Celsius to Fahrenheit Converter

About the Celsius to Fahrenheit Converter

Convert degrees Celsius to degrees Fahrenheit and back — type in either box and the other updates. The formula is °F = °C × 1.8 + 32, and the other way °C = (°F − 32) ÷ 1.8, so 37 °C is exactly 98.6 °F and 180 °C is exactly 356 °F. Each conversion is worked step by step under the result.

You also see how far the popular “double it and add 30” shortcut is off for your number, the temperature in kelvin, and both scales drawn side by side. Switch to A temperature difference for rises, falls and gaps between two temperatures — a change of 10 °C is a change of 18 °F, with no + 32. Printable tables list weather temperatures from −40 to 50 °C, oven settings in °C and in °F, and the body-temperature range in steps of 0.1 °C.

Common uses

• Weather forecasts and travel: reading °F in the US, °C almost everywhere else.
• Oven temperatures in recipes written for the other scale.
• Thermometer readings in °C or °F (the converter gives numbers, not medical advice).
• Science homework: the formula, kelvin and the reasoning step by step.
• Temperature changes — a 5 °C warmer day, a 3 °F rise — which do not use + 32.

The formula

NIST SP 811, Appendix B.8 gives t/°C = (t/°F − 32)/1.8, and the BIPM SI Brochure (9th edition, section 2.3.1) defines the degree Celsius by t/°C = T/K − 273.15.

• °F = °C × 1.8 + 32 (1.8 is 9/5)
• °C = (°F − 32) ÷ 1.8 (dividing by 1.8 is multiplying by 5/9)
• K = °C + 273.15

1.8, 32 and 273.15 are exact, so a conversion is exact whenever the decimals end: 36.6 °C is exactly 97.88 °F. Only results such as 100 °F = 37.777… °C are rounded, to 10 significant figures.

Double and add 30 — how good is it?

Doubling and adding 30 turns °C into °F in your head. It is exact only at 10 °C (50 °F) and is off by a further 0.2 °F for every degree Celsius away from 10: 2 °F too high at 20 °C, 5.4 °F at 37 °C and 34 °F at 180 °C — close enough for the weather, not for an oven or a body thermometer.

The reverse, subtract 30 and halve, is exact at 50 °F and drifts by 1/18 °C (about 0.06 °C) per degree Fahrenheit: 2.7 °C too low at 98.6 °F. The converter shows the shortcut and its error for every number you type.

Temperatures and temperature differences

A temperature and a difference between two temperatures convert differently. 20 °C is 68 °F, but a rise of 20 °C is a rise of 36 °F: the 32 shifts the starting point of the scale and has nothing to do with the size of a degree. One Celsius degree is 1.8 Fahrenheit degrees, and a Celsius degree is the same size as a kelvin, so a difference has the same number in °C and in K (SI Brochure, section 2.3.1). Pick A temperature difference for forecasts (“5 °C warmer”), cooling and heating ranges or tolerances such as ±0.5 °C.

About the tables

The weather table runs from −40 to 50 °C in 5 °C steps, the oven tables from 100 to 260 °C and from 200 to 500 °F, and the body table from 35.0 to 42.0 °C in steps of 0.1 °C. The oven tables add the nearest 25 °F or 10 °C, for dials and recipes marked in those steps. The tables convert numbers only: they do not say which temperatures are normal, safe or a fever.

Limitations

• Temperatures below absolute zero (−273.15 °C or −459.67 °F) are rejected; temperature differences can be any size and sign.
• Results are exact; numbers with endless decimals are shown to 10 significant figures (choose a Precision for fewer).
• The body-temperature table converts numbers only and is not medical guidance.
• Kelvin is shown under the result; for Rankine, Réaumur and other scales use the Temperature Converter.

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