How to Convert Celsius to Fahrenheit and Back

To convert a temperature from degrees Celsius to degrees Fahrenheit, multiply by 1.8 and add 32. To go the other way, subtract 32 and divide by 1.8.

• °F = °C × 1.8 + 32
• °C = (°F − 32) ÷ 1.8

The factor 1.8 is the same as 9/5, so you will also see the formulas written as °F = °C × 9/5 + 32 and °C = (°F − 32) × 5/9. Both versions are exact.

Example: 25 °C × 1.8 = 45, and 45 + 32 = 77 °F. Back again: 77 − 32 = 45, and 45 ÷ 1.8 = 25 °C.

The two scales differ in two ways. First, the degrees have different sizes. Between the freezing and boiling points of water, the Celsius scale has 100 degrees and the Fahrenheit scale has 180. One Celsius degree is therefore 180 ÷ 100 = 1.8 Fahrenheit degrees.

Second, the zero points are in different places. Water freezes at 0 on the Celsius scale but at 32 on the Fahrenheit scale. That is why you cannot just multiply: you also have to shift by 32.

Today the Celsius scale is defined from the kelvin, the SI unit of temperature: a temperature in degrees Celsius is the kelvin value minus exactly 273.15. The Fahrenheit scale is defined from the Celsius scale through the formula above.

• Water freezes at 0 °C, which is 32 °F (at standard atmospheric pressure).
• Water boils at about 100 °C, which is about 212 °F (at standard atmospheric pressure).
• Normal human body temperature is commonly given as 37 °C, which is 98.6 °F.
• A comfortable room at 20 °C is 68 °F.
• The two scales meet at −40: −40 °C is exactly −40 °F.
• Absolute zero, 0 K, is −273.15 °C or −459.67 °F.

Going the other way, 0 °F is −17.78 °C, 50 °F is 10 °C, 70 °F is 21.11 °C and 350 °F, a common oven setting, is 176.7 °C.

For a quick estimate, double the Celsius value and add 30. To go back, subtract 30 from the Fahrenheit value and halve the result.

The shortcut uses 2 instead of 1.8 and 30 instead of 32. The two errors cancel at 10 °C, where the shortcut is exact. Below 10 °C it reads too low, above 10 °C it reads too high, and the error grows by 0.2 °F for every degree Celsius away from 10.

Between about 0 °C and 30 °C, the range of everyday weather, the shortcut is within a few degrees Fahrenheit. For cooking or any other high temperature, use the exact formula.

The formulas above convert a temperature, a point on the scale. A temperature difference, such as "the water warmed by 10 degrees", has no offset and needs only the factor.

• A change of 10 °C is a change of 18 °F (multiply by 1.8 only).
• Using the full formula on that change would give 50 °F, which is wrong because it adds the 32-degree offset to a difference.
• A change of 9 °F is a change of 5 °C (divide by 1.8 only).

The same rule applies to rates such as "degrees per hour" and to tolerances such as "±2 °C". Both are differences, so only the factor 1.8 applies.

• Adding 32 before multiplying. The order matters: multiply first, then add 32. Going back, subtract 32 first, then divide.
• Doubling a temperature on one scale and expecting the same on the other. Because of the offset, 20 °C is not "twice as warm" as 10 °C, and the Fahrenheit values do not double either.
• Converting a temperature difference with the full formula, as shown above.
• Rounding too early. Keep 1.8 and 32 as they are, since both are exact, and round only the final result.