Celsius to Fahrenheit

Free instant celsius to fahrenheit converter. °F = (°C × 9 / 5) + 32.

33.8
Formula
°F = (°C × 9 / 5) + 32

Common Celsius to Fahrenheit values

Common Celsius to Fahrenheit conversion values.
Celsius (°C)Fahrenheit (°F)
-40-40
032
1050
2068
2577
3798.6
100212
10001832

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How does Celsius to Fahrenheit conversion work?

Type a value in the Celsius (°C) field and the equivalent in Fahrenheit (°F) appears instantly to the right. The math uses the exact formula shown above — no rounding errors, no approximations beyond standard floating-point precision. Use the swap button to flip the units and see the inverse conversion.

Celsius. The metric temperature unit. 0 °C is the freezing point of water; 100 °C is the boiling point at sea level.

Fahrenheit. The temperature unit used in the United States. 32 °F is the freezing point of water; 212 °F is the boiling point at sea level.

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🎯 Accurate conversions

Conversion factors come from the official standard (NIST, BIPM, ISO definitions where applicable). Values are precise to standard floating-point limits.

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How it works — the formula

F = C × 9/5 + 32 C = (F − 32) × 5/9 K = C + 273.15 C = K − 273.15

Temperature scales are affine, not linear: they have both a slope and an offset because zero on one scale is not zero on another. Celsius and Fahrenheit share a slope ratio of 9:5 and intersect at −40° (where °C = °F). Kelvin uses the same magnitude as Celsius but its zero is absolute zero, the lowest physically possible temperature; the 2019 SI redefinition fixed the Boltzmann constant k = 1.380649 × 10⁻²³ J/K exactly.

Worked examples

Example 1
Body temperature
Inputs:
37 °C = ? °F
Output:
37 × 9/5 + 32 = 98.6 °F
Example 2
Freezing & boiling
Inputs:
0 °C, 100 °C → °F
Output:
32 °F and 212 °F (definitions of the Fahrenheit scale)
Example 3
Equal-value crossover
Inputs:
−40 °C = ? °F
Output:
−40 °F (the unique fixed point where °C = °F)

Limitations

  • Negative kelvin is unphysical — absolute zero (0 K = −273.15 °C) is the floor for ordinary thermodynamic temperature.
  • Rankine (°R) is a US-engineering absolute scale (R = F + 459.67) sometimes seen in older HVAC / aerospace work.
  • Wind chill, "feels-like" temperatures, and humidity-adjusted indices are NOT pure unit conversions — they are derived metrics with their own formulas.
  • Above ~10⁹ K, plasma physics uses electronvolt as a temperature unit (1 eV ≈ 11,605 K) — out of scope for everyday converters.

Conversions are exact rational identities between Celsius/Fahrenheit/Kelvin; trailing-digit differences come from binary floating-point representation only.

Frequently asked

What is the formula for converting Celsius to Fahrenheit?+
The formula is: °F = (°C × 9 / 5) + 32. Type any value into the calculator above and the result appears instantly.
How do I convert Fahrenheit back to Celsius?+
Click the swap button (⇄) above to go to the Fahrenheit → Celsius converter, or use the inverse formula derived from the one shown.
How accurate is the conversion?+
Conversion factors used here are exact rational values from NIST SP 811 and the BIPM SI brochure (e.g. 1 ft = 0.3048 m exactly, 1 lb = 0.45359237 kg exactly). Trailing-digit differences vs hand calculation come only from binary floating-point representation, never from the conversion factor itself.
Where do these conversion factors come from?+
Length and mass factors come from the 1959 international yard-and-pound agreement; SI base units (metre, kilogram, second, kelvin) come from the 2019 BIPM redefinition; energy and pressure factors are NIST SP 811 reference values. Each editorial section above lists the specific source for that category.
Why does temperature conversion use offset, not just multiplication?+
Unlike most units, the zero point of Celsius and Fahrenheit are different (water freezes at 0 °C but 32 °F). That offset must be subtracted before — or added after — the multiplication. Kelvin shares the same scale as Celsius but starts at absolute zero (−273.15 °C).

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