What this calculator does
This tool converts temperatures between the Celsius (°C) and Fahrenheit (°F) scales using the standard linear algebra formulas. Pick the direction, enter your temperature, and it returns the converted value along with the original input so you can check the work. The formulas are universal and used worldwide — no country-specific rules apply.
How to use it
Select whether you are converting Celsius to Fahrenheit or Fahrenheit to Celsius. Type the temperature (it can be negative, e.g. −40). Press calculate and read the converted result in the hero box, with the input echoed in the table below for clarity.
The formula explained
Both scales are linear, so a single straight-line equation relates them. To go from Celsius to Fahrenheit you scale by the ratio 9/5 (because there are 180 Fahrenheit degrees between freezing and boiling versus 100 Celsius degrees) and shift the zero point by 32, since water freezes at 0 °C but 32 °F. That gives $$\degree F = \frac{9}{5} \cdot \text{Temp (\degree C)} + 32$$ Rearranging algebraically for C gives the inverse $$\degree C = \frac{5}{9} \left( \text{Temp (\degree F)} - 32 \right)$$ first undo the +32 offset, then undo the 9/5 scaling.
Worked example
Convert 37 °C (body temperature) to Fahrenheit: $$\degree F = \frac{9}{5} \times 37 + 32 = 66.6 + 32 = 98.6 \degree F$$ Going back: $$\degree C = \frac{5}{9} \times (98.6 - 32) = \frac{5}{9} \times 66.6 = 37 \degree C$$ confirming the inverse.
FAQ
At what temperature do both scales read the same? At −40°, where \(-40\,\degree C = -40\,\degree F\). Setting \(C = F\) in either formula solves to −40.
Why 9/5 and 32? 9/5 is the ratio of the size of the two degree intervals, and 32 aligns the freezing point of water on both scales.
Can I enter decimals or negatives? Yes. The calculator accepts any real number, including fractions and below-zero values.
