Celsius to Fahrenheit Formula
The formula to convert a temperature from degrees Celsius to degrees Fahrenheit is:
°F = (°C × 9/5) + 32
Decimal form: °F = °C × 1.8 + 32
Where the formula comes from
Both scales are defined by two fixed points of water at standard pressure:
| Reference point | Celsius | Fahrenheit |
|---|---|---|
| Water freezes | 0 °C | 32 °F |
| Water boils | 100 °C | 212 °F |
| Difference | 100 degrees | 180 degrees |
The same temperature range spans 100 Celsius degrees but 180 Fahrenheit degrees, so one Celsius degree equals 180 ÷ 100 = 9/5 = 1.8 Fahrenheit degrees. That gives the slope. Because 0 °C corresponds to 32 °F, the line is shifted up by 32. Put together: °F = °C × 9/5 + 32.
Examples using the formula
The reverse formula (Fahrenheit to Celsius)
°C = (°F − 32) × 5/9
Subtract 32 first, then multiply by 5/9 (about 0.5556). For example, 98.6 °F − 32 = 66.6, and 66.6 × 5/9 = 37 °C. Use the Fahrenheit to Celsius converter for instant results.
Related formulas
- Celsius to Kelvin: K = °C + 273.15
- Fahrenheit to Kelvin: K = (°F − 32) × 5/9 + 273.15
- The scales are equal at −40: −40 °C = −40 °F, the only solution of x = 1.8x + 32.
Use the formula with the calculator
Frequently asked questions
Is the formula 9/5 or 5/9?
Use 9/5 (1.8) when converting Celsius to Fahrenheit and 5/9 when converting Fahrenheit to Celsius.
Is °F = °C × 1.8 + 32 the same formula?
Yes. 9/5 is exactly 1.8, so both forms always give identical results.
Does the formula work for negative temperatures?
Yes. Keep the minus sign through the multiplication: −20 °C × 1.8 = −36, and −36 + 32 = −4 °F.