Temperature Conversion Formula
The three main temperature scales–Celsius, Fahrenheit, and Kelvin–measure the same physical property but use different starting points and increments. Converting between them requires specific formulas that work consistently across all ranges.
Temperature Conversion Formula Overview
Temperature conversion relies on linear relationships between scales. Each scale has a different reference point and degree size, so conversions involve both multiplication and addition.
Celsius (°C) – used worldwide, freezes at 0° and boils at 100° Fahrenheit (°F) – primarily used in the United States, freezes at 32° and boils at 212° Kelvin (K) – the absolute temperature scale used in science, starts at 0 (absolute zero)
Celsius to Fahrenheit Formula
The formula converts Celsius degrees to Fahrenheit:
(°C × 9/5) + 32 = °F
The ratio 9/5 (or 1.8) comes from the different degree sizes: a Celsius degree is smaller than a Fahrenheit degree. Adding 32 accounts for the offset between freezing points.
Example: Convert 25°C to Fahrenheit
- (25 × 9/5) + 32
- (25 × 1.8) + 32
- 45 + 32
- 25°C = 77°F
Example: Convert −10°C to Fahrenheit
- (−10 × 9/5) + 32
- (−10 × 1.8) + 32
- −18 + 32
- −10°C = 14°F
Fahrenheit to Celsius Formula
To reverse the conversion, subtract the offset first, then apply the inverse ratio:
(°F − 32) × 5/9 = °C
The 5/9 ratio is the inverse of 9/5, converting Fahrenheit’s smaller degrees back to Celsius’s larger ones.
Example: Convert 98.6°F (human body temperature) to Celsius
- (98.6 − 32) × 5/9
- 66.6 × 5/9
- 333 ÷ 9
- 98.6°F = 37°C
Example: Convert 32°F to Celsius
- (32 − 32) × 5/9
- 0 × 5/9
- 32°F = 0°C
Kelvin Conversion Formula
Kelvin uses the same degree size as Celsius but starts at absolute zero. Convert between these two directly:
°C + 273.15 = K
K − 273.15 = °C
Unlike Celsius and Fahrenheit, Kelvin requires no multiplication–only a fixed offset. The value 273.15 represents the Celsius temperature of absolute zero.
Example: Convert 20°C to Kelvin
- 20 + 273.15
- 20°C = 293.15 K
Example: Convert 0 K to Celsius
- 0 − 273.15
- 0 K = −273.15°C
For Fahrenheit to Kelvin conversions, combine both formulas:
(°F − 32) × 5/9 + 273.15 = K
Example: Convert 77°F to Kelvin
- (77 − 32) × 5/9 + 273.15
- 45 × 5/9 + 273.15
- 25 + 273.15
- 77°F = 298.15 K
Common Temperature Conversions
| Celsius | Fahrenheit | Kelvin | Description |
|---|---|---|---|
| −273.15 | −459.67 | 0 | Absolute zero |
| −40 | −40 | 233.15 | Celsius = Fahrenheit |
| 0 | 32 | 273.15 | Water freezes |
| 20 | 68 | 293.15 | Room temperature |
| 37 | 98.6 | 310.15 | Human body temperature |
| 100 | 212 | 373.15 | Water boils |
Which Formula Should You Use?
For everyday use: Celsius and Fahrenheit conversions are most common. Use (°C × 9/5) + 32 or (°F − 32) × 5/9 depending on your direction.
For scientific work: Convert to Kelvin. The formula K = °C + 273.15 is simpler and avoids the multiplication step.
For temperature differences: The degree size differs between scales. A change of 1°C equals 1.8°F (or 9/5°F) in magnitude, but for absolute temperatures, always use the full conversion formulas above.
These formulas are standard definitions of temperature scales; no assumptions are made about climate, weather, or measurement conditions.