# Temperature converter

> Convert Celsius to Fahrenheit, °F to °C and both to kelvin with °F = °C × 9/5 + 32. Includes Rankine and Réaumur; rejects values below absolute zero.

Interactive version: https://www.calcopenly.com/conversion/temperature-converter
Subject: Unit converters

Temperature scales differ in the size of a degree and in where zero sits, so a conversion adds an offset as well as multiplying: °F = °C × 9/5 + 32, and K = °C + 273.15. The converter works through kelvin, whose zero is absolute zero, and rejects any value below it (−273.15 °C or −459.67 °F).

The default converts normal body temperature: 37 × 9/5 + 32 = 98.6 °F. Weather forecasts, oven settings and fever readings are the everyday uses; the 38 °C fever threshold is 100.4 °F.

A temperature difference converts without the offset: a rise of 10 °C is a rise of 18 °F. Rankine is the absolute scale with Fahrenheit-sized degrees, and Réaumur is a historical scale with 80 degrees between the freezing and boiling points of water.

## Inputs

- **Value**: A number in the “from” unit, or with its own unit
- **From** (options: kelvin (K), degree Celsius (°C), degree Fahrenheit (°F), degree Rankine (°R), degree Réaumur (°Ré))
- **To** (options: kelvin (K), degree Celsius (°C), degree Fahrenheit (°F), degree Rankine (°R), degree Réaumur (°Ré))

## Results

- Converted value — main result
- Conversion
- Conversion factor
- Exactness

## Formula

$$
\begin{gathered} t_{\text{°F}} = t_{\text{°C}} \times \tfrac{9}{5} + 32 \\ T_{\text{K}} = t_{\text{°C}} + 273.15 \\ T_{\text{°R}} = T_{\text{K}} \times \tfrac{9}{5} \\ t_{\text{°Ré}} = t_{\text{°C}} \times \tfrac{4}{5} \end{gathered}
$$

## Worked examples

### Body temperature, 37 °C in °F

- Value: 37 °C
- From: degree Celsius (°C)
- To: degree Fahrenheit (°F)
- **Converted value: 98.6 °F**
- **Conversion: 37 °C = 98.6 °F**
- **Exactness: Exact**
- Checked against: °F = °C × 9/5 + 32 (NIST SP 811 §4.2.1.1): 37 × 1.8 + 32 = 98.6

### −40 is the same in both scales

- Value: -40 °C
- From: degree Celsius (°C)
- To: degree Fahrenheit (°F)
- **Converted value: -40 °F**
- Checked against: −40 × 9/5 + 32 = −40

### Absolute zero in °F

- Value: 0 K
- From: kelvin (K)
- To: degree Fahrenheit (°F)
- **Converted value: -459.67 °F**
- **Exactness: Exact**
- Checked against: 0 K = −273.15 °C; −273.15 × 9/5 + 32 = −459.67 °F (NIST SP 811 App. B.9)

### 100 °F in °C

- Value: 100 °F
- From: degree Fahrenheit (°F)
- To: degree Celsius (°C)
- **Converted value: 37.7777777778 °C**
- **Exactness: Exact definitions, repeating decimal**
- Checked against: (100 − 32) × 5/9 = 340/9 (Python 3.8 fractions from the legal definitions)

### 300 K in °R

- Value: 300 K
- From: kelvin (K)
- To: degree Rankine (°R)
- **Converted value: 540 °R**
- **Conversion factor: 1.8**
- Checked against: °R = K × 9/5 (NIST SP 811 App. B.9)

## Questions

### How do I convert Celsius to Fahrenheit?

Multiply by 9/5 (1.8) and add 32. For 37 °C, 37 × 1.8 = 66.6, and adding 32 gives 98.6 °F. To go back, subtract 32 and multiply by 5/9: (100 °F − 32) × 5/9 = 37.78 °C. NIST SP 811 states the same relation as t/°F = 1.8 t/°C + 32.

### Is 98.6 °F normal body temperature?

98.6 °F is the exact Fahrenheit value of 37 °C, the average Carl Wunderlich published in 1868; individual readings vary with the person, the time of day and where the thermometer goes. For illness the threshold matters more: the NHS treats 38 °C or above as a high temperature, and the US CDC defines fever as 100.4 °F, the same value.

### At what temperature are Celsius and Fahrenheit equal?

At −40. Setting the two numbers equal in °F = °C × 9/5 + 32 gives x = 1.8x + 32, so x = −40, and −40 °C is exactly −40 °F. It is the only crossing point because the degrees differ in size; above −40 the Fahrenheit number is always the larger one.

### How do I convert Celsius to kelvin?

Add 273.15: 25 °C is 298.15 K, and absolute zero, 0 K, is −273.15 °C. A kelvin is the same size as a Celsius degree and, since 2019, is defined by fixing the Boltzmann constant at 1.380649 × 10⁻²³ J/K (BIPM SI Brochure). Kelvin is written without a degree sign.

### Why is a 10 °C rise an 18 °F rise and not 50 °F?

Because a difference has no zero point to shift. One Celsius degree is 1.8 Fahrenheit degrees, so a change of 10 °C is a change of 18 °F; the +32 applies only to a reading on the scale. The converter's steps show the offset and the per-degree factor separately for this reason.

### How accurate is the temperature converter?

Accuracy depends on your inputs and the method's assumptions. Decimal arithmetic uses 50 significant digits, but estimates, numerical methods and source data can be less precise; the displayed rounding does not remove those limits. It is checked against 5 worked examples whose answers come from independent sources; for example, “Body temperature, 37 °C in °F” is checked against °F = °C × 9/5 + 32 (NIST SP 811 §4.2.1.1): 37 × 1.8 + 32 = 98.6.

### Where does the method come from?

NIST SP 811 (2008), Guide for the Use of the SI, Appendix B — conversion factors; NIST Handbook 44, Appendix C — General tables of units of measurement; BIPM SI Brochure, 9th edition (2019), §2.3.1 — the kelvin and degree Celsius.

## Sources

- [NIST SP 811 (2008), Guide for the Use of the SI, Appendix B — conversion factors](https://www.nist.gov/pml/special-publication-811)
- [NIST Handbook 44, Appendix C — General tables of units of measurement](https://www.nist.gov/pml/owm/nist-handbook-44-current-edition)
- [BIPM SI Brochure, 9th edition (2019), §2.3.1 — the kelvin and degree Celsius](https://www.bipm.org/en/publications/si-brochure)