Celsius to Fahrenheit Converter — Convert Celsius to Fahrenheit

Temperature

37°C

Formula

F = C × 9/5 + 32

1. 1

   Multiply by 9/5 (= 1.8).

   37 × 1.8 = 66.6
2. 2

   Add the 32° offset.

   66.6 + 32 = 98.6

37°C = 98.6°F — normal human body temperature.

The familiar “98.6°F” figure is not an independent measurement. Carl Wunderlich established 37°C as normal body temperature in 1851; the Fahrenheit equivalent is just the arithmetic result of the conversion formula.

Temperature

−40°C

1. 1

   Multiply by 1.8.

   −40 × 1.8 = −72
2. 2

   Add 32.

   −72 + 32 = −40

−40°C = −40°F. The scales cross here and only here.

You can verify this algebraically: set F = C in the formula and solve. C × 1.8 + 32 = C → 0.8C = −32 → C = −40. Both scales agree at exactly −40 degrees.

1. [1]BIPM SI Brochure — Thermodynamic temperature and the kelvin · Bureau International des Poids et Mesures · 2019
2. [2]NIST SP 811 — Temperature conversions and ITS-90 · National Institute of Standards and Technology · 2008

Degree Celsius (°C)

The SI-accepted temperature unit. Zero is the freezing point of water; 100 is the boiling point at 1 atm.

Formally defined via the Kelvin scale: T(°C) = T(K) − 273.15. A change of 1°C equals a change of 1 K. Used in all scientific work and in everyday life outside the United States.

Degree Fahrenheit (°F)

The US customary temperature unit. Water freezes at 32°F and boils at 212°F at sea level.

One Fahrenheit degree is exactly 5/9 the size of one Celsius degree. The scale is still used for weather forecasts, cooking temperatures, and body temperature reporting in the United States.

The 9/5 Ratio

The scale factor between Celsius and Fahrenheit. 1°C change = 1.8°F change.

Comes from the ratio of the two scales’ degree sizes: 212 − 32 = 180°F spans the same range as 100 − 0 = 100°C. So 180/100 = 9/5 = 1.8. This is why temperature differences multiply by 1.8 even though absolute temperatures need the +32 offset too.

The 32°F Offset

The Fahrenheit value of 0°C (the freezing point of water). Added after scaling.

Because the two scales have different zero points — Celsius zeros at the freezing point of water, Fahrenheit at an older brine-ice reference — you must add 32 when converting absolute temperatures. Temperature differences do not need this offset.

Kelvin (K)

The SI base unit of thermodynamic temperature. 0 K is absolute zero; 273.15 K = 0°C.

Unlike Celsius and Fahrenheit, Kelvin has no negative values — 0 K is the theoretical minimum temperature. To convert Celsius to Kelvin, add 273.15. Scientific formulas for thermodynamics, radiation, and gas laws require Kelvin.

Normal Body Temperature

37°C / 98.6°F. The clinical average established by Carl Wunderlich (1851).

Modern research shows individual variation: healthy adults range from about 36.1°C to 37.2°C (97°F to 99°F). The 98.6°F figure is a Celsius-rounded number — 37°C converts to exactly 98.6°F.

Fever Threshold

37.8°C / 100.0°F (US clinical standard). Above this, a temperature is typically considered a fever.

The CDC and most US healthcare providers define fever as an oral temperature above 100°F (37.8°C) in adults. The World Health Organization and European guidelines often use 38°C (100.4°F) as the threshold.

The −40 Crossover

The only temperature where °C and °F are numerically equal: −40°C = −40°F.

Algebraically derived by setting C = F in F = 1.8C + 32 and solving: 1.8C + 32 = C → 0.8C = −32 → C = −40. This curiosity is also a real temperature: −40°F occurs in Arctic and Antarctic continental winters.