# How Do You Convert Kwh To Watts Per Hour?

Kilowatt hours (kWh) and watts per hour are two common units used to measure power consumption and usage. Knowing how to convert between them is useful for calculating electric bills, estimating appliance energy use, and comparing power ratings.

kWh represents the total energy used over time, while watts per hour measures instantaneous power. Both quantify power but in different ways. Converting between the two helps relate time-based consumption (kWh) to power capacity (watts). This allows comparison of appliance energy ratings or estimating usage costs based on billing units.

With some basic math, it’s straightforward to convert kWh to watts per hour and vice versa. This guide explains the relationship between the two units and provides examples for practical conversion. Understanding these fundamental energy metrics enables better energy literacy in our homes and businesses.

## Define Kilowatt Hours

A kilowatt hour (kWh) is a unit of energy equal to the work done by power of 1 kilowatt over the period of 1 hour. In other words, 1 kWh is the amount of energy consumed if a device that requires 1,000 watts (1 kilowatt) of power runs for 1 hour. For example, if a 100 watt light bulb runs for 10 hours, it has used 1,000 watt hours or 1 kWh of energy (100 watts x 10 hours = 1,000 watt hours = 1 kWh).

The kilowatt hour is commonly used for billing electrical energy consumption and is the typical unit seen on residential and commercial utility bills. Utility companies measure a household’s energy use in kilowatt hours over a monthly or yearly period, then charge for that energy use based on the rate per kWh. The kilowatt hour allows easy comparisons between energy use and costs over time.

## Define Watts Per Hour

Watts per hour (W/h or W h^-1) is a measure of power, defined as joules per second or kg m^2/s^3. In other words, a watt per hour measures the rate at which energy is being used or generated. By definition, one watt (W) of power is equal to one joule per second. So one W/h is the amount of energy used by a 1 W device over the course of 1 hour. This unit allows us to easily calculate electric energy consumption by appliances and equipment over time. For example, a 60W light bulb uses 60 W/h of energy if left on for one hour. Watts per hour are commonly used alongside kilowatt-hours (kWh) for billing and energy monitoring of larger systems.

## The Relationship Between kWh and Watts

The key to understanding the relationship between kilowatt hours (kWh) and watts is recognizing that they represent different but related aspects of electricity usage. kWh is a measure of energy and watts is a measure of power.

Specifically, a kilowatt hour represents the amount of energy used over time. It refers to using 1,000 watts of power for one hour. For example, a 100 watt light bulb used for 10 hours would consume 1,000 watt hours or 1 kWh of energy (100 watts x 10 hours = 1,000 watt hours = 1 kWh).

In contrast, a watt is a measure of instantaneous power. It refers to the rate at which energy is being used or generated at any given moment. For example, a 100 watt light bulb uses 100 watts of power at any moment when turned on. The longer that 100 watt bulb remains on, the more energy it consumes over time, measured in kWh.

So in summary, kWh measures total energy used over time, while watts measures the rate of power usage at an instant. kWh is “consumed” over time, while watts is “used” at any moment. By understanding this key difference, you can better grasp the relationship between these two important electricity metrics.

## Converting kWh to Watts

The key to converting between kilowatt hours (kWh) and watts is to understand their relationship with time. A watt is a unit of power, meaning the rate at which energy is consumed or produced. A kilowatt hour is a unit of energy, meaning the total amount of energy consumed or produced over time.

To convert kWh to watts, we need to determine the rate of energy usage over one hour that is equivalent to the amount of energy in kilowatt hours. This can be done using the following formula:

Watts = kWh x 3,600

Where 3,600 is the number of seconds in one hour. So by multiplying the kilowatt hours by 3,600, we calculate the number of watts that would be needed to consume that amount of energy in one hour.

For example, if a device uses 5 kWh of energy, then converting to watts gives us:

Watts = 5 kWh x 3,600 = 18,000 Watts

So 5 kWh is equivalent to a power rating of 18,000 watts over one hour. This conversion formula allows us to easily switch between energy usage over time (kWh) and the instantaneous rate of energy usage (watts).

## Converting Watts to kWh

To convert from watts to kilowatt hours, you need to divide the watts by 3600 (the number of watts in a kilowatt hour). Here is the formula:

kWh = Watts / 3600

So if you have a 1500 watt appliance that runs for 2 hours, you would calculate the kWh usage like this:

kWh = 1500 Watts x 2 hours / 3600
kWh = 3000 / 3600
kWh = 0.83

Therefore, a 1500 watt appliance running for 2 hours consumes 0.83 kWh of electricity.

## Examples

Here are a couple examples showing the calculations for converting between kWh and watts per hour:

Example 1: Convert 10 kWh to watts per hour:
10 kWh x (1000 W/kW) = 10,000 Wh

10,000 Wh / 1 h = 10,000 W per hour

Example 2: Convert 5000 watts per hour to kWh:
5000 W per hour x 1 h / 1000 W/kW = 5 kWh

## Applications

Knowing how to convert between kilowatt-hours and watts per hour is useful in several real-world applications:

Utility Billing: Electricity usage on utility bills is typically measured in kilowatt-hours (kWh). To better understand the power demands involved, customers may want to convert kWh to watts per hour. This gives a sense of the instantaneous rate of power usage over time.

Device Power Ratings: Many electrical devices list their power consumption in watts. To estimate the energy usage over time, you can convert watts to kilowatt-hours. This helps determine the operating cost of running the device.

Load Planning: Engineers size electrical systems and components based on peak power demand in watts. Knowing the typical energy usage patterns in kWh helps plan appropriate load capacity.

Cost Analysis: Commercial and industrial electric rates are often charged per kilowatt-hour. Converting kWh to watts provides a comparison point for estimating costs of running different types of equipment.

Solar Sizing: When designing a solar power system, you need to know the power rating (watts) to size the panels and inverter. You also need the total energy demand (kWh) to properly size the battery storage.

In summary, being able to move between watts and kilowatt-hours gives both an instantaneous power perspective and a sense of energy usage over time. This dual understanding helps inform better decision making across a variety of applications.

## Conclusion

In summary, kilowatt hours and watts per hour are related but distinct units for measuring power. The kilowatt hour measures energy usage or consumption over time, while watts per hour measures instantaneous power or the rate of energy flow. To convert between the two, you can simply multiply or divide by the number of hours to get the equivalent value. The formulas are:

kWh x 1000 = Watts

Watts / 1000 = kWh

With these straightforward conversions, you can easily determine the kWh usage based on wattage or find the wattage if given usage in kWh. Understanding the relationship between these fundamental power units can help with electricity billing calculations and determining the energy consumption and costs of electrical devices and appliances.

## References

• US Energy Information Administration. “How much electricity does an American home use?” Accessed January 1, 2023. https://www.eia.gov/tools/faqs/faq.php?id=97&t=3
• IEEE Standard 1459-2010 – IEEE Standard Definitions for the Measurement of Electric Power Quantities Under Sinusoidal, Nonsinusoidal, Balanced, or Unbalanced Conditions. 2010.
• Young, Hugh D. and Roger A. Freedman. “University Physics with Modern Physics.” 14th ed., Pearson, 2012.