Celsius vs Fahrenheit: How the Scales Differ and How to Convert

Two scales, two reference points

Both scales are defined by how they divide the range between two familiar physical events. On the Celsius scale, water freezes at 0 degrees and boils at 100, a span of exactly 100 degrees. On the Fahrenheit scale, the same two events sit at 32 and 212, a span of 180 degrees. NIST states the relationship plainly: an interval of one Celsius degree corresponds to an interval of 1.8 Fahrenheit degrees.

That ratio, 180 to 100, is where the factor 1.8 comes from, and the offset of 32 exists because the Fahrenheit scale places freezing at 32 instead of zero.

The conversion formulas

NIST lists the conversions in both directions.

Worked examples

A room at 21 °C: multiply by 1.8 to get 37.8, then add 32, giving 69.8 °F. A fever reading of 101.3 °F: subtract 32 to get 69.3, then divide by 1.8, giving 38.5 °C. A cold day at −10 °C: multiplying gives −18, adding 32 gives 14 °F. Note that the offset is added after multiplying in one direction and subtracted before dividing in the other, and getting that order wrong is the most common conversion error.

Mental shortcuts

For a quick estimate, double the Celsius number and add 30 to get approximate Fahrenheit. At 20 °C this gives 70 °F, close to the exact 68 °F. Going the other way, subtract 30 and halve. The shortcut is accurate within a couple of degrees around ordinary weather temperatures and drifts for extremes, so use the exact formula when precision matters, as it does in cooking, laboratory work and medicine.

A helpful landmark set: 0 °C is 32 °F, 10 °C is 50 °F, 20 °C is 68 °F, 30 °C is 86 °F, and 37 °C, normal body temperature, is 98.6 °F.

Where kelvin fits

Scientists use a third scale. NIST explains that one Celsius degree is an interval of exactly 1 kelvin, and zero degrees Celsius is 273.15 K, so the Celsius and kelvin scales differ only by an offset. Kelvin starts at absolute zero, 0 K, which is why it carries no degree sign and never goes negative. The modern definition of the kelvin fixes the numerical value of the Boltzmann constant at 1.380649 × 10⁻²³ joules per kelvin.

Why two scales still exist

The Celsius scale is part of the metric system and used in science and in most countries. Fahrenheit remains in everyday use in the United States and a few other places, so people routinely meet both, for example in recipes, weather forecasts and product manuals. When a figure matters, check which scale it uses: a thermostat setting of 20 means a pleasant room in Celsius and a freezing one in Fahrenheit.