The International System of Units (SI Brochure), for the kelvin.