Celsius, Fahrenheit, Kelvin and Rankine: Formulas, Chart and Differences

Temperature is the only common measurement that does not convert with a single multiplication. Two of the scales in everyday use have offsets, two have different-sized degrees, and two start counting from absolute zero rather than from a property of water. That is why “1 degree Fahrenheit” and “1 degree Celsius” are not the same size, and why you cannot convert between them with a single factor.

The Five Scales at a Glance

Celsius (°C)

Water freezes at 0 °C and boils at 100 °C at one standard atmosphere. Formally, the degree Celsius is now defined from the kelvin: a temperature in °C is the temperature in kelvins minus 273.15. A change of 1 °C equals a change of 1 K. Used almost everywhere outside the United States for weather, cooking and daily life.

Fahrenheit (°F)

Water freezes at 32 °F and boils at 212 °F, a gap of 180 Fahrenheit degrees against 100 Celsius degrees. A Fahrenheit degree is therefore 5⁄9 the size of a Celsius degree, and the 32-degree offset is why the formulas look awkward. Used for weather, cooking and body temperature in the United States.

Kelvin (K)

Same degree size as Celsius, but zero is absolute zero — the lowest possible temperature, where a system has its minimum possible energy. 0 K = −273.15 °C. The kelvin is the SI base unit for temperature and is used wherever absolute temperatures matter: gas laws, thermodynamics, astronomy, colour temperature of lighting. It is written without a degree sign, and the unit name is lowercase (“300 kelvins”).

Rankine (°R)

An absolute scale that uses the Fahrenheit degree size. 0 °R is absolute zero, like 0 K, but each Rankine degree is 5⁄9 of a kelvin. You meet it mainly in older US engineering texts, particularly in thermodynamics, HVAC and aerospace work that is done in US customary units.

Réaumur (°Ré)

Water freezes at 0 °Ré and boils at 80 °Ré, so each degree is 5⁄4 the size of a Celsius degree. Largely historical, it survives in some older European recipes, traditional cheese-making and sugar work, and in nineteenth-century literature.

Temperature Conversion Formulas

The formulas below convert temperature readings. Temperature differences behave differently: a rise of 10 °C is a rise of 10 K but a rise of 18 °F (and 18 °R), because only the degree size matters, not the offset.

For one-off values, the dedicated converters are quicker: Celsius to Fahrenheit, Fahrenheit to Celsius, Celsius to kelvin, kelvin to Celsius, kelvin to Rankine and Fahrenheit to Rankine.

Reference Temperatures on Every Scale

Kelvin vs Rankine: The Two Absolute Scales

Kelvin and Rankine both start at absolute zero, so both are absolute (or thermodynamic) scales: a reading of zero means no lower temperature is possible, and doubling the number genuinely doubles the thermodynamic temperature. The only difference is the size of the degree:

• 1 K = 1.8 °R, so °R = K × 1.8.
• Kelvin pairs with Celsius (same step size); Rankine pairs with Fahrenheit (same step size).
• Because one is a fixed multiple of the other with no offset, the two scales only show the same number at zero — absolute zero itself.

Celsius, Fahrenheit and Réaumur are relative scales: their zero is a convenient reference point, not the bottom of the scale, so negative readings are normal and ratios are meaningless (20 °C is not “twice as hot” as 10 °C). This is why equations such as the ideal-gas law PV = nRT, Carnot efficiency and radiation laws need temperatures in kelvins or Rankine.

Quick Mental Approximations

For everyday conversions where a degree or two does not matter:

• Fahrenheit to Celsius, fast: subtract 30, then halve. 70 °F → 40 → 20 °C (actual 21.1 °C).
• Celsius to Fahrenheit, fast: double, then add 30. 20 °C → 40 → 70 °F (actual 68 °F).
• The two scales meet at −40. −40 °C = −40 °F — a useful sanity check.
• Every 5 °C is 9 °F. 10 °C = 50 °F, 15 °C = 59 °F, 20 °C = 68 °F, 25 °C = 77 °F, 30 °C = 86 °F.
• Body temperature: 37 °C ≈ 98.6 °F.
• Oven baseline: 180 °C ≈ 350 °F (exactly 356 °F; recipes round).

Why the Offsets Exist

Celsius was built around water — a substance every laboratory and kitchen has — with two reproducible reference points. Fahrenheit predates it and was originally calibrated against a brine mixture and human body temperature; it survived in some countries through habit. Kelvin and Rankine were introduced once thermodynamics needed scales that start at absolute zero, so that ratios of temperatures behave correctly.

Common Mistakes

• Forgetting the offset. Multiplying 32 °F by 5⁄9 gives 17.78, not 0. The minus-32 step comes first.
• Treating readings and differences the same way. A “10 °C rise” is a 10 K rise, but an 18 °F rise.
• Writing a degree sign on kelvin. The unit is “K”, not “°K” — the degree sign was dropped in 1967.
• Mixing absolute and relative scales in equations. Anything involving ratios (efficiency, gas behaviour) needs kelvins or Rankine.
• Unlabelled oven temperatures. “Bake at 180” means a moderate oven in Celsius but barely warm in Fahrenheit. Check where the recipe comes from.

Worked Example: Adapting an Oven Recipe

A recipe says to bake at 425 °F. Convert to Celsius:

1. 425 − 32 = 393.
2. 393 × 5⁄9 ≈ 218.3 °C.
3. Round to the oven dial: 220 °C, or about 200 °C in a fan-assisted oven.

In reverse, a recipe written for 200 °C is 200 × 9⁄5 + 32 = 392 °F, usually rounded to 400 °F on a US oven. The cooking conversions guide has a full oven temperature chart.

Related Guides

• SI base units & prefixesWhere the kelvin fits among the seven base units.
• Metric vs. imperialWhy the US still uses Fahrenheit.
• Cooking conversionsOven temperatures, cups and grams.

Frequently Asked Questions

When do a Kelvin and a Rankine thermometer show the same reading?

Only at 0, which is absolute zero. Because °R = K × 1.8 with no offset, the two numbers can only be equal when both are zero. Expressed on the other scales, that temperature is −273.15 °C and −459.67 °F.

At what temperature are Celsius and Fahrenheit the same?

At −40. Setting °F = °C in °F = °C × 9⁄5 + 32 gives °C = −40, so −40 °C = −40 °F.

At what temperature are Fahrenheit and Kelvin equal?

At about 574.59. Solving K = (K − 273.15) × 9⁄5 + 32 gives K = 574.5875, so 574.59 K = 574.59 °F, which is about 301.44 °C.

What is the difference between an absolute and a relative temperature scale?

An absolute scale (kelvin, Rankine) starts at absolute zero, the lowest possible temperature, so it has no negative values and ratios are meaningful: 600 K is twice the thermodynamic temperature of 300 K. A relative scale (Celsius, Fahrenheit, Réaumur) puts zero at a convenient reference point such as freezing water, so negative readings are normal and ratios are meaningless.

How do Celsius, Fahrenheit, Kelvin and Rankine relate to each other?

Celsius and kelvin share the same degree size and differ by 273.15 (K = °C + 273.15). Fahrenheit and Rankine share the same, smaller degree size and differ by 459.67 (°R = °F + 459.67). One Celsius degree or kelvin equals 1.8 Fahrenheit degrees or Rankine degrees.

Why is kelvin written without a degree symbol?

Since 1967 the kelvin has been a unit in its own right, like the metre or the second, rather than a “degree” on a scale. So you write 300 K, not 300 °K. Celsius, Fahrenheit, Rankine and Réaumur keep the degree sign.

Which temperature unit is the SI unit?

The kelvin (K) is the SI base unit of thermodynamic temperature. The degree Celsius is an SI derived unit with exactly the same size, offset by 273.15. Fahrenheit and Rankine are not SI units.

Is the Rankine scale still used?

Yes, but narrowly — mainly in US engineering thermodynamics, HVAC and aerospace calculations carried out in US customary units, where an absolute scale with Fahrenheit-sized degrees is convenient. Most modern scientific work uses kelvins.