For weather temperatures you can make a rough conversion from Celsius to Fahrenheit by doubling the figure and adding 30.
Although initially defined by the freezing point of water (and later the melting point of ice), the Celsius scale is now officially a derived scale, defined in relation to the Kelvin temperature scale.
Zero on the Celsius scale (0 °C) is now defined as the equivalent to 273.15 K, with a temperature difference of 1 deg C equivalent to a difference of 1 K, meaning the unit size in each scale is the same. This means that 100 °C, previously defined as the boiling point of water, is now defined as the equivalent to 373.15 K.
The Celsius scale is an interval system but not a ratio system, meaning it follows a relative scale but not an absolute scale. This can be seen because the temperature interval between 20 °C and 30 °C is the same as between 30 °C and 40 °C, but 40 °C does not have twice the air heat energy of 20 °C.
A temperature difference of 1 deg C is the equivalent of a temperature difference 1.8°F.
Fahrenheit is a thermodynamic temperature scale, where the freezing point of water is 32 degrees Fahrenheit (°F) and the boiling point 212°F (at standard atmospheric pressure). This puts the boiling and freezing points of water exactly 180 degrees apart. Therefore, a degree on the Fahrenheit scale is 1/180 of the interval between the freezing point and the boiling point of water. Absolute zero is defined as -459.67°F.
A temperature difference of 1°F is the equivalent of a temperature difference 0.556°C.