How to Convert Joules to Watts

Joules and watts measure related but different quantities. A joule tells you how much energy is transferred or used; a watt tells you how quickly that energy is transferred or used. So there is no single conversion from joules to watts unless you also know the time interval.

To find average power, divide energy in joules by time in seconds. This article shows how to apply that relationship, convert time units, and avoid confusing an energy amount with a power rating.

The relationship between joules and watts

The watt is the SI unit of power, and the joule is the SI unit of energy. One watt is defined as one joule per second:

$$1\ \mathrm{W}=1\ \mathrm{J/s}$$

If an amount of energy $E$ is transferred over a time interval $t$, the average power is

$$P=\frac{E}{t}$$

Here, $P$ is in watts when $E$ is in joules and $t$ is in seconds. Equivalently, rearranging the formula gives $E=Pt$: energy equals power multiplied by time.

The word average matters. If the rate changes during the interval, $E/t$ gives the average power over that interval, not necessarily the power at every instant. Instantaneous power is the rate of energy transfer at a particular moment; in calculus notation, it is $P=dE/dt$.

How to calculate watts from joules

1. Identify the energy amount in joules.
2. Identify the duration over which that energy is transferred or used.
3. Convert the duration to seconds.
4. Divide the joules by the seconds.
5. Label the result in watts, and describe it as average power if the rate varies.

For example, suppose a device uses $900\ \mathrm{J}$ of energy in $45\ \mathrm{s}$. Then

$$P=\frac{900\ \mathrm{J}}{45\ \mathrm{s}}=20\ \mathrm{J/s}=20\ \mathrm{W}$$

The device’s average power over those 45 seconds is $20\ \mathrm{W}$.

Worked examples with different time units

Energy used over minutes: A lamp uses $1{,}500\ \mathrm{J}$ over 2.5 minutes. Convert the time first: $2.5\times60=150\ \mathrm{s}$. Then

$$P=\frac{1{,}500\ \mathrm{J}}{150\ \mathrm{s}}=10\ \mathrm{W}$$

Energy transferred in a fraction of a second: A pulse transfers $120\ \mathrm{J}$ in $0.4\ \mathrm{s}$. Its average power during that pulse is

$$P=\frac{120\ \mathrm{J}}{0.4\ \mathrm{s}}=300\ \mathrm{W}$$

A large watt value can describe a brief event. It does not mean the event transferred a large amount of energy overall: here, the total energy is still $120\ \mathrm{J}$.

You can also use the relationship in reverse. A $60\ \mathrm{W}$ device running for 10 seconds transfers or uses $60\times10=600\ \mathrm{J}$ of energy, assuming its power stays constant over that time.

Common mistakes

• Trying to convert without a duration: Joules alone do not determine watts. For example, $100\ \mathrm{J}$ delivered in one second is an average of $100\ \mathrm{W}$, but delivered in 10 seconds it is an average of $10\ \mathrm{W}$.
• Using minutes as if they were seconds: If the duration is given in minutes, multiply it by 60 before dividing. Using minutes directly produces joules per minute, not watts.
• Reversing the division: To find power, divide energy by time. Multiplying joules by seconds does not give watts.
• Treating power and energy as interchangeable: A label such as $500\ \mathrm{W}$ describes a rate, not a total amount of energy. To find the energy used, you also need the operating time.
• Calling an average an instantaneous value: If power fluctuates, total energy divided by total time gives only the average over the chosen interval.

A quick check using units

Check the units as well as the arithmetic:

$$\frac{\mathrm{J}}{\mathrm{s}}=\mathrm{W}$$

If your calculation does not reduce to joules per second, you may have used the wrong operation or left the time in the wrong unit. In practical problems, also state the interval used to calculate the average; the same energy can correspond to different powers when the transfer takes different amounts of time.