Réaumur to Celsius converter

What is the Réaumur and Celsius scale?

The Réaumur scale (°Re or °R) and the Celsius scale (°C) are both temperature scales used to measure thermal conditions, but they are based on different fixed points.
The Réaumur scale was developed in 1730 by René Antoine Ferchault de Réaumur, a French scientist who proposed that the freezing point of water is 0 degrees Réaumur and the boiling point is 80 degrees Réaumur. This means the entire range between freezing and boiling was divided into 80 equal parts.

The Celsius scale, on the other hand, designed by Anders Celsius in 1742, divides this same range into 100 parts — from 0°C for freezing water to 100°C for boiling water. The Celsius scale eventually replaced Réaumur in scientific and everyday use because of its simplicity and compatibility with the metric system.

Despite being largely obsolete, Réaumur is still of historical interest and occasionally appears in older research works, recipes, or measurements from continental Europe. Converting between these scales helps interpret data or historical documents more effectively.

Formula

The relationship between the Réaumur and Celsius scales is linear, meaning each value has a direct proportional correspondence with no offset other than the reference point at zero.

The conversion formulas are as follows:

From Réaumur to Celsius

$$°C = °Re \times \frac{5}{4}$$

From Celsius to Réaumur

$$°Re = °C \times \frac{4}{5}$$

Since both scales have their zero point at the freezing temperature of water, no addition or subtraction is required in conversion — only a proportional scaling.

Example:

If the temperature is 40°Re, what is it in °C?

$$°C = 40 \times \frac{5}{4} = 50°C$$

So, a temperature of 40°Re corresponds to 50°C.

Historical background

Réaumur proposed his scale in the early 18th century while studying thermometers based on alcohol. Early thermometers were not standardized — scientists used various liquids and calibrations. Réaumur’s method gained some popularity across continental Europe, particularly in France, Germany, and Russia.

However, his system gradually lost ground after the introduction of the centigrade (Celsius) scale. It’s worth noting that Anders Celsius originally proposed his scale in 1742 with 0° as the boiling point of water and 100° as the freezing point. It was later reversed after his death to the familiar form we use today (0° for freezing, 100° for boiling), which helped its adoption.

Understanding temperature proportions

To better grasp why the conversion involves multiplying by 5/4, consider that:

• The Celsius scale spans 100 units between water’s freezing and boiling points.
• The Réaumur scale spans 80 units for the same temperature interval.

Thus:

$$100°C equivalent = 80°Re$$

If we represent both scales on a ratio,

$$1°Re = \frac{100}{80}°C = 1.25°C$$

or

$$°C = °Re × \frac{5}{4}$$

This ratio ensures that both scales increase proportionally — that is, a temperature increase of 1 degree Réaumur corresponds to an increase of 1.25 degrees Celsius.

Examples

Example 1: Converting 20°Re to Celsius

$$°C = 20 × \frac{5}{4} = 25°C$$

So, 20°Re represents 25°C.

Example 2: Converting from Celsius to Réaumur

If you have a measurement of 16°C:

$$°Re = 16 × \frac{4}{5} = 12.8°Re$$

This reverse calculation shows how you can translate Celsius readings back into Réaumur for completeness.

Application in various fields

1. Culinary uses

In traditional European recipes, particularly in confectionery or cheesemaking, older thermometers calibrated in Réaumur units were common. When interpreting old cookbooks or culinary guides, converting Réaumur to Celsius helps modern cooks reproduce authentic results. For instance, a temperature for incubating yogurt listed as 24°Re translates to:

$$°C = 24 × \frac{5}{4} = 30°C$$

2. Historical research

Historians or scientists studying 18th- and 19th-century European laboratory notes often encounter Réaumur readings. The conversion allows accurate reinterpretation in the modern Celsius system for comparison and replication of experiments.

3. Educational context

Learning about obsolete temperature scales enhances understanding of measurement system evolution and scientific standardization. It also provides practical examples of proportional and linear conversions used in mathematics and physics classes.

Interesting facts

• Réaumur’s original thermometers used ethanol instead of mercury because ethanol expands more uniformly. However, ethanol’s use made high-temperature measurements less accurate due to evaporation.
• Some early Russian and German industrial equipment adopted Réaumur readings until the 20th century. The term “grad Reaumur” still appears in older industrial charts.
• The Celsius scale was initially called “centigrade” because it spanned 100 degrees between freezing and boiling points; the name “Celsius” was officially adopted in 1948.
• The Réaumur and Celsius scales share one convenient property — both start at 0° for the freezing point of water.

Notes

• Both the Réaumur and Celsius scales are linear, simplifying conversion. Users only need to multiply or divide by the correct ratio.
• Since neither scale uses an offset, conversions do not require adding or subtracting constants (unlike Kelvin or Fahrenheit).
• Always ensure when reading or converting historical temperature values, the context (liquid used in the thermometer or pressure conditions) is similar, as early instruments could produce minor variations.

Frequently Asked Questions

How to convert 25°Réaumur into Celsius?

Use the formula $°C = °Re × \frac{5}{4}$.

$$°C = 25 × \frac{5}{4} = 31.25°C$$

So, 25°Re equals 31.25°C.

How many degrees Celsius correspond to 10 Réaumur?

$$°C = 10 × \frac{5}{4} = 12.5°C$$

Therefore, 10°Re equals 12.5°C.

What temperature in Réaumur equals 80°C?

To find the corresponding value:

$$°Re = 80 × \frac{4}{5} = 64°Re$$

So 80°C is equal to 64°Re.

How accurate is the conversion between Réaumur and Celsius?

Since both scales are directly proportional with no offset, the conversion is perfectly accurate within the precision limits of measurement instruments.

Why is the Réaumur scale rarely used today?

The Réaumur scale fell out of favor with the adoption of the Celsius scale and the metric system. Celsius offered a simpler, decimal-based structure that aligned with other metric measures, making it more practical for scientific and industrial applications.