Réaumur calculator

What is the Réaumur scale?

The Réaumur scale is a historical temperature scale developed in 1731 by René Antoine Ferchault de Réaumur, a French scientist well known for his work in physics and natural sciences. Although it is rarely used today, the Réaumur scale played an important role in early thermometry, particularly in continental Europe and Russia during the 18th and early 19th centuries.

In the Réaumur system, the freezing point of water is defined as 0 °Ré (or 0 °Re), while the boiling point of water is defined as 80 °Ré under standard atmospheric pressure. This means that a total of 80 equal divisions separate the two points, similar in concept to how 100 divisions separate the freezing and boiling points in the Celsius scale. Because of this, the scale’s reference interval is smaller, making each Réaumur degree larger than a degree Celsius.

Today, the Réaumur scale is largely of historical or specialized interest, and most modern thermodynamic and meteorological applications use Celsius or Kelvin. Nonetheless, for historical data interpretation, engineering archives, or specific academic research, it remains useful to understand and convert Réaumur temperatures into modern units.

Formula

The Réaumur scale can be interconverted with other temperature scales using the following relationships. Let $T_{Ré}$ represent a temperature in degrees Réaumur.

Conversion between Réaumur and Celsius

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

Because 80 Réaumur degrees correspond to 100 Celsius degrees, the conversion factor between the two is $\frac{5}{4}$ or 1.25.

Conversion between Réaumur and Fahrenheit

$$T_{°F} = T_{Ré} \times \frac{9}{4} + 32$$ $$T_{Ré} = (T_{°F} - 32) \times \frac{4}{9}$$

This relationship uses the standard Fahrenheit water freezing point of 32 °F.

Conversion between Réaumur and Kelvin

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

Kelvin, like Celsius, uses the same incremental step, so the Réaumur-to-Kelvin transformation parallels that between Réaumur and Celsius, except for the addition of the absolute zero offset.

Example calculations

Let’s explore how the Réaumur calculator works using practical examples.

Example 1: Convert 20 °Ré to Celsius

$$T_{°C} = 20 \times \frac{5}{4} = 25$$

So, 20 °Ré = 25 °C.

Example 2: Convert 20 °Ré to Fahrenheit

$$T_{°F} = 20 \times \frac{9}{4} + 32 = 45 + 32 = 77$$

Hence, 20 °Ré = 77 °F.

Example 3: Convert 20 °Ré to Kelvin

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

Therefore, 20 °Ré = 298.15 K.

The Réaumur scale in history

For much of the 18th and early 19th centuries, the Réaumur scale enjoyed widespread use in Europe, especially in France, Germany, and parts of Russia. Thermometers manufactured according to Réaumur’s specifications were often used for scientific experiments, culinary processes such as sugar refining, and industrial measurements.

Notably, the Réaumur scale was one of several competing temperature systems of the time, alongside the Fahrenheit and Celsius (then called centigrade) scales. Over time, the Réaumur scale fell out of favor because metrication favored the Celsius system, which provided a simpler 100-point separation between water’s freezing and boiling points.

Despite its decline, the scale’s legacy endures: some old recipes, mechanical drawings, and historical weather logs still present temperature values in Réaumur units.

Relation to temperature scales

To better understand where Réaumur fits among temperature scales, consider the alignment at key physical benchmarks:

From this table, note that one Réaumur degree occupies a larger interval than its Celsius equivalent. Since the interval between the freezing and boiling points of water is divided into 80 parts in the Reaumur scale and into 100 parts in the Celsius scale, a change in temperature of one degree Reaumur is equivalent to a change of 1.25 degrees Celsius.

Frequently Asked Questions

How to convert 40 degrees Réaumur to Celsius, Fahrenheit, and Kelvin?

Using the standard formulas:

$$T_{°C} = 40 \times \frac{5}{4} = 50,$$ $$T_{°F} = 40 \times \frac{9}{4} + 32 = 90 + 32 = 122,$$ $$T_{K} = 40 \times \frac{5}{4} + 273.15 = 50 + 273.15 = 323.15.$$

So 40 °Ré = 50 °C = 122 °F = 323.15 K.

How many Réaumur degrees correspond to 100 Kelvin above absolute zero?

Since 0 K = -273.15 °C, we first find the Celsius equivalent of 100 K:

$$T_{°C} = 100 - 273.15 = -173.15,$$ $$T_{Ré} = -173.15 \times \frac{4}{5} = -138.52.$$

Therefore, 100 K = -138.52 °Ré.

How does the Réaumur scale differ from the Celsius scale?

The key difference lies in the division between the freezing and boiling points of water: the Réaumur scale uses 80 degrees, while Celsius uses 100 degrees. Hence, 1 °Ré = 1.25 °C. Both start at 0 for the freezing point, but the Réaumur reading at boiling water is 80 instead of 100.

How to convert -10 °C into Réaumur and Fahrenheit?

$$T_{Ré} = -10 \times \frac{4}{5} = -8,$$ $$T_{°F} = (-10) \times \frac{9}{5} + 32 = -18 + 32 = 14.$$

Thus, -10 °C = -8 °Ré = 14 °F.

How did the Réaumur thermometer operate?

Classic Réaumur thermometers used alcohol as the thermometric fluid rather than mercury. Alcohol was chosen because it expanded more uniformly with temperature over a wide range, making it suitable for calibrating the 0–80 scale divisions.