Temperature Conversion Equations and Examples

Temperature conversion equations translate a reading between Celsius, Fahrenheit, and Kelvin. Enter a temperature and choose its current scale to calculate the equivalent value in the other two scales; the equations below show how each result is obtained.

Formula

The calculator takes Celsius as its input. To convert Celsius to Fahrenheit, multiply by 9/5 and add 32. To convert Celsius to Kelvin, add 273.15.

• C or t is the temperature in degrees Celsius (°C).
• F is the equivalent temperature in degrees Fahrenheit (°F): F = C × 9/5 + 32.
• K is the equivalent temperature in kelvins (K): K = C + 273.15.

The calculator’s default input is 20 °C. Its Fahrenheit output is rounded to one decimal place; its Kelvin output is rounded to two. The kelvin unit is written K, without a degree sign.

Worked Example

Using the default value, C = 20 °C:

1. Fahrenheit: 20 × 9/5 + 32 = 36 + 32 = 68.0 °F.
2. Kelvin: 20 + 273.15 = 293.15 K.

So 20 °C is 68.0 °F and 293.15 K. The conversion is exact before display rounding.

Temperature Conversion Equations

For a conversion between any of the three common scales, use the equation that matches the starting and destination units:

• Celsius to Fahrenheit: °F = (°C × 9/5) + 32.
• Fahrenheit to Celsius: °C = (°F − 32) × 5/9.
• Celsius to Kelvin: K = °C + 273.15.
• Kelvin to Celsius: °C = K − 273.15.
• Fahrenheit to Kelvin: K = (°F − 32) × 5/9 + 273.15.
• Kelvin to Fahrenheit: °F = (K − 273.15) × 9/5 + 32.

The fractions 9/5 and 5/9 are the scale factors between Celsius and Fahrenheit. The added or subtracted constants account for where the scales place their zero points. A temperature difference converts differently from a temperature reading: a change of 1 °C equals a change of 1.8 °F, with no +32 offset.

How the Scales Differ

Celsius and Fahrenheit are everyday temperature scales, but their degree sizes and zero points differ. Water freezes at 0 °C, which corresponds to 32 °F, and boils at 100 °C, corresponding to 212 °F, at standard atmospheric pressure. Those reference points are separated by 100 Celsius degrees or 180 Fahrenheit degrees, giving the 9/5 relationship.

Kelvin is an absolute temperature scale used in scientific contexts. Its zero, 0 K, is absolute zero: the theoretical lower limit of thermodynamic temperature. Kelvin has the same size increments as Celsius, so a difference of 1 K is equal to a difference of 1 °C. The scales differ only in their zero points: 0 °C is 273.15 K.

When to Use Each Conversion

Choose the conversion based on the units expected by the person, device, or calculation you are working with. Celsius is common in weather reporting and many practical contexts around the world; Fahrenheit is used for everyday temperatures in some countries, including the United States. Kelvin is commonly used in scientific equations and measurements where an absolute scale is required.

For an everyday estimate, 0 °C is 32 °F, 20 °C is 68 °F, and 30 °C is 86 °F. For a quick mental conversion from Celsius to Fahrenheit, double the Celsius value and add 30. This is only an approximation: at 20 °C it gives 70 °F, rather than the exact 68 °F. Use the equation when accuracy matters.

Common Conversion Mistakes and Limits

• Forgetting the offset: Multiplying Celsius by 9/5 alone does not give Fahrenheit. Add 32 after scaling. For Fahrenheit to Celsius, subtract 32 before multiplying by 5/9.
• Reversing the fraction: Use 9/5 for Celsius-to-Fahrenheit and 5/9 for Fahrenheit-to-Celsius.
• Applying an offset to a temperature change: When converting a difference or interval, multiply by the scale factor only. For instance, a 10 °C rise is an 18 °F rise.
• Rounding too early: Keep the unrounded value through intermediate steps, then round the final answer to the precision needed. The displayed digits do not imply that a thermometer measured the original value that precisely.
• Confusing the Kelvin notation: Write kelvins as K, not °K. Celsius and Fahrenheit use degree symbols.

These equations convert a numerical reading between scales; they do not account for measurement uncertainty, sensor calibration, or local conditions. For example, the quoted freezing and boiling points of water assume standard atmospheric pressure, and boiling temperature can change when pressure changes.

Frequently Asked Questions

What is the equation for Celsius to Fahrenheit?
Multiply the Celsius temperature by 9/5, then add 32: °F = (°C × 9/5) + 32.

How do I convert Fahrenheit to Celsius?
Subtract 32 from the Fahrenheit reading and multiply the result by 5/9: °C = (°F − 32) × 5/9.

How do I convert Celsius to Kelvin?
Add 273.15 to the Celsius reading: K = °C + 273.15. For example, 0 °C equals 273.15 K.

Is a change of 1 °C the same as a change of 1 °F?
No. A change of 1 °C equals a change of 1.8 °F. The +32 in the Celsius-to-Fahrenheit equation is for converting a reading, not a temperature difference.

Can Celsius temperatures be negative?
Yes. A negative Celsius value is below 0 °C, the freezing point of water under standard atmospheric pressure. Negative readings can be converted with the same equations; for example, −40 °C equals −40 °F.

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in t | Temperature | °C | 20
out f | Fahrenheit | °F | t * 9 / 5 + 32 | 1
out k | Kelvin | K | t + 273.15 | 2