Celsius, Réaumur and Fahrenheit converter

What is a temperature conversion?

Temperature conversion is the process of expressing a temperature reading in one scale (for example, Celsius) in another scale such as Fahrenheit or Réaumur. Each of these scales is based on a different calibration of the freezing and boiling points of water. This converter automatically performs these conversions and clearly displays results in all three scales simultaneously, allowing easier comparisons and practical use in science, meteorology, cooking, and daily life.

Understanding the temperature scales

Celsius scale (°C)

The Celsius scale, sometimes called the centigrade scale, was introduced by Anders Celsius in 1742. On this scale, the freezing point of water is 0°C, and the boiling point is 100°C under standard atmospheric pressure (1 atm). Celsius is commonly used in most countries and in nearly all scientific contexts because it is simple and based on a decimal system.

Fahrenheit scale (°F)

The Fahrenheit scale was developed by Daniel Gabriel Fahrenheit in 1724. It sets the freezing point of water at 32°F and the boiling point at 212°F. The scale divides the temperature difference between these points into 180 equal parts. Fahrenheit is still widely used in the United States for everyday temperature measurement.

Réaumur scale (°Ré or °Re)

The Réaumur scale, introduced by René Antoine Ferchault de Réaumur in 1730, takes 0°Ré as the freezing point of water and 80°Ré as its boiling point. Although less commonly used today, it was once popular in parts of Europe, particularly in the 18th and 19th centuries, and still appears in older scientific literature and some specialized applications in brewing, cheese making, and sugar processing.

Formula

Temperature conversions between Celsius (C), Fahrenheit (F), and Réaumur (R) can be carried out using the following formulas:

$$F = \frac{9}{5}C + 32$$ $$C = \frac{5}{9}(F - 32)$$ $$R = \frac{4}{5}C$$ $$C = \frac{5}{4}R$$ $$F = \frac{9}{4}R + 32$$ $$R = \frac{4}{9}(F - 32)$$

These relationships allow any one temperature to be expressed in all three scales with high accuracy.

Degree scale comparison

Each scale has linear increments. Key relationships:

• 1 °F = 5/9 °C ≈ 0.5556 °C
• 1 °C = 9/5 °F = 1.8 °F
• 1 °Ré = 1.25 °C = 2.25 °F
• 1 °F ≈ 0.69444 °Ré

Thus, Réaumur degrees are larger than Celsius degrees (1 °Ré = 1.25 °C), and Fahrenheit degrees are smaller than Celsius degrees (1 °F ≈ 0.5556 °C).

Practical conversion examples

Example 1: Converting 25°C

Let’s convert 25°C to Fahrenheit and Réaumur.

Using the formula for Fahrenheit:

$$F = \frac{9}{5} \times 25 + 32 = 45 + 32 = 77°F$$

Using the formula for Réaumur:

$$R = \frac{4}{5} \times 25 = 20°Ré$$

So, 25°C = 77°F = 20°Ré.

Example 2: Converting 68°F

Now convert 68°F to Celsius and Réaumur.

$$C = \frac{5}{9}(68 - 32) = \frac{5}{9} \times 36 = 20°C$$ $$R = \frac{4}{5} \times 20 = 16°Ré$$

Thus, 68°F = 20°C = 16°Ré.

Example 3: Converting 40°Ré

Convert 40°Ré to Celsius and Fahrenheit.

$$C = \frac{5}{4} \times 40 = 50°C$$ $$F = \frac{9}{5} \times 50 + 32 = 90 + 32 = 122°F$$

Therefore, 40°Ré = 50°C = 122°F.

Historical notes

The differences among these temperature scales were motivated by the efforts of early scientists to standardize thermometry.

• René de Réaumur proposed his scale based on ethanol’s expansion range, which led to practical applications in food production.
• Anders Celsius originally defined his scale the other way round (100 for freezing and 0 for boiling) before it was inverted by Carl Linnæus to its present form.
• Daniel Fahrenheit built the first reliable mercury thermometer and used brine freezing and human body temperature as his reference points.

Understanding these historical roots helps appreciate why temperature scales differ and how they evolved.

Tips for Accurate Conversion

1. Always use correct mathematical rounding rules when necessary, especially in laboratory contexts.
2. Remember that negative values are converted the same way—you only need to follow the formula carefully.
3. When absolute accuracy is required, it is best to calculate using extended decimal values before rounding.
4. For physical and engineering calculations, temperatures in Celsius should first be converted to Kelvin by adding 273.15 if thermodynamic formulas are used.

Frequently Asked Questions

How many Fahrenheit degrees equal 1 Celsius degree?

A change of 1°C corresponds to a change of $\frac{9}{5} = 1.8°F$. This means that an increase of 10°C equals an increase of 18°F.

How to convert 100°F to Celsius and Réaumur?

Start with the conversion to Celsius:

$$C = \frac{5}{9}(100 - 32) = \frac{5}{9} \times 68 = 37.78°C$$

Then convert to Réaumur:

$$R = \frac{4}{5} \times 37.78 = 30.22°Ré$$

So, 100°F = 37.78°C = 30.22°Ré.

What is the freezing point of water in all three scales?

The freezing point of water is 0°C, 32°F, and 0°Ré. These are the baseline reference temperatures in each respective scale.

How many degrees separate freezing and boiling points of water in each scale?

There are 100 degrees between freezing and boiling points in Celsius, 180 degrees in Fahrenheit, and 80 degrees in Réaumur. These differences show why conversion factors differ among scales.

Why is the Réaumur scale rarely used today?

Although practical in certain historic industrial applications, its limited temperature range and regional specificity caused it to fall out of scientific favor after Celsius and Kelvin became internationally standardized.