Temperature Converter: Celsius, Fahrenheit, Kelvin

Temperature Converter

A temperature converter changes a temperature reading from one scale to another, for example from Celsius to Fahrenheit. This page converts a single reading into all four common scales at once: Celsius, Fahrenheit, Kelvin and Rankine.

What the calculator does

Enter a temperature and pick the scale it was measured in. The page converts it to Celsius first, then out to each of the four scales, and shows the four answers together. A copy button puts all four on the clipboard.

Nothing is colder than absolute zero, so a reading below it is refused instead of converted. The page says what absolute zero is on the chosen scale and shows no numbers.

How to convert between temperature scales

Celsius and Fahrenheit disagree about two things: how big one degree is, and where zero sits. A Fahrenheit degree is 5/9 the size of a Celsius degree, and 0 °C is 32 °F, not 0 °F. A conversion therefore needs a multiplication and an addition:

$F = C \times \frac{9}{5} + 32$

$K = C + 273.15$

$R = (C + 273.15) \times \frac{9}{5}$

where C is the temperature in degrees Celsius, F in degrees Fahrenheit, K in kelvin and R in degrees Rankine.

Each relation can be turned around to go the other way:

$C = (F - 32) \times \frac{5}{9}$

$C = K - 273.15$

$C = R \times \frac{5}{9} - 273.15$

Kelvin and Celsius degrees are the same size, so that pair needs only a shift. Rankine degrees are the same size as Fahrenheit degrees, and Rankine starts at absolute zero, so 0 °R is 0 K and a Rankine reading is always a Fahrenheit reading plus 459.67.

Treating 9/5 as the whole story is the common mistake. A converter that multiplied and forgot the shift would report 0 °C as 0 °F, and the arithmetic would look fine while the answer was 32 degrees wrong.

The one rule the page actually runs

The converter does not carry a separate formula per pair of scales. It stores two numbers per scale, a size and a shift, and applies one relation:

$b = v \times s + o$

where v is the value entered, s is the size of one of its degrees measured in Celsius degrees, o is the shift that moves its zero onto the Celsius zero, and b is the reading in Celsius. Fahrenheit has a size of 5/9 and a shift of −160/9, kelvin a size of 1 and a shift of −273.15. Going the other way undoes the same two steps. Every scale on the page is one row of that table, which is why the four answers cannot drift apart.

Which constants are exact

All four numbers used above are definitions, not measurements, so none of them will ever be revised by a better experiment.

Two things on this page are rounded, and neither is a defining constant. The fraction 5/9 has no exact decimal form, so any decimal written for it is a truncation; the code keeps 5/9 and 160/9 as fractions rather than as decimals. And the four results are displayed to eight significant figures. Only the display is rounded. The conversion itself runs on the value as typed.

Worked example

A reading of 20 °C, a mild room temperature, converts like this.

Fahrenheit: 20 × 9/5 is 36, and 36 + 32 is 68 °F.

Kelvin: 20 + 273.15 is 293.15 K.

Rankine: 20 + 273.15 is 293.15, and 293.15 × 9/5 is 527.67 °R.

A second example runs the other way and does not come out even. For 350 °F, a hot oven: 350 − 32 is 318, and 318 × 5/9 is 176.6666… °C, which the page shows as 176.66667 °C after rounding to eight significant figures.

Fixed points

These readings are worth recognising, and each row is checked by a test entered on all four scales in turn.

The −40 row is not a coincidence. Fahrenheit numbers grow faster than Celsius numbers and start higher, so the two lines cross once, and −40 is where they meet.

Absolute zero

Absolute zero is the point where a substance has no thermal energy left to give up. It sits at −273.15 °C, and that figure is exact: the kelvin and the degree Celsius are the same size and their zeros are 273.15 apart by definition (13th CGPM, 1967/68). On the other scales it is −459.67 °F, 0 K and 0 °R.

The page refuses any reading below it. A number below absolute zero is not a very cold temperature; it is not a temperature.

The check rounds both sides before comparing them. Absolute zero can reach the internal Celsius value as −273.15 by one route and as −273.15000000000003 by another, because a computer stores these numbers in binary and 273.15 has no exact binary form. Comparing the raw values would tell a user that absolute zero is below absolute zero.

The same rounding noise shows up in the answers. Converting −459.67 °F lands on about −0.000000000000028 K rather than 0 K. The converter recognises a residue that small as noise left by subtracting two numbers of similar size, and reports a clean 0 K.

Frequently asked questions

How do you convert Celsius to Fahrenheit? Multiply the Celsius reading by 9/5, then add 32. For 20 °C: 20 × 9/5 is 36, and 36 + 32 is 68 °F.

How do you convert Fahrenheit to Celsius? Subtract 32 first, then multiply by 5/9. For 68 °F: 68 − 32 is 36, and 36 × 5/9 is 20 °C.

Why is subtracting 32 not enough on its own? Because the two scales also use different sized degrees. One Fahrenheit degree is 5/9 of a Celsius degree, so the gap between the two readings grows as the temperature rises. At 0 °C the gap is 32; at 100 °C it is 112.

Is there a quick way to estimate it in your head? Doubling the Celsius reading and adding 30 is close for everyday temperatures. It gives 70 for 20 °C against a true 68 °F. The error grows with the temperature, so it is a rough guide rather than a conversion.

What is Rankine, and who uses it? Rankine is an absolute scale built on Fahrenheit-sized degrees, starting at absolute zero. It appears in some engineering work in the United States, where an absolute temperature is needed but the surrounding figures are in Fahrenheit.

Why does the page sometimes show fewer decimals than expected? Results are rounded to eight significant figures. A value such as 176.6666… °C repeats forever, so it is shown as 176.66667 °C. The rounding is applied to the display only.