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How to Convert Temperatures (and Why the Formula Has Both Multiplication and Addition)

Most unit conversions are just multiplication — inches to centimeters is x 2.54, pounds to kilograms is x 0.453592. Temperature is different. Converting Celsius to Fahrenheit requires multiplying by 9/5 AND adding 32, because the two scales have different zero points. Celsius puts zero at the freezing point of water. Fahrenheit put zero at a brine solution in 1724. Learn why the offset exists, why Kelvin has no degree symbol and never goes negative (absolute zero at 0 K = -273.15 C), why Rankine is Fahrenheit-based Kelvin, what Gas Mark means in UK ovens, why the historical scales (Delisle, Newton, Reaumur, Romer) died out, how wind chill is calculated (temperature + wind speed, NWS 2001 formula), and how the heat index combines temperature and humidity into apparent temperature.

The Toolbox TeamAugust 13, 20268 min read

The problem: temperature conversion has an offset, and people forget it

Most unit conversions are multiplication. Inches to centimeters: multiply by 2.54. Pounds to kilograms: multiply by 0.453592. Miles to kilometers: multiply by 1.60934. You scale the number. Zero stays zero. Zero inches and zero centimeters are the same length — no length at all.

Temperature is not like this. Converting 100 degrees Celsius to Fahrenheit gives 212, not 180. The formula is F = C x 9/5 + 32. The multiplication (9/5 = 1.8) handles the fact that a Fahrenheit degree is smaller than a Celsius degree — there are 180 Fahrenheit degrees between freezing and boiling, but only 100 Celsius degrees in the same range. The addition (+ 32) handles the fact that the two scales put zero at different temperatures. Celsius puts zero at the freezing point of water. Fahrenheit put zero at the temperature of a brine solution he made from water, ice, and ammonium chloride in 1724 — which happens to be about -17.8 degrees Celsius.

The offset is the part people forget. Multiply 100 by 1.8 and you get 180. But water boils at 212 degrees Fahrenheit, not 180. The missing 32 is the offset between the two zero points. Every temperature conversion between scales with different zero points requires both a scale factor and an offset. The Temperature Converter handles this for 12 scales — four common (Celsius, Fahrenheit, Kelvin, Gas Mark), two scientific (Rankine, Planck), and six historical (Delisle, Newton, Reaumur, Romer, Leiden, Wedgwood).

Fastest path

Open the Temperature Converter, enter a temperature value, pick the source unit and target unit from the dropdowns, and the result appears instantly. The tool converts through Celsius as an intermediate — every unit has a toCelsius and fromCelsius function, so any-to-any conversion is fromCelsius(toCelsius(value)). The swap button reverses the direction. The All Units table shows your value in all 12 scales simultaneously. The Feels Like tab calculates wind chill or heat index from temperature plus wind speed or humidity.

The three common scales and their formulas

Celsius (C) sets 0 at the freezing point of water and 100 at the boiling point (at 1 atmosphere). The scale was defined by Anders Celsius in 1742, though he originally put 0 at boiling and 100 at freezing — the scale was reversed after his death. One degree Celsius equals one Kelvin, so the two scales have the same degree size but different zero points.

Fahrenheit (F) sets 32 at the freezing point of water and 212 at the boiling point. Daniel Gabriel Fahrenheit defined it in 1724 using three reference points: 0 for his brine solution, 32 for water freezing, and 96 (approximately body temperature, though the actual value is 98.6). The 180-degree span between freezing and boiling (212 - 32 = 180) makes each Fahrenheit degree 5/9 of a Celsius degree.

Kelvin (K) sets 0 at absolute zero — the temperature at which all thermal motion ceases, defined as -273.15 degrees Celsius. Kelvin uses the same degree size as Celsius, so K = C + 273.15. Kelvin never goes negative because absolute zero is the lowest possible temperature. The scale has no degree symbol — you write "293 K," not "293 degrees Kelvin." Kelvin is an absolute scale (zero means zero thermal energy), while Celsius and Fahrenheit are relative scales (zero is an arbitrary reference point).

The conversion formulas between the three common scales:

C to F:  F = C x 9/5 + 32
F to C:  C = (F - 32) x 5/9
C to K:  K = C + 273.15
K to C:  C = K - 273.15
F to K:  K = (F - 32) x 5/9 + 273.15
K to F:  F = (K - 273.15) x 9/5 + 32

The tool implements these as JavaScript functions. For Celsius, toCelsius is the identity function (returns the input) and fromCelsius is also the identity. For Fahrenheit, toCelsius = (v) => (v - 32) * 5 / 9 and fromCelsius = (v) => v * 9 / 5 + 32. For Kelvin, toCelsius = (v) => v - 273.15 and fromCelsius = (v) => v + 273.15. Every other unit follows the same pattern — a pair of functions that convert to and from the Celsius intermediary.

Absolute zero and why Kelvin matters

Absolute zero (0 K, -273.15 C, -459.67 F) is the temperature at which all classical thermal motion stops. Atoms still have quantum zero-point energy, but their kinetic energy is at its minimum. You cannot cool something below absolute zero because there is no less thermal energy to remove — it is the floor of the temperature scale.

Kelvin is the SI unit of temperature. Scientific measurements use Kelvin because it is an absolute scale — 200 K is literally twice as hot as 100 K, meaning twice the thermal energy. "Twice as hot" is meaningless in Celsius or Fahrenheit because their zeros are arbitrary. 20 C is not twice as hot as 10 C — the ratio of thermal energies is (20 + 273.15) / (10 + 273.15) = 1.035, not 2.0. Kelvin preserves ratios.

The tool includes absolute zero as a preset (-273.15 C). Converting it to Fahrenheit gives -459.67 F. Converting to Kelvin gives 0 K. The preset lets you verify that the tool handles the boundary correctly — and it does, because the conversion functions are linear and well-defined at any input.

Gas Mark: the UK oven scale

Gas Mark is a temperature scale used in UK and Irish ovens. It maps integer values (GM 1 through GM 9) to oven temperatures in degrees Celsius. The tool converts Gas Mark using C = 121.11 + GM x 13.89, which gives:

  • GM 1: 135 C (275 F) — slow
  • GM 4: 177 C (350 F) — medium
  • GM 6: 204 C (400 F) — hot
  • GM 9: 246 C (475 F) — very hot

Gas Mark exists because UK ovens historically used gas rather than electricity, and the dial was marked in gas flow settings rather than temperatures. The mapping is approximately linear but not exact — the real relationship varies slightly by oven model. The tool's formula is the standard approximation used in UK cookbooks.

Historical scales: why they died

The tool includes six historical temperature scales, none of which are used today outside of historical contexts:

Delisle (De) was created by Joseph-Nicolas Delisle in 1732. It is inverted — higher numbers mean colder temperatures. Water boils at 0 De and freezes at 150 De. The inversion made it confusing, and it was replaced by Celsius within Delisle's lifetime.

Newton (N) was Isaac Newton's own temperature scale, defined around 1701. He set 0 as "the heat of air in winter" and used linseed oil expansion as his thermometric fluid. One degree Newton equals approximately 3.03 degrees Celsius. The scale never gained wide adoption.

Reaumur (Re) set 0 at freezing and 80 at boiling. Rene Antoine Ferchault de Reaumur proposed it in 1730. It was used in parts of Europe, particularly France and Germany, through the 19th century. It lost to Celsius because 100 (boiling) is a rounder number than 80.

Romer (Ro) was proposed by Ole Romer in 1701. He set 0 at the freezing point of brine, 60 at the boiling point of water, and 7.5 at the freezing point of water. Fahrenheit visited Romer in 1708 and based his own scale partly on Romer's work. The scale was never widely used.

Leiden (L) was used at Leiden University in the Netherlands. It sets 0 at the boiling point of hydrogen and uses absolute zero as -20 Leiden degrees. It is obsolete and included for historical completeness.

Wedgwood (W) was a pyrometric scale invented by Josiah Wedgwood in the 1780s for measuring kiln temperatures. It used clay shrinkage rather than liquid expansion. One degree Wedgwood equals approximately 24.857 degrees Celsius. It was superseded by pyrometric cones and later by thermocouples.

Feels-like temperature: wind chill and heat index

The tool includes a Feels Like calculator that computes apparent temperature — what it actually feels like on your skin, not what the thermometer says. Two formulas are used depending on conditions:

Wind chill applies when the temperature is at or below 10 C and wind speed exceeds 4.8 km/h. The tool uses the NWS 2001 formula:

WC = 13.12 + 0.6215 x T - 11.37 x V^0.16 + 0.3965 x T x V^0.16

where T is temperature in Celsius and V is wind speed in km/h. Wind chill matters because wind strips the warm air layer next to your skin, accelerating heat loss. At -10 C with 30 km/h wind, the wind chill is -23 C — your skin loses heat as if the air were 23 degrees below zero, even though the thermometer reads -10.

Heat index applies when the temperature is at or above 27 C and humidity is provided. The tool uses the Rothfusz regression formula, which computes heat index in Fahrenheit and converts back to Celsius:

HI = -42.379 + 2.04901523 x T + 10.14333 x H
     - 0.22476 x T x H - 0.00683783 x T^2
     - 0.05481717 x H^2 + 0.00122874 x T^2 x H
     + 0.00085282 x T x H^2 - 0.00000199 x T^2 x H^2

where T is in Fahrenheit and H is relative humidity in percent. Heat index matters because high humidity prevents sweat evaporation, which is your body's primary cooling mechanism. At 35 C with 80 percent humidity, the heat index is 57 C — dangerously hot, even though the thermometer reads 35.

The tool automatically selects wind chill or heat index based on the inputs. If you enter temperature and wind speed (and the temperature is at or below 10 C), it computes wind chill. If you enter temperature and humidity (and the temperature is at or above 27 C), it computes heat index. If you enter only temperature, it returns the actual temperature with a prompt to add wind or humidity for an adjusted value.

Gotchas

  • The offset is the part people get wrong. The most common conversion error is multiplying by 1.8 without adding 32. This gives 180 F for 100 C instead of 212 F. The tool eliminates this by computing both the scale and the offset in one function call, but if you are doing it by hand, write the full formula: F = C x 9/5 + 32. Not F = C x 1.8.
  • Kelvin has no degree symbol. The unit is "kelvin" (lowercase) with symbol "K" (uppercase, no degree sign). You write "300 K," not "300 degrees K" or "300 K." The tool displays "K" without the degree symbol, matching the SI convention. Celsius and Fahrenheit use the degree symbol because they are relative scales; Kelvin does not because it is an absolute scale.
  • The wind chill formula is only valid for specific conditions. The NWS formula applies at temperatures at or below 10 C and wind speeds above 4.8 km/h. Outside this range, the formula produces nonsense — wind chill at 20 C is not a meaningful concept. The tool guards against this by checking the temperature threshold, but if you manually enter warm temperatures with high wind, the tool falls back to the heat index or returns the actual temperature.
  • The heat index formula assumes you are in the shade. Direct sunlight adds approximately 8 C to the heat index. The tool does not account for solar radiation. If you are in direct sun at 35 C with 60 percent humidity, the heat index from the tool will be about 41 C, but the actual apparent temperature in direct sun is closer to 49 C.
  • Gas Mark conversion is an approximation. The linear formula C = 121.11 + GM x 13.89 is the standard cookbook approximation. Real gas ovens vary — the same Gas Mark setting on different ovens can produce temperatures differing by 10-15 C. The tool gives you the nominal temperature, not what your specific oven actually delivers. Use an oven thermometer for precision baking.

Summary

  • Temperature conversion requires both scaling (degree size) and offset (zero point). Celsius to Fahrenheit is F = C x 9/5 + 32 — the 9/5 scales the degree size, the 32 shifts the zero. Every other unit conversion is just multiplication because they share a zero point. Temperature scales do not.
  • The three common scales are Celsius (0 = freezing, 100 = boiling), Fahrenheit (32 = freezing, 212 = boiling), and Kelvin (0 = absolute zero, same degree size as Celsius). Kelvin is the SI unit and has no degree symbol. Absolute zero (-273.15 C, -459.67 F, 0 K) is the theoretical floor of temperature.
  • The tool supports 12 scales including Gas Mark (UK oven), Rankine (Fahrenheit-based Kelvin), and six historical scales (Delisle, Newton, Reaumur, Romer, Leiden, Wedgwood). All convert through Celsius as an intermediary. The Feels Like calculator computes wind chill (cold + wind) or heat index (hot + humidity).
  • Wind chill uses the NWS 2001 formula and applies at or below 10 C with wind above 4.8 km/h. Heat index uses the Rothfusz regression and applies at or above 27 C with humidity. Direct sunlight adds about 8 C to the heat index — the tool does not account for solar radiation.
  • Use the Temperature Converter for all 12 scales and feels-like calculations, the Length Converter for distance conversions, the Unit Converter for general measurement conversions, and the Water Intake Calculator for hydration needs that change with temperature and climate.