Temperature Conversion Formula

Temperature conversion means changing a temperature from one scale to another, such as Celsius to Fahrenheit, Fahrenheit to Celsius, or Celsius to Kelvin.

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The main temperature conversion formulas are:

Quick Examples

25°C to Fahrenheit:

°F = (25 × 9/5) + 32

= 45 + 32

= 77°F

68°F to Celsius:

°C = (68 - 32) × 5/9

= 36 × 5/9

= 20°C

25°C to Kelvin:

K = 25 + 273.15

= 298.15 K

What Is Temperature Conversion?

Temperature conversion is the process of changing a temperature from one measurement scale to another while representing the same temperature.

For example:

0°C = 32°F = 273.15 K

These three values represent the same temperature.

Temperature conversion is commonly used in:

• Weather reports

• Science experiments

• Cooking

• Medicine

• Engineering

• Physics and chemistry

• International temperature comparisons

Read More - Binary to Octal Conversion

Temperature Scales and Their Formulas

The three temperature scales most commonly used in basic temperature conversion are Celsius, Fahrenheit, and Kelvin.

Celsius Scale

The Celsius scale is written using °C.

At standard atmospheric pressure:

• Water freezes at 0°C

• Water boils at 100°C

There are 100 Celsius degrees between these two reference points.

Fahrenheit Scale

The Fahrenheit scale is written using °F.

At standard atmospheric pressure:

• Water freezes at 32°F

• Water boils at 212°F

There are 180 Fahrenheit degrees between these two reference points.

Kelvin Scale

The Kelvin scale is written as K, without a degree symbol.

Kelvin is an absolute temperature scale used extensively in science.

• Absolute zero = 0 K

• Water freezes at approximately 273.15 K

• Water boils at approximately 373.15 K, at standard atmospheric pressure

The size of one kelvin is the same as the size of one Celsius degree. The difference between the two scales is their zero point.

Celsius to Fahrenheit Formula

To convert Celsius to Fahrenheit, use:

°F = (°C × 9/5) + 32

Steps

1. Multiply the Celsius temperature by 9.

2. Divide the result by 5.

3. Add 32.

Example

Convert 30°C to Fahrenheit.

°F = (30 × 9/5) + 32

°F = 54 + 32

°F = 86°F

Therefore:

30°C = 86°F

Fahrenheit to Celsius Formula

The F to C formula is:

°C = (°F - 32) × 5/9

Steps

1. Subtract 32 from the Fahrenheit temperature.

2. Multiply the result by 5.

3. Divide by 9.

Example

Convert 50°F to Celsius.

°C = (50 - 32) × 5/9

°C = 18 × 5/9

°C = 10°C

Therefore:

50°F = 10°C

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Celsius to Kelvin Formula

To convert Celsius to Kelvin:

K = °C + 273.15

Example

Convert 25°C to Kelvin.

K = 25 + 273.15

K = 298.15 K

Therefore:

25°C = 298.15 K

For school-level calculations, a question may sometimes instruct you to use 273 instead of 273.15. Always follow the value of the constant given in the question.

Kelvin to Celsius Formula

To convert Kelvin to Celsius:

°C = K - 273.15

Example

Convert 300 K to Celsius.

°C = 300 - 273.15

°C = 26.85°C

Therefore:

300 K = 26.85°C

Fahrenheit to Kelvin Formula

To convert Fahrenheit directly to Kelvin:

K = (°F - 32) × 5/9 + 273.15

Example

Convert 68°F to Kelvin.

First convert Fahrenheit to Celsius:

°C = (68 - 32) × 5/9

°C = 20°C

Then convert Celsius to Kelvin:

K = 20 + 273.15

K = 293.15 K

Therefore:

68°F = 293.15 K

Kelvin to Fahrenheit Formula

To convert Kelvin directly to Fahrenheit:

°F = (K - 273.15) × 9/5 + 32

Example

Convert 300 K to Fahrenheit.

°F = (300 - 273.15) × 9/5 + 32

°F = 26.85 × 9/5 + 32

°F = 48.33 + 32

°F ≈ 80.33°F

Therefore:

300 K ≈ 80.33°F

Temperature Conversion Formula Table

Use this table for quick revision:

Easy Memory Trick

For Celsius and Fahrenheit:

C to F: multiply by 9/5, then add 32.

F to C: subtract 32, then multiply by 5/9.

Notice that the order matters.

Why Is There a 32 in the Celsius to Fahrenheit Formula?

The 32 appears because water freezes at 32°F but at 0°C under standard atmospheric pressure.

The two scales therefore have different zero points.

For example:

0°C = 32°F

This is why converting Celsius to Fahrenheit requires adding 32 after adjusting the size of the temperature interval.

Why Are 9/5 and 5/9 Used?

Between the freezing and boiling points of water:

• Celsius has a difference of 100 degrees

• Fahrenheit has a difference of 180 degrees

So the ratio between their degree intervals is:

180/100 = 9/5

Therefore:

1°C = 9/5°F in terms of temperature interval size.

The reverse ratio is:

5/9

This gives the two conversion formulas:

°F = (°C × 9/5) + 32

°C = (°F - 32) × 5/9

Temperature Conversion Formula Derivation

The Celsius and Fahrenheit scales can be related using their freezing and boiling points.

For Celsius:

• Freezing point = 0°C

• Boiling point = 100°C

For Fahrenheit:

• Freezing point = 32°F

• Boiling point = 212°F

The relative positions can be written as:

C/100 = (F - 32)/180

Cross-multiplying:

180C = 100(F - 32)

Dividing by 20:

9C = 5(F - 32)

Therefore:

F = (9C/5) + 32

So:

°F = (°C × 9/5) + 32

Rearranging the same relationship gives:

°C = (°F - 32) × 5/9

Temperature Change Formula

Temperature change is different from temperature conversion.

If the initial temperature is T₁ and the final temperature is T₂, then:

ΔT = T₂ - T₁

where ΔT represents the change in temperature.

Example

A temperature increases from 15°C to 25°C.

ΔT = 25 - 15

ΔT = 10°C

So the temperature increased by 10°C.

For a temperature difference, a change of 10°C has the same size as a change of 10 K.

Solved Temperature Conversion Examples

Example 1: Celsius to Fahrenheit

Question: Convert 37°C to Fahrenheit.

Formula:

°F = (°C × 9/5) + 32

Substitute 37:

°F = (37 × 9/5) + 32

°F = 66.6 + 32

°F = 98.6°F

Therefore:

37°C = 98.6°F

Example 2: Fahrenheit to Celsius

Question: Convert 50°F to Celsius.

Formula:

°C = (°F - 32) × 5/9

°C = (50 - 32) × 5/9

°C = 18 × 5/9

°C = 10°C

Therefore:

50°F = 10°C

Example 3: Celsius to Kelvin

Question: Convert 25°C to Kelvin.

Formula:

K = °C + 273.15

K = 25 + 273.15

K = 298.15 K

Example 4: Kelvin to Celsius

Question: Convert 77 K to Celsius.

Formula:

°C = K - 273.15

°C = 77 - 273.15

°C = -196.15°C

Example 5: Fahrenheit to Kelvin

Question: Convert 212°F to Kelvin.

First convert Fahrenheit to Celsius:

°C = (212 - 32) × 5/9

°C = 180 × 5/9

°C = 100°C

Now convert Celsius to Kelvin:

K = 100 + 273.15

K = 373.15 K

Therefore:

Example 6: Kelvin to Fahrenheit

Question: Convert 273.15 K to Fahrenheit.

First convert Kelvin to Celsius:

°C = 273.15 - 273.15

°C = 0°C

Then convert Celsius to Fahrenheit:

°F = (0 × 9/5) + 32

°F = 32°F

Therefore:

273.15 K = 32°F

Important Temperature Conversion Values

Some temperatures are useful to remember:

The -40° point is special because:

-40°C = -40°F

Common Temperature Conversion Mistakes

Mistake 1: Forgetting 32

Incorrect:

°F = °C × 9/5

Correct:

°F = (°C × 9/5) + 32

Mistake 2: Subtracting 32 in the Wrong Direction

For Fahrenheit to Celsius:

°C = (°F - 32) × 5/9

Do not add 32 when converting Fahrenheit to Celsius.

Mistake 3: Reversing 9/5 and 5/9

Remember:

Celsius to Fahrenheit → 9/5

Fahrenheit to Celsius → 5/9

Mistake 4: Writing Degrees With Kelvin

Correct:

300 K

Incorrect:

300°K

Kelvin is written without the degree symbol.

Mistake 5: Confusing Temperature With Temperature Change

A temperature conversion changes the scale used to express a temperature.

A temperature change measures how much the temperature has increased or decreased.

For example:

20°C = 68°F

is a temperature conversion.

But:

25°C - 15°C = 10°C

describes a temperature change.

Is Kelvin the Same as Celsius?

Kelvin and Celsius have the same size unit interval, but their zero points are different.

The relationship is:

K = °C + 273.15

For example:

0°C = 273.15 K

and

100°C = 373.15 K

So Celsius and Kelvin are related, but they are not the same temperature scale.

Students can use CuriousJr to practise temperature conversions and understand the relationship between Celsius and Kelvin through simple examples.

Can 273.15 Be Rounded to 273?

Yes, if the question or calculation allows an approximation.

The precise conversion is:

K = °C + 273.15

In some school-level calculations, 273 may be used as an approximation:

K ≈ °C + 273

For example:

25°C ≈ 298 K

But when greater precision is required, use 273.15.

Temperature Conversion in Daily Life

Temperature conversion is useful when different temperature scales are used in different situations.

Weather

A weather report may use Celsius in one country and Fahrenheit in another.

Science

Scientific calculations commonly use Kelvin, especially in physics and thermodynamics.

Medicine

Body temperature is often expressed in Celsius or Fahrenheit depending on the country and context.

Cooking

Recipes and ovens may use different temperature units, so conversion can be useful when following an international recipe.

Quick Temperature Formula Revision

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

Temperature Change

ΔT = T₂ - T₁