Temperature

How to Convert Fahrenheit, Celsius, and Kelvin

Temperature conversion looks like other unit conversion until you notice the zeros. A meter and a foot both measure from the same kind of nothing: zero length is zero length. Zero Celsius is not zero Fahrenheit, and neither is zero Kelvin. The three common temperature scales therefore need formulas with an offset, not a single multiplication. The temperature converter applies those formulas and refuses physically impossible values below absolute zero.

Three common temperature scales

Everyday weather and cooking in the United States often use Fahrenheit. Much of the rest of the world uses Celsius for the same jobs. Science and engineering use Kelvin when an absolute thermodynamic temperature is required. All three can describe the same thermal state. They simply place the numbers on different axes.

This article does not claim that every historical temperature scale is covered. Rankine, Réaumur, and others exist. Measurewell Atlas supports Celsius, Fahrenheit, and Kelvin because those three appear in most household and introductory technical work.

Celsius

On the Celsius scale, 0 °C is the freezing point of water and 100 °C is the boiling point of water under standard conditions. The size of one Celsius degree is the same as one kelvin. The difference is the zero: Kelvin starts at absolute zero, while Celsius is shifted by 273.15.

K = °C + 273.15
°C = K − 273.15

Accessible text: kelvin equals Celsius plus two hundred seventy-three point one five.

Fahrenheit

On the Fahrenheit scale, water freezes at 32 °F and boils at 212 °F under standard conditions. There are 180 Fahrenheit degrees between those landmarks and 100 Celsius degrees between the same landmarks, so the degree sizes are in the ratio 9/5.

°F = (°C × 9/5) + 32
°C = (°F − 32) × 5/9

Accessible text: Fahrenheit equals Celsius times nine-fifths plus thirty-two. The plus thirty-two is the offset that lines up the freezing point. Omit it and 0 °C would be reported as 0 °F, which is wrong.

Kelvin

Kelvin is an absolute scale. 0 K is absolute zero. Negative Kelvin is not a valid thermodynamic temperature on this scale, so the converter rejects it. 273.15 K is 0 °C. 373.15 K is 100 °C. Because a kelvin and a Celsius degree have the same size, converting between them is an addition or subtraction, not a stretch of the degree.

Temperature conversion formulas

The six directional formulas used on this site are:

°F = (°C × 9/5) + 32
°C = (°F − 32) × 5/9
K = °C + 273.15
°C = K − 273.15
K = (°F − 32) × 5/9 + 273.15
°F = (K − 273.15) × 9/5 + 32

Internally, the engine converts the input to kelvin, checks that the kelvin value is not below zero, then converts to the destination scale. That single checkpoint covers Celsius below −273.15 and Fahrenheit below −459.67 as well.

Freezing and boiling points of water under standard conditions

Under standard conditions, water freezes at 0 °C = 32 °F = 273.15 K and boils at 100 °C = 212 °F = 373.15 K. Those pairs are the usual classroom checks. They assume the conventional landmarks used to define the everyday scales, not a claim about every sample of water at every pressure. Boiling point changes with altitude; this guide is about unit conversion, not a steam table.

Absolute zero

Absolute zero is 0 K = −273.15 °C = −459.67 °F. The converter will accept 0 K and will reject −0.01 K. It will accept −273.15 °C and reject −273.16 °C. Those checks are physical constraints, not formatting preferences. A length of zero is allowed because a zero distance is meaningful. A temperature below absolute zero is not treated as an ordinary input.

Why multiplication alone does not work

If you multiply 0 °C by 1.8 you get 0, not 32 °F. The offset is doing real work. Interval sizes can be scaled: a change of 1 °C is a change of 1.8 °F. Absolute readings cannot be scaled from an arbitrary zero. The comparison graphic on the temperature desk therefore places markers on a Kelvin axis instead of drawing bars from zero as if 20 °C were “twice” 10 °F.

Worked example: 25 °C to Fahrenheit

(25 × 9/5) + 32 = 45 + 32 = 77 °F. Open 25 °C → °F. Reverse: (77 − 32) × 5/9 = 45 × 5/9 = 25 °C.

Worked example: 350 °F to Celsius

(350 − 32) × 5/9 = 318 × 5/9 = 176.666… °C. The automatic display will not invent extra junk digits beyond useful precision. Try 350 °F → °C. Another landmark: 98.6 °F is 37 °C exactly under the formula, which is why it appears as a quick example on the converter.

Checking your work

Convert 0 °C to Fahrenheit and expect 32. Convert 100 °C and expect 212. Convert −40 °C and expect −40 °F; that coincidence is a property of the two formulas, not a third scale. Convert 273.15 K to Celsius and expect 0. If a tool reports 0 °C as 0 °F, it is using the wrong model. See also how to convert units of measurement and the formula reference.