Engineering
Celsius to Fahrenheit and Kelvin conversion formulas (and back)
Convert temperatures accurately between °C, °F, and Kelvin with exact 9/5 and 5/9 affine formulas.
Exact temperature conversion equations
Fahrenheit scales 100 Celsius degrees (0°C freezing to 100°C boiling) across 180 Fahrenheit degrees (32°F to 212°F), giving a slope of 180 / 100 = 9 / 5 (1.8) plus the 32° offset: °F = °C * 9 / 5 + 32.
Going from Fahrenheit back to Celsius requires subtracting 32 inside parentheses BEFORE multiplying by 5 / 9: °C = (°F - 32) * 5 / 9. Kelvin shifts Celsius by absolute zero: K = °C + 273.15.
The water freezing and boiling benchmarks assume standard atmospheric pressure. The 37°C row is illustrative, not a universal body-temperature value. Physical thermodynamic temperatures must not fall below 0 K; these arithmetic formulas do not validate that domain.
| Benchmark | Celsius (°C) | Fahrenheit (°F) | Kelvin (K) |
|---|---|---|---|
| Scale crossover | -40 | -40 | 233.15 |
| Room temp | 25 | 77 | 298.15 |
| Body temp | 37 | 98.6 | 310.15 |
| Water boiling | 100 | 212 | 373.15 |
°C to °F, °F to °C, and Kelvin checks
Testing -40°C confirms the unique crossover point where both Celsius and Fahrenheit equal -40.
=ROUND(A2 * 9 / 5 + 32, 2)Reverse Fahrenheit-to-Celsius formula
(98.6 - 32) * 5 / 9 = 66.6 * 5 / 9 = 37°C.
=ROUND((B2 - 32) * 5 / 9, 2)Try the example
Use the original values or change them to test your understanding.