Réaumur to Kelvin converter

What is the Réaumur and Kelvin scale?

The Réaumur and Kelvin scales are both temperature measurement systems, each based on a distinct historical or physical principle. The Réaumur scale (°Ré or °Re), named after the French scientist René-Antoine Ferchault de Réaumur, was widely used in Europe—especially in France, Germany, and Russia—before the Celsius scale gained dominance. On this scale, the freezing point of water is 0°Ré and the boiling point is 80°Ré under standard atmospheric pressure.

The Kelvin scale (K), on the other hand, is the absolute thermodynamic temperature scale, developed by Lord Kelvin (William Thomson) in the 19th century. It starts at absolute zero (0 K), which corresponds to -273.15 °C. Unlike Celsius and Réaumur, the Kelvin scale does not use the degree symbol; it is expressed simply as K.

When converting between these two scales, the Réaumur temperature is first related to Celsius or directly converted to Kelvin by applying a linear transformation based on equal increments.

Formula

The mathematical relationship between Réaumur (°Ré) and Kelvin (K) is derived from their respective relations to the Celsius scale:

$$T_{°C} = T_{°Ré} \times \frac{5}{4}$$ $$T_{K} = T_{°C} + 273.15$$

Combining these two formulas gives the direct conversion from Réaumur to Kelvin:

$$T_{K} = T_{°Ré} \times \frac{5}{4} + 273.15$$

where:
$T_{K}$ = temperature in Kelvin
$T_{°Ré}$ = temperature in degrees Réaumur

Step-by-step conversion process

1. Start with the temperature in degrees Réaumur (°Ré).
   Example: let’s assume $40°Ré$.

2. Convert Réaumur to Celsius using the relation:
   $T_{°C} = 40 \times \frac{5}{4} = 50°C$.

3. Convert Celsius to Kelvin by adding 273.15:
   $50 + 273.15 = 323.15 K$.

So, 40°Ré equals 323.15 K.

The process shows how a simple linear conversion allows one to switch between scales while preserving proportional increments.

Examples

Convert $20°Ré$ to Kelvin.

$$T_{K} = 20 \times \frac{5}{4} + 273.15 = 25 + 273.15 = 298.15~K$$

Thus, $20°Ré = 298.15~K$.

Convert $-5°Ré$ to Kelvin.

$$T_{K} = (-5) \times \frac{5}{4} + 273.15 = -6.25 + 273.15 = 266.90~K$$

Therefore, $-5°Ré$ corresponds to 266.9 K.

Find the Kelvin value of the boiling point of water in the Réaumur scale.

Boiling point of water = 80°Ré

$$T_{K} = 80 \times \frac{5}{4} + 273.15 = 100 + 273.15 = 373.15~K$$

As expected, boiling water at standard pressure equals 373.15 K or 100°C in Celsius.

Historical background

The Réaumur scale was introduced in 1731 and remained in use for scientific and industrial purposes for more than a century. It was particularly favored in the brewing and food industries, as instruments calibrated in Réaumur were widely available across Continental Europe.

Lord Kelvin proposed his absolute scale nearly a century later, in 1848, as a response to the need for a standard based on absolute thermal energy—independent of the properties of water. This shift marked a fundamental moment in thermodynamics, where absolute zero became a universal reference point for energy and molecular motion.

Interestingly, older French thermometers engraved with Réaumur units can still be found in some historical laboratories and antique shops. Although the system is no longer used in scientific measurements, the Réaumur name endures as a symbol of early metrological innovation.

Notes

1. The Kelvin scale begins at absolute zero (−273.15 °C), the point where a system reaches its lowest possible energy state, and no thermal energy remains.
2. Réaumur temperatures below 0°Ré are possible and represent sub-freezing conditions.
3. When using temperature differences rather than absolute temperatures, the offset +273.15 is omitted because only incremental change matters.
4. Always ensure that thermometers or historical documents specify whether temperatures are in Réaumur (°Ré), Celsius (°C), or Fahrenheit (°F) to avoid confusion.

Frequently Asked Questions

How to convert 25°Ré to Kelvin?

To convert 25°Ré, use $T_{K} = 25 \times \frac{5}{4} + 273.15$.
$T_{K} = 31.25 + 273.15 = 304.40~K$.
Thus, 25°Ré equals 304.40 K.

How many kelvins is −10°Ré?

$T_{K} = (-10) \times \frac{5}{4} + 273.15 = -12.5 + 273.15 = 260.65~K$.
So, −10°Ré corresponds to 260.65 K.

What is the difference between 1°Ré and 1 K?

Each degree Réaumur corresponds to 1.25 K of temperature change because the Réaumur scale subdivides the water freezing-to-boiling range (0–100°C) into 80 parts instead of 100.

Can the Réaumur to Kelvin conversion yield decimals?

Yes. Because the ratio $\frac{5}{4}$ produces non-integer values, fractional results (e.g., 298.15 K) are common and accurate.

Is the Kelvin temperature ever written with a degree symbol?

No. Kelvin is a representation of thermodynamic temperature and is expressed only in K, not °K. This distinguishes it from Celsius and Réaumur, which use the degree symbol (°).