The scales use different zero points
Celsius and Fahrenheit are common in weather, cooking, and everyday life. At standard atmospheric pressure, pure water freezes near 0 °C (32 °F) and boils near 100 °C (212 °F). These are useful reference points, but actual phase-change temperatures vary with pressure and composition, and modern unit definitions do not depend on a kitchen observation of boiling water.
Kelvin is the SI unit of thermodynamic temperature. Its interval is the same size as a Celsius degree, but its zero is absolute zero. Celsius temperature is offset from kelvin by exactly 273.15: 0 °C = 273.15 K. The kelvin symbol is K, without a degree sign.
Use an offset as well as a scale factor
Temperature values cannot be converted by a scale factor alone because the scales do not share zero. Apply the operations in the stated order and retain guard digits until the final result.
- °F = (°C × 9/5) + 32
- °C = (°F − 32) × 5/9
- K = °C + 273.15
- °C = K − 273.15
- K = (°F + 459.67) × 5/9
Temperature changes use different rules
A temperature point and a temperature interval are not the same quantity. A rise from 10 °C to 15 °C is a change of 5 °C or 5 K, but it is a change of 9 °F. Do not add the 32-degree offset when converting an interval.
For changes, Δ°F = Δ°C × 9/5 and Δ°C = Δ°F × 5/9. A Celsius interval and a kelvin interval have the same numerical value. Label changes with Δ or words such as ‘increase’ and ‘difference’ so readers do not mistake them for scale readings.
Reference points and useful checks
A comfortable room temperature of 20 °C equals 68 °F and 293.15 K. The Celsius and Fahrenheit scales meet at −40, so −40 °C = −40 °F. A reading of 100 °F is about 37.78 °C, not the boiling point of water.
Direction offers a quick check: above −40, a Fahrenheit reading is numerically larger than the matching Celsius reading. A thermodynamic temperature in kelvins cannot be below 0 K. If a conversion produces a negative kelvin value, the input is below absolute zero and is not a valid ordinary thermodynamic temperature.
Match precision to the measurement
The formulas contain exact relationships, but the source reading may be approximate. A weather observation given to the nearest degree should not become a laboratory-grade result merely because a converter displays decimals. Keep extra digits while calculating, then round to suit the instrument and use case.
Cooking, clinical, industrial, and scientific work can have their own required instruments, calibration, tolerances, and reporting rules. Use the converter for the scale transformation, then follow the applicable procedure for the decision that depends on it.
Put this guide into practice
Use point-temperature converters for readings; for temperature increases or differences, apply the interval rules in the guide instead.
- Celsius to Fahrenheit: Convert an everyday temperature reading.
- Fahrenheit to Celsius: Reverse the offset-and-scale formula.
- Celsius to kelvin: Shift a Celsius reading to the absolute scale.
- Kelvin to Celsius: Convert thermodynamic temperature to Celsius.
Sources and standards
The definitions and factors in this guide were checked against these primary standards and government references.