How Do You Convert Between Energy And Power?

Energy and power are two related but distinct concepts in physics and engineering. In this article, we will briefly introduce the difference between energy and power, the units used to measure them, and how to convert between energy and power. The key concepts covered will be:

Defining energy and power
Common units used for energy and power

Converting between energy and power using basic equations
Practice problems to reinforce these conversions

Understanding the relationship between energy and power is important for solving many physics and engineering problems. With the fundamentals covered here, you’ll gain the knowledge needed to perform these conversions yourself.

Table of Contents

Defining Energy

In physics, energy is the quantitative property that is transferred between systems when they interact. More specifically, energy is the ability to do work or produce heat. Energy comes in many different forms that can be categorized into two main types: potential energy and kinetic energy.

Some examples of potential energy include:

Chemical energy stored in the bonds of atoms and molecules

Nuclear energy from the binding forces between nucleons in an atomic nucleus
Gravitational potential energy from an object’s height above the ground
Elastic potential energy stored in stretched or compressed springs

Some examples of kinetic energy include:

Radiant energy like heat and light from motion at the atomic and molecular levels
Motion energy from objects moving

Sound energy from vibrating objects
Electrical energy from moving electrons

In physics, energy is measured in units like joules, calories, electron-volts, etc. The law of conservation of energy states that energy can transform from one form to another, but it cannot be created or destroyed within a closed system.

Defining Power

Power in physics is defined as the rate at which energy is transferred or converted per unit of time. Power represents the speed at which work is done or energy is converted from one form to another.

The standard unit of power is the watt (W), which is equal to 1 joule of energy transferred per second. For example, a 60-watt lightbulb uses 60 joules of electrical energy every second to produce light and heat. Some other examples of power include:

The engine power of a car measured in horsepower or kilowatts

The electrical power consumption of appliances and devices
The metabolic power of animals and humans

Power is closely related to energy. While energy is the capacity to do work, power is the rate at which that energy is consumed. Power can also refer to the rate at which energy is converted from one form to another, such as electrical power being converted to light and heat by a lightbulb.

Units of Energy

Energy can be measured in a variety of units, depending on the system being used. Some of the most common units used to measure energy include:

Joule (J) – The standard unit of energy in the International System of Units (SI). One joule is defined as the energy required to produce one watt of power for one second.
Kilojoule (kJ) – Equal to 1000 joules.

Megajoule (MJ) – Equal to 1 million joules.
Gigajoule (GJ) – Equal to 1 billion joules.
Kilowatt-hour (kWh) – Commonly used to measure electric energy consumption. Equal to the energy consumed at a rate of 1 kilowatt for 1 hour, or 3,600,000 joules.

Calorie (cal) – The amount of energy required to raise 1 gram of water by 1 degree Celsius at standard atmospheric pressure. Roughly equal to 4.2 joules.
British Thermal Unit (BTU) – Defined as the amount of energy required to heat 1 pound of water by 1 degree Fahrenheit. Roughly equal to 1055 joules.

These are some of the most common units used when measuring energy across different industries and applications.

Units of Power

There are several common units used to measure power:

Watts (W) – Watts are the standard SI unit for power. Power consumption of devices is usually measured in Watts.

Kilowatts (kW) – Kilowatts are equal to 1,000 Watts. Kilowatts are commonly used to measure the power output of electrical generators.
Megawatts (MW) – Megawatts are equal to 1,000,000 Watts. The power output of large power plants is often measured in Megawatts.
Horsepower (hp) – Horsepower is a non-SI unit commonly used to rate the power of engines and motors. 1 hp is approximately equal to 746 Watts.

BTUs per hour – BTU (British Thermal Unit) per hour is a unit commonly used for heating and cooling systems. 1 BTU/hour is approximately equal to 0.2931 Watts.

These are some of the most common units used to measure power. Being able to convert between them is important for power calculations.

Converting Energy to Power

The formula for converting between energy and power is:

Power (P) = Energy (E) / Time (t)

Where:

Power is measured in Watts (W)

Energy is measured in Joules (J)
Time is measured in seconds (s)

Let’s walk through some examples:

Example 1

If a battery stores 360,000 Joules of energy and delivers 12,000 Joules of energy per minute, what is the power output of the battery?

We are given the energy (E) and the time (t), so we can calculate the power (P) using the formula:

E = 360,000 J

t = 1 minute = 60 seconds

P = E/t

P = 360,000 J / 60 s

P = 200 Watts

Therefore, the power output of the battery is 200 Watts.

Example 2

A motor generates 100 Watts of power. If it operates for 30 minutes, how much energy does it use?

We are given the power (P) and the time (t), so we can calculate the energy (E) using the formula:

P = 100 Watts

t = 30 minutes x (60 seconds / 1 minute) = 1,800 seconds

E = P x t

E = 100 W x 1,800 s

E = 180,000 Joules

Therefore, the energy used by the motor is 180,000 Joules.

Converting Power to Energy

To convert from power to energy, we use the formula:

Energy = Power x Time

Where:

Energy is measured in units like joules (J) or kilowatt-hours (kWh)
Power is measured in units like watts (W) or kilowatts (kW)
Time is measured in units like seconds (s) or hours (h)

Let’s look at some examples:

Example 1:

If a light bulb has a power rating of 60W and is left on for 5 hours, what is the energy consumed?

Solution:

Power = 60W

Time = 5h

Energy = Power x Time

= 60W x 5h

= 300Wh

So the energy consumed is 300Wh.

Example 2:

A motor operates at a power of 15kW. How much energy does it use in 30 minutes?

Solution:

Power = 15kW

Time = 0.5h (30 minutes)

Energy = Power x Time

= 15kW x 0.5h

= 7.5kWh

So in 30 minutes the motor consumes 7.5kWh of energy.

Common Conversions

Here are some of the most common conversions people may need to make between energy and power units:

Kilowatt-hours (kWh) to Joules (J): 1 kWh = 3,600,000 J

Joules (J) to kilowatt-hours (kWh): 1 J = 0.0000002778 kWh
Watts (W) to kilowatts (kW): 1 W = 0.001 kW
Kilowatts (kW) to watts (W): 1 kW = 1000 W

Horsepower (hp) to watts (W): 1 hp = 746 W
Watts (W) to horsepower (hp): 1 W = 0.00134 hp
BTUs to kilowatt-hours (kWh): 1 BTU = 0.0002931 kWh

Kilowatt-hours (kWh) to BTUs: 1 kWh = 3412 BTUs

Practice converting between these common energy and power units using the conversion factors provided.

Practice Problems

Let’s go through a few practice problems to help solidify your understanding of converting between energy and power:

Problem 1: A car engine generates 120 horsepower of power. Convert this to watts.

Solution: Use the conversion 1 hp = 746 W. So 120 hp x 746 W/hp = 89,520 W.

Problem 2: A light bulb consumes 60 watts of power. How much energy does it use if left on for 5 hours?

Solution: Use the equation Power x Time = Energy. So 60 W x 5 hrs x (3600 sec/1 hr) = 1,080,000 Joules or 1,080 kJ.

Problem 3: A battery stores 500,000 Joules of energy. If a toy car’s motor consumes 5 watts of power, how long can it run using this battery?

Solution: Use Power x Time = Energy. Rearranging gives Time = Energy / Power. So Time = 500,000 J / 5 W = 100,000 seconds or 27.8 hours.

Conclusion

In this article, we covered the important fundamentals of energy and power, and how to convert between the two. We started by defining energy as the capacity to do work or produce heat, and power as the rate at which energy is transferred or work is done. We looked at common units used for measuring energy and power, like Joules, Kilowatt-hours, Watts, and Horsepower.

We then discussed how to convert between energy and power, using simple formulas like Power = Energy / Time. We did some practice calculations to reinforce how to convert Joules to Watts, Kilowatt-hours to Horsepower, and more. The key takeaway is that power and energy are related but distinct concepts.

Understanding the relationship between energy and power is essential for fields like physics, engineering, and energy management. With the fundamentals covered in this article, you should now feel confident converting between energy and power units and applying these important concepts.