# What is the formula for joules to calories?

Converting between joules and calories is important in many scientific and nutritional contexts. While they are both units of energy, they are defined differently and have a specific conversion factor.

The formula for converting joules to calories is:

Calories = Joules x 0.239006

Or

Calories = Joules / 4.184

Where 4.184 joules equals 1 calorie. This conversion factor is derived from the specific definitions of the joule and calorie units.

## What is a Joule?

The joule is the SI unit of energy. One joule (abbreviated J) is defined as the amount of work done by a force of one newton exerted over a distance of one meter. It is also equivalent to one watt of power exerted over one second.

• 1 joule = the work done by a force of 1 newton that moves an object 1 meter.
• 1 joule = 1 watt of power applied for 1 second.
• 1 joule = 0.737 foot-pounds of energy.
• 1 kilojoule (kJ) = 1000 joules.

Joules are commonly used to measure energy in scientific contexts such as physics, engineering, and chemistry. Some examples of energy measured in joules include:

• The kinetic energy of a moving object
• The potential energy stored in a compressed spring
• The energy released in a chemical reaction
• The heat energy gained or lost by an object

## What is a Calorie?

The calorie is a unit of energy in the cgs (centimeter-gram-second) system. There are two common definitions of the calorie:

• Small calorie (cal) – The amount of energy needed to raise 1 gram of water by 1°C at standard atmospheric pressure. This is approximately 4.184 joules.
• Large calorie (Cal/kcal) – Also known as the food calorie. Equal to 1000 small calories or 4184 joules.

Calories are commonly used to measure energy content and expenditure in food and nutrition applications. For example:

• The energy content of foods is given in Calories (large calories) or kcal.
• Metabolic rate and energy expenditure is measured in calories (small calories) per hour or day.
• Weight loss diets count calories consumed and burned.

## Joules to Calories Conversion

To convert between joules and calories, we need to use a conversion factor derived from their definitions:

• 1 calorie = 4.184 joules (by definition)
• 1 Calorie (food calorie) = 4184 joules

Using these conversion factors, we can derive the following relationships:

To convert joules to calories:

Calories = Joules x 0.239006

To convert joules to Calories (food):

Calories (food) = Joules x 0.000239006

To convert calories to joules:

Joules = Calories x 4.184

To convert Calories (food) to joules:

Joules = Calories (food) x 4184

### Joules to Calories Formula Examples

Here are some examples using the formulas to convert joules to calories:

Joules Calories Conversion
10 J 10 x 0.239006 = 2.39006 cal ~ 2.4 calories
150 J 150 x 0.239006 = 35.85089 cal ~ 36 calories
5000 J 5000 x 0.239006 = 1195.03 cal ~ 1195 calories

To convert in the opposite direction from calories to joules, simply use the conversion factor of 4.184 joules per calorie.

## Why Convert Between Joules and Calories?

Being able to convert between joules and calories is useful for many applications in science, engineering, nutrition and more. Here are some examples of when you might need to convert between the units:

• Nutrition information. Food labels provide energy content in Calories (kcal), so converting to joules can be useful.
• Diets and weight loss. Calorie counting for diets requires converting exercise in joules to calories burned.
• Physics calculations. Problems may provide energy data in joules or calories, requiring conversion between the units.
• Engineering work. When dealing with measurements of heat, power and energy, it may be necessary to convert between joules and calories.
• Chemical reactions. Heats of reaction or combustion may be provided in either calories or joules.

So in many scientific and practical contexts, the ability to move between joules and calories using the conversion factor of 4.184 joules per calorie is very useful.

## Joule vs Calorie Summary

• The joule (J) is the SI unit of energy, defined in terms of force and distance.
• The calorie (cal) is a non-SI unit defined based on heating water. Larger food Calories (kcal) are often used.
• The conversion factor between joules and calories is 1 cal = 4.184 J.
• Use the formula: Calories = Joules x 0.239006 to convert joules to calories
• This conversion is useful across science, engineering, nutrition and other fields.

### What are some examples of joules in everyday life?

Here are some examples of energy amounts in joules that we encounter in everyday life:

• A 100 watt light bulb consumes 100 joules of energy every second
• A 2 liter bottle of soda contains approximately 836,800 joules of energy
• Boiling a pot of water requires around 30,000 joules
• A 180 pound person climbing 10 stairs expends around 180 joules
• A peanut butter and jelly sandwich provides approximately 850,000 joules of energy

### What are some examples of calories in food?

Here are the typical Calories (food calories) provided by some common foods:

• Apple – 95 Calories
• Hamburger – 260 Calories
• Slice of pizza – 285 Calories
• Bowl of pasta – 500 Calories
• Bagel with cream cheese – 350 Calories
• Chocolate bar – 230 Calories

Daily recommended calorie intake depends on age, gender, and activity level but is typically around 2000-2500 Calories per day for adults.

### How many joules are in a food Calorie?

One food Calorie (with a capital C) is equal to 4184 joules. This is because a food Calorie is the same as a kilocalorie (kcal), which is 1000 small calories, and there are 4.184 joules in 1 small calorie. So for nutrition labels, the calories listed for foods in Calories are really kilocalories, each equal to 4184 joules.

### What is the difference between a calorie and a Calorie?

The main difference between a calorie and a Calorie is capitalization. A calorie (lower case c) is defined as the amount of energy to heat 1 gram of water 1°C. A Calorie (upper case C) is 1000 calories, equivalent to a kilocalorie (kcal), and is the amount typically used to represent food energy. The reason capital Calories are used is that the energy content of foods is so high that the smaller calorie values would require inconveniently large numbers.

### Why are there two different definitions of the calorie?

There are two main definitions of the calorie in common use:

• Small calorie (cal) – Based on heating 1 g water 1°C
• Large calorie (Cal/kcal) – Equal to 1000 small calories, used in nutrition

The small calorie definition is convenient for thermochemistry and defining the joule. But expressing food energies in thousands of small calories resulted in the use of the large Calorie. The confusing double definition arose from the history of the calorie being defined and used before the joule was adopted as the standard SI energy unit.

## Conclusion

In summary, converting between joules and calories is straightforward using the conversion factor of 4.184 joules per calorie. This allows moving between the SI-derived joule unit and the non-SI calorie unit commonly used in nutrition. Being able to make this conversion is useful across many scientific, engineering and practical applications.