Calculators & everyday math
How Temperature Conversion Formulas Work
The Fahrenheit–Celsius formulas look arbitrary, but each part has a reason: the 32 accounts for the different zero points and the 5/9 for the different step sizes. Once you see that, you can rebuild the formulas yourself — and avoid the most common mistake.
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Two differences between the scales
- Different zero points: water freezes at 0 °C but at 32 °F.
- Different step sizes: 100 Celsius degrees span the same range as 180 Fahrenheit degrees, so a Fahrenheit degree is 100/180 = 5/9 of a Celsius degree.
Building the Fahrenheit-to-Celsius formula
- Remove the offset so both scales start at freezing: F − 32.
- Rescale the degrees: multiply by 5/9.
- Result: C = (F − 32) × 5/9. For 212 °F: (212 − 32) × 5/9 = 180 × 5/9 = 100 °C.
Reversing it
Undo the steps in the opposite order: multiply by 9/5, then add 32. So F = C × 9/5 + 32, and 37 °C is 37 × 1.8 + 32 = 98.6 °F.
Readings vs. differences
The offset applies only to readings. A change in temperature is converted by the step size alone: a 10 °C rise is an 18 °F rise, not 50 °F. The Temperature Converter converts readings.
Adding kelvin
Kelvin uses Celsius-sized degrees but starts at absolute zero, so K = °C + 273.15. Combining the formulas gives K = (°F − 32) × 5/9 + 273.15.
Temperature Formulas FAQ
- Why subtract 32 before multiplying?
- The 32 is the gap between the zero points, so it has to be removed before the degrees are rescaled.
- Where does 5/9 come from?
- 100 Celsius degrees cover the same range as 180 Fahrenheit degrees, and 100/180 simplifies to 5/9.
- Can I use 1.8 instead of 9/5?
- Yes, they are the same number: F = C × 1.8 + 32, and C = (F − 32) ÷ 1.8.
- How do I convert a temperature change?
- Multiply or divide by 1.8 and ignore the 32. A change of 20 °F is a change of about 11.1 °C.
- Why is −40 the same on both scales?
- It is where the two formulas meet: (−40 − 32) × 5/9 = −40.
Related guides
- Fahrenheit vs. CelsiusLandmark temperatures on both scales, why a Celsius degree is 1.8 Fahrenheit degrees, quick estimates, and where each scale is used.
- Celsius, Fahrenheit, KelvinAbsolute zero, freezing, room temperature, and boiling on all three scales, why kelvin has no degree sign, and when scientists use each.
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