Converting between different units of power or energy can be useful in many situations. For example, when looking at nutritional information, calories are commonly used to measure the energy content of foods. However, in physics, power is more often expressed in watts. Being able to convert between watts and calories allows you to compare power usage across different systems and applications.
What is a watt?
A watt (symbol: W) is a unit of power. Power is defined as the rate at which energy is transferred or the rate at which work is done. One watt is equal to 1 joule of energy transferred per second. For example, a 100 watt light bulb uses 100 joules of electrical energy every second to produce light and heat. Watts are commonly used to measure the power consumption of electrical devices and appliances.
What is a calorie?
A calorie (symbol: cal) is a unit of energy. Specifically, 1 calorie is the amount of energy needed to raise the temperature of 1 gram of water by 1 degree Celsius. Calories are commonly used to measure the energy content of foods. For example, a food item containing 10 calories provides enough energy to raise the temperature of 10 grams of water by 1 degree Celsius. In nutrition, Calories (capital C) refer to kilocalories, which are equal to 1000 calories (lowercase c).
The relationship between watts and calories
Watts and calories are both units of power and energy. The key difference is that watts are units in the metric system, while calories are non-metric units. However, we can convert between the two units using a simple conversion factor.
The conversion between watts and calories is based on the definitions of the two units:
- 1 watt (W) = 1 joule (J) per second (s)
- 1 calorie (cal) = 4.184 joules (J)
Using these definitions and some basic algebra, we can derive the conversion factor:
1 W = 1 J/s
1 cal = 4.184 J
Therefore:
1 W = (1 J/s) * (1 cal/4.184 J) = 0.2388 cal/s
Or conversely:
1 cal/s = 1 W/0.2388 = 4.184 W
So in summary, the conversion factors are:
- 1 W = 0.2388 cal/s
- 1 cal/s = 4.184 W
Keeping these conversion factors in mind allows you to convert back and forth between watts and calories/sec.
Converting watts to calories
Using the conversion factors derived above, we can convert a power in watts to calories/sec by multiplying by 0.2388.
For example, to convert 100 W to calories/sec:
100 W * (0.2388 cal/s) / 1 W = 23.88 cal/s
So 100 watts is equivalent to 23.88 calories/second.
As another example, to convert 50 W to calories/sec:
50 W * (0.2388 cal/s) / 1 W = 11.94 cal/s
In general, to convert a power P in watts to calories/sec, use:
Calories/sec = P (W) * 0.2388 cal/s / 1 W
Examples of converting watts to calories
| Power (W) | Conversion to cal/s |
|---|---|
| 10 W | 10 * 0.2388 = 2.388 cal/s |
| 100 W | 100 * 0.2388 = 23.88 cal/s |
| 500 W | 500 * 0.2388 = 119.4 cal/s |
Converting calories to watts
We can also convert in the opposite direction, from calories/sec to watts. Using the conversion factor of 1 cal/s = 4.184 W, we simply multiply the power in calories/sec by 4.184.
For example, to convert 20 cal/s to watts:
20 cal/s * (4.184 W) / 1 cal/s = 83.68 W
As another example, to convert 50 cal/s to watts:
50 cal/s * (4.184 W) / 1 cal/s = 209.2 W
In general, to convert a power P in calories/sec to watts, use:
Watts = P (cal/s) * 4.184 W / 1 cal/s
Examples of converting calories to watts
| Power (cal/s) | Conversion to W |
|---|---|
| 5 cal/s | 5 * 4.184 = 20.92 W |
| 20 cal/s | 20 * 4.184 = 83.68 W |
| 100 cal/s | 100 * 4.184 = 418.4 W |
Converting Calories to watt-hours
When dealing with energy consumption over time, it can also be useful to convert Calories (food energy) to watt-hours (electrical energy).
A watt-hour (Wh) is equal to the energy delivered by a power of 1 watt for 1 hour. Since 1 Wh = 1 W * 1 h = 3600 J, we can derive the following conversion:
1 Calorie = 4.184 J
1 Wh = 3600 J
Therefore:
1 Calorie = 1 Wh/860
Or conversely:
1 Wh = 860 Calories
So the conversion factors are:
- 1 Calorie = 0.001163 Wh
- 1 Wh = 860 Calories
This allows us to convert food energy in Calories to electrical energy in watt-hours. For example:
A 300 Calorie food item contains:
300 Calories * (0.001163 Wh/Cal) = 0.3489 Wh
So 300 Calories is equivalent to 0.3489 watt-hours.
Practical examples of watt and calorie conversions
Nutrition facts label
Nutrition facts labels on food packages typically list the energy content in Calories (per serving). To convert this to more familiar units of power, you can use the watt-calorie conversions:
For example, a granola bar with 210 Calories per serving would provide energy equivalent to:
210 Calories * (4.184 W/Cal) = 878 W
So if you ate the entire granola bar in 1 second, it would provide 878 W of power!
Power rating of appliances
The power rating of appliances and devices is usually listed in watts. This specifies how much energy the appliance consumes per second of operation. You can convert the wattage to Calories/sec to understand the equivalent food energy required:
For example, a typical laptop computer may be rated at 45 W. Converting this:
45 W * (0.2388 Cal/s)/1 W = 10.75 Cal/s
So to power your 45 W laptop, you would need to burn food energy at a rate of 10.75 Calories per second.
Daily energy requirement
Your daily Calorie intake represents the food energy you need to power all of your body’s activities in a day. Suppose your required daily intake is 2000 Calories. We can convert this to watt-hours to understand your daily energy requirement:
2000 Calories * (0.001163 Wh/Cal) = 2.326 Wh
So your daily energy requirement is about 2.326 watt-hours. This is the amount of electrical energy needed to power a 1 watt device for 2.326 hours.
Conclusion
In summary, watts and calories are both units of power and energy that can be converted using the following relationships:
- 1 W = 0.2388 cal/s
- 1 cal/s = 4.184 W
- 1 Calorie = 0.001163 Wh
- 1 Wh = 860 Calories
These conversions allow you to determine the equivalent watts or calories for a given power. Understanding these conversions allows you to compare power and energy usage across different systems and applications. The calculations provide insight into the meaning of power and energy units in real world contexts.