AP Chemistry Temperature Conversions

Converting between Celsius, Kelvin, and Fahrenheit, and knowing when conversion is needed at all, in four worked examples.

Temperature shows up in gas laws, calorimetry, kinetics, and thermodynamics, and each topic treats it a little differently. Most errors come from one of two slips: using Celsius where kelvins are required, or converting when only a temperature change is involved. This page gives the conversion formulas and then the rule for when each applies. The calculations it supports are in the gas laws and calorimetry pages.

The Temperature Conversion Formulas and Reference Points

Celsius to kelvin: K = °C + 273 (more precisely, 273.15).
Kelvin to Celsius: °C = K − 273.
Fahrenheit to Celsius: °C = (°F − 32) × 5/9.
Celsius to Fahrenheit: °F = (°C × 9/5) + 32.

The Kelvin scale starts at absolute zero, so it has no negative values, and a kelvin is the same size as a Celsius degree. The chart marks common temperatures on all three scales. A good habit is to write the unit with every temperature, because a bare number cannot be checked.

Worked Example 1: Converting Between Celsius and Kelvin

Convert 25°C, 100°C, and −40°C to kelvins, and 350 K to Celsius.

25°C: 25 + 273 = 298 K.
100°C: 100 + 273 = 373 K.
−40°C: −40 + 273 = 233 K.
350 K: 350 − 273 = 77°C.

A negative Celsius value still gives a positive kelvin value, and a kelvin value below 273 is below the freezing point of water. If a result is negative in kelvins, an error has occurred, since absolute zero is the lower limit. Using 273.15 instead of 273 changes the answers in the second decimal place, which rarely matters with the number of significant figures in a typical problem; see significant figures.

Worked Example 2: Converting Fahrenheit to Kelvin in Two Steps

Normal body temperature is 98.6°F. Express it in degrees Celsius and in kelvins.

Celsius: (98.6 − 32) × 5/9 = 66.6 × 5/9 = 37.0°C.
Kelvin: 37.0 + 273 = 310 K.

There is no direct Fahrenheit-to-kelvin step in a formula to memorize: go to Celsius, then add 273. Chemistry problems in the United States sometimes give a Fahrenheit value for an everyday context, and the gas constant and other quantities need kelvins.

Worked Example 3: Using a Temperature Change Without Converting

A 50.0 g sample of water warms from 22.0°C to 35.5°C. Find the heat absorbed, using c = 4.184 J/(g·K).

Temperature change: ΔT = 35.5 − 22.0 = 13.5°C, which is also 13.5 K.
Heat: q = mcΔT = (50.0 g)(4.184 J/g·K)(13.5 K) = 2824 J = 2.82 kJ.

The specific heat is written per kelvin, but the Celsius change can be used directly because a kelvin and a Celsius degree are the same size. Converting each temperature first (295.0 K and 308.5 K) gives the same 13.5 K, so the conversion is unnecessary work. The method is explained further in calorimetry and specific heat.

Worked Example 4: Doubling the Kelvin Temperature in a Gas Law Problem

A gas at constant pressure is at 27°C. To double its volume, to what Celsius temperature must it be heated?

Start in kelvins: 27 + 273 = 300 K.
Double the volume: V is proportional to the Kelvin temperature, so T doubles to 600 K.
Back to Celsius: 600 − 273 = 327°C.

Doubling the Celsius value, to 54°C, is the common mistake; that would raise the Kelvin temperature only from 300 K to 327 K, a 9% change. Volume and pressure follow the Kelvin scale, which is why gas law setups start with a conversion. The same requirement applies to PV = nRT.

Five Temperature Conversion Practice Questions With Answers

Convert 0°C and 100°C to kelvins.
Show answer
0 + 273 = 273 K and 100 + 273 = 373 K.
Convert 310 K to degrees Celsius.
Show answer
310 − 273 = 37°C.
A solution warms from 20.0°C to 26.5°C. What is ΔT in kelvins?
Show answer
6.5 K. The change is the same number in °C and K.
Is 80°C twice as hot as 40°C? Explain.
Show answer
No. In kelvins the temperatures are 353 K and 313 K, a ratio of about 1.13. A ratio of temperatures only has meaning on the Kelvin scale.
Convert 68°F to kelvins.
Show answer
(68 − 32) × 5/9 = 20.0°C, and 20.0 + 273 = 293 K.

Common Temperature Conversion Mistakes

Using Celsius in a gas law or thermodynamics formula. Convert to kelvins first.
Converting a temperature change. A change in °C and a change in K are the same number.
Subtracting instead of adding 273. Celsius to kelvin adds; kelvin to Celsius subtracts.
Scaling Celsius values by a ratio. Doubling the Celsius value does not double the energy or volume.
Writing a degree sign on kelvins. The unit is K, not °K.
Forgetting the Fahrenheit offset. Subtract 32 before multiplying by 5/9.

Getting temperatures right is a small step that protects larger calculations. To see how a stronger Unit 3 or Unit 6 would shift your overall estimate, the AP Chem Score Calculator turns section scores into a 1–5 range.

Frequently Asked Questions

How do you convert Celsius to Kelvin?

Add 273 to the Celsius temperature (more precisely 273.15): K = °C + 273. For example, 25°C is 298 K. To convert kelvins to Celsius, subtract 273.

How do you convert Fahrenheit to Kelvin?

Convert to Celsius first with °C = (°F − 32) × 5/9, then add 273. For 98.6°F, (98.6 − 32) × 5/9 = 37.0°C, which is 310 K.

Why must temperature be in kelvins in chemistry calculations?

Many relationships, including the gas laws and the equations of thermodynamics, are proportional to absolute temperature, which is zero at 0 K. Celsius and Fahrenheit zeros are arbitrary, so using them gives wrong ratios.

Do you convert to kelvins when calculating a temperature change?

No. A kelvin and a Celsius degree are the same size, so a change in temperature has the same number in either unit, for example 13.5 °C is a change of 13.5 K. Convert only when the temperature itself is used in a ratio or a formula.

What is absolute zero?

Absolute zero is 0 K, or −273.15°C, the lowest possible temperature, where particles have the minimum possible motion. No Kelvin temperature is negative.

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