Converting between calories and watts is useful for understanding the energy content of food and how that energy is used by the human body. While calories measure the energy content of food, watts measure the rate at which energy is consumed or expended. Knowing how to convert between these units allows us to quantify both the energy we ingest as food and the rate at which we use that energy through metabolic processes and physical activity.

## Quick Answers

– 1 calorie = 4.184 joules

– 1 joule per second = 1 watt

– So 1 calorie = 4.184 joules = 4.184 watt-seconds

– To convert calories to watts, divide calories by seconds

## What are calories?

A calorie (cal) is a unit of energy. Specifically, 1 calorie is the amount of energy required to raise the temperature of 1 gram of water by 1 degree Celsius. Calories measure the energy content in food that can be extracted and used by the human body.

The Calorie (note the capital C), also known as the food calorie or the kilocalorie (kcal), is 1000 regular calories. Food labels in most countries, including the United States, report Calories rather than calories. So if a food item contains 300 Calories, this is equivalent to 300,000 calories.

## What are watts?

A watt (W) is a unit of power. Power measures the rate at which energy is generated or consumed. 1 watt is equal to 1 joule (J) of energy per second (s).

For example, a 100 watt light bulb uses 100 joules of energy every second. Watts measure power, or the rate of energy usage, while joules or calories measure total energy.

## The relationship between calories and watts

We can convert between calories and watts because there is a well-defined relationship between them:

- 1 calorie = 4.184 joules
- 1 joule/second = 1 watt

So one calorie is equal to 4.184 joules. And one joule per second equals one watt. Therefore:

**1 calorie = 4.184 joules = 4.184 watt-seconds**

To summarize:

- Calories measure the total energy content in food.
- Joules measure total energy.
- Watts measure the rate of energy usage or generation.

## Converting calories to watts

To convert calories to watts, we need to account for the time period over which the calories are expended. Here are the step-by-step directions:

- Determine the number of calories
- Convert calories to joules by multiplying by 4.184 joules/calorie
- Determine the time period (in seconds) over which the calories are used
- Divide the total joules by the time period in seconds to obtain watts

For example, if a person expends 300 Calories (300,000 calories) by running for 30 minutes (1800 seconds):

- 300 Calories x 1000 calories/Calorie = 300,000 calories
- 300,000 calories x 4.184 joules/calorie = 1,255,200 joules
- Time period is 1800 seconds
- 1,255,200 joules / 1800 seconds = 697 watts

So expending 300 Calories over 30 minutes of running is equivalent to 697 watts of power.

## Converting watts to calories

We can also convert in the opposite direction, from watts to calories:

- Determine the number of watts
- Determine the time period (in seconds) over which the power is expended
- Multiply watts by seconds to obtain total joules
- Divide joules by 4.184 joules/calorie to convert to calories

For example, if a 75 watt light bulb is left on for 5 hours (18,000 seconds):

- 75 watts
- Time period is 18,000 seconds
- 75 watts x 18,000 seconds = 1,350,000 joules
- 1,350,000 joules / 4.184 joules/calorie = 322,650 calories

So a 75 watt light bulb expended 322,650 calories of energy over 5 hours.

## Converting between Calories and watt-hours

Another useful energy conversion is between food Calories and watt-hours (Wh). A watt-hour represents one watt of power expended over one hour:

- 1 Wh = 1 watt x 1 hour = 3600 joules

To convert between Calories and watt-hours:

- 1000 Calories x 4184 joules/Calorie = 4,184,000 joules
- 4,184,000 joules / 3600 joules/Wh = 1162 Wh

So one Calorie is equivalent to 1162 watt-hours. This means that the 300 Calorie sandwich you ate for lunch represents 300 x 1162 = 348,600 watt-hours of energy!

## Applications: Food calories to exercise watts

One useful application of converting calories to watts is quantifying the exercise required to “burn off” calories from food. As an example, here is how to determine how many watts are required to burn 300 Calories with 30 minutes of exercise:

- 300 Calories x 1000 calories/Calorie = 300,000 calories
- 300,000 calories x 4.184 joules/calorie = 1,255,200 joules
- Exercise duration is 30 minutes = 1800 seconds
- 1,255,200 joules / 1800 seconds = 697 watts

So to expend 300 Calories in 30 minutes of exercise requires an average power output of 697 watts. This table shows some example Calorie and watt values for different exercises and durations:

Exercise | Duration | Calories burned | Average watts |
---|---|---|---|

Running (10 min mile pace) | 30 minutes | 300 Calories | 697 W |

Bicycling (12-14 mph) | 60 minutes | 600 Calories | 184 W |

Swimming (freestyle laps) | 45 minutes | 450 Calories | 213 W |

This demonstrates how converting Calories to watts can quantify the rate of energy expenditure for various forms of exercise.

## Applications: Watts generated by the human body

Converting watts to calories is useful for quantifying the total energy a person generates over time through metabolic processes and physical activity:

- Basal metabolic rate (energy used for basic functions): ~100 W
- Typical daily metabolic rate: ~125 W
- Vigorous cycling: ~200-500 W
- Running at 10 min/mile pace: ~700 W

Some examples conversions:

- 100 W basal metabolic rate x 24 hours = 86,400,000 joules = 20,640 Calories per day
- 700 W running x 1 hour = 2,520,000 joules = 603 Calories burned

So a person at rest burns about 100 watts or 2100 Calories per day. Vigorous exercise like running requires 600-700 watts, burning hundreds of additional Calories per hour.

## Larger-Scale Power Generation

On a larger scale, converting between watts, Calories, and other energy units helps quantify power generation from various sources:

Power source | Power output |
---|---|

Hoover Dam hydroelectric plant | 2.08 gigawatts (2,080,000,000 watts) |

Typical coal power plant | 600 megawatts (600,000,000 watts) |

Typical commercial wind turbine | 2.5 megawatts (2,500,000 watts) |

Single solar PV panel | 250-400 watts |

Some example conversions:

- 2.08 gigawatts Hoover Dam x 1 year = 1.8 x 10^13 watt-hours = 4.3 x 10^13 Calories per year
- 2.5 megawatt wind turbine x 1 day = 216,000 kWh = 250 million Calories per day

So the massive generation capacity of facilities like the Hoover Dam can be quantified in (very large!) calories or Calorie units per unit time.

## Limitations and Considerations

While straightforward unit conversions provide useful ballpark estimates, some limitations should be kept in mind:

- Calories and watts measure different aspects of energy, so conversions generally require assuming a time period.
- Biological systems are not 100% efficient, so not all calories consumed as food convert directly into usable energy.
- Power generation facilities also have inefficiencies, so their net energy output is lower than their rated capacity.
- Variability in exercise intensity and metabolism means wattages are just estimates, even for the same person.
- Technical note: Strictly speaking, the calories referenced are actually kilocalories – the conversions use the common nutrition Calorie of 4184 J, not the physics calorie of 4.184 J.

While approximations, calorie-watt conversions provide a useful bridge between the domains of nutrition, exercise physiology, and power engineering. They help put the enormous energies involved in food, the human body, and power infrastructure into a common framework!

## Conclusion

In summary, calories and watts are linked units for measuring energy and power:

- 1 Calorie = 4184 joules of energy
- 1 watt = 1 joule/second of power
- Converting between them requires knowing the time period over which the energy is expended
- Calorie-watt conversions help quantify metabolism, exercise, food energy content, and power generation
- But generic conversions give only approximations due to complex biological and thermodynamic factors

While not exact, converting between calories and watts provides a useful bridge between nutrition, biology, and engineering. It enables quantifying both the massive energy we consume as food and the rates at which our bodies use that energy through life-sustaining metabolic processes and varied physical activities across the human power range.