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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.

Updated Checked against 5 worked examples

A number in the “from” unit, or with its own unit
Try
Converted value
°F
Converted value: 98.6 °F
Shown to 12 significant figures, half-up
Conversion
37 °C = 98.6 °F
Exactness
Exact

37 °C is exactly 98.6 °F.

On a thermometer

IceLiquid waterSteam1032212240Water freezesWater boils at 1 atm98.6 °F
37 °C in every temperature unit (5 rows)
UnitValueDefinition
kelvin (K)310.15Base unit
degree Celsius (°C)37K = °C + 273.15, exact
degree Fahrenheit (°F)98.6K = (°F + 459.67) × 5/9, exact
degree Rankine (°R)558.271 °R = 5/9 K, exact
degree Réaumur (°Ré)29.6K = (°Ré + 218.52) × 5/4, exact
How it's calculated S

  1. Convert degree Celsius to kelvin

    37+273.15=310.15 K37 + 273.15 = 310.15\ \text{K}

    K = °C + 273.15, exact

  2. Convert kelvin to degree Fahrenheit

    310.15÷59−459.67=98.6 °F310.15 \div \tfrac{5}{9} - 459.67 = 98.6\ \text{°F}

    K = (°F + 459.67) × 5/9, exact

  3. An offset as well as a factor

    Temperature scales have different zero points, so a conversion adds an offset as well as scaling. A temperature difference of 1 °C equals 1.8 °F.

    Both units are defined exactly and the converted value is a terminating decimal, so every digit shown in it is exact.

About the temperature converter

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.

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)

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.

About this calculator

t°F=t°C×95+32TK=t°C+273.15T°R=TK×95t°Reˊ=t°C×45\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}

Sources

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

Checked against references

5 worked examples with independently sourced answers ship with this calculator. They run in the test suite; you can run them here too.

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