Joules to Watts Calculator

P = E / t, where E is the energy in joules and t is the time in seconds; equivalently E = P × t

E

The energy delivered, in joules. It is a quantity, not a rate: a battery holds it, a tank of hot water holds it, a flying mass holds it as kinetic energy. Because it is a quantity, it says nothing about how fast anything happened — a kilowatt-hour is a kilowatt-hour whether it was drawn over an hour or dumped in a millisecond, and the difference between those two cases is the whole subject of this page (J)

t

The time over which the energy was delivered, in seconds. It is a required input rather than an optional one, because without it the question has no answer at all: energy divided by an unspecified time is not a large number or a small one, it is undefined. Enter it in minutes or hours if that is what you measured, and the page converts to seconds before dividing

P

The average power in watts, which is the energy divided by the time. Average is the operative word: a device that draws a steady 1 kW and one that draws nothing for half the interval and 2 kW for the other half both average 1 kW over the whole interval, and this calculation cannot tell them apart. A watt is one joule per second, which is the definition the whole page rests on. The third output restates the same energy in kilowatt-hours — one kilowatt sustained for one hour, exactly 3 600 000 joules — which is the unit meters, tariffs and appliance labels are written in, and the fastest way to check a joule figure against reality: somewhere between 0.1 and 2 kWh is the range a domestic appliance doing an hour's work falls in (W)

Use it whenever a question pairs an amount of energy with a duration, and especially when that pairing is the thing being asked about — how many watts is a kilowatt-hour, what average power does a 100 kJ burst represent, what does a 2 kWh charge over eight hours draw. It is the page for turning an energy figure from a bill, a battery datasheet or a calorie count into a rate, and for the reverse check: a device rated in watts, over a known time, uses a computable number of joules and kilowatt-hours. It is not the page for electricity cost, which is this result multiplied by a tariff.

1. The defaults: 3.6 million joules over one hour

   1. Energy 3 600 000 J, time 3600 s (one hour)
   2. Power is 3 600 000 / 3600 = 1000 W
   3. In kilowatts that is 1000 / 1000 = 1 kW
   4. The energy is 3 600 000 / 3 600 000 = 1 kWh

   This is the row that answers "how many watts is a kilowatt-hour": 1000, and only because the hour was specified. Change the time field to 1 second and the same energy gives 3.6 MW — a figure that sounds absurd for a domestic supply and is entirely correct for a capacitor bank discharging or a pulse. The fact that both numbers came from identical energy is the point of the page, and it is why the kilowatt-hour output sits next to the watts: it is the only one of the three that does not depend on the time you entered.

2. One kilocalorie delivered in a minute

   1. Energy 4184 J (one thermochemical kilocalorie), time 60 s
   2. Power is 4184 / 60 = 69.733 W
   3. In kilowatts that is 0.069733 kW
   4. The energy is 4184 / 3 600 000 = 0.001162 kWh, which rounds to 0.001

   A food calorie is 4184 joules, and a human body spends roughly that in a minute at rest — so the 69.7 W here is not a coincidence, it is the metabolic rate, and it is about the same as an old incandescent bulb. It is worth seeing how small the kilowatt-hour figure is: one kilocalorie is 0.00116 kWh, so a day's worth of food at 2000 kcal is about 2.3 kWh of chemical energy, which is roughly what a small electric heater uses in an hour.

3. A laptop battery's 20 watt-hours in one minute

   1. Energy 72 000 J (= 20 Wh), time 60 s
   2. Power is 72 000 / 60 = 1200 W
   3. In kilowatts that is 1.2 kW
   4. The energy is 72 000 / 3 600 000 = 0.02 kWh, which is the 20 Wh the battery is rated at

   The point here is the gap between how much energy is stored and how fast it is asked to come out: 20 Wh delivered in 60 seconds is 1200 W, which is sixty times the 20 W the same battery would deliver spread over an hour. The third output is the check in the other direction, and it is the one figure of the three that the time field cannot touch: 0.02 kWh is exactly the 20 Wh printed on the label.

4. The same energy spread over a whole day

   1. Energy 3 600 000 J, time 86 400 s (24 hours)
   2. Power is 3 600 000 / 86 400 = 41.667 W
   3. In kilowatts that is 0.041667 kW
   4. The energy is still 1 kWh

   Same joule figure as the first example, same kilowatt-hour figure, and a power more than twenty times smaller. This is a continuous trickle of about 42 W — a router, a standby load, a small circulating pump — and it is what a single kilowatt-hour per day works out to. The comparison is the useful part: a device that draws 1000 W for an hour and one that draws 41.667 W for a day use identical energy, and both will show up on a bill as the same kilowatt-hour.

This is an average power, not an instantaneous one. Every device that switches, pulses or varies its draw is represented here by a single number equal to the total energy divided by the total time, which is the right answer for a bill and the wrong one for sizing a fuse: a 100 W average that arrives in 1 ms bursts draws 100 kW during each burst. The energy is treated as delivered steadily across the whole interval, so ramp-up, cool-down and idle periods are all averaged in without being modelled. Heat losses are not included — the energy in is the energy used, not the energy that came out as useful work, so an efficiency figure has to be applied to the result rather than to the inputs.

How many watts is a kilowatt-hour?

Three thousand six hundred if it is delivered over an hour, and the question has no answer until a time is supplied — that is the entire reason this page has a time field rather than an assumed one. One kilowatt-hour is 3 600 000 joules, so used in one hour it is 1000 W, used in one second it is 3.6 MW, and used over a full day it is 41.667 W. The kilowatt-hour is a quantity of energy and the watt is a rate, so the same energy gives every one of those powers depending on the interval.

What is a joule per second?

A joule per second is a watt — that is the definition of the watt, and it is why dividing energy by time is the whole of the arithmetic here. It is also why the unit is named after a rate: a 60 W bulb uses 60 joules every second, so an hour of it is 60 × 3600 = 216 000 J, or 0.06 kWh. Any conversion between an energy unit and a power unit passes through a time for exactly this reason.

How do I work out the cost of running an appliance?

Divide the energy in joules by 3 600 000 to get kilowatt-hours, then multiply by the price per kilowatt-hour. The third output on this page does the first step: a 2000 W heater left on for three hours is 6000 Wh, which is 6 kWh, and at a typical tariff somewhere near 0.20 per unit that is about 1.20. The page deliberately stops before the price, because a tariff is a local and changing number and the arithmetic that matters is the energy.

Why does the same energy give different wattages?

Because watts measure how fast the energy is spent, not how much of it there is. The four examples on this page all divide a fixed joule figure by different times: 3.6 MJ over 3600 seconds is 1000 W, over 86 400 seconds it is 41.667 W, and over 1 second it is 3.6 MW. Imagine the same quantity of water poured through a narrow pipe over a day, or through a wide one in a second — the volume is identical, the flow rate is not.

Can I enter the time in hours instead of seconds?

Yes, and the page converts before dividing, so the arithmetic is the same either way. The time field accepts seconds, minutes and hours, and what matters is only the duration, not the unit it was measured in. One caution: the internal calculation is done in seconds, so a time entered as 1 hour is 3600 — if you are checking the arithmetic by hand, remember that the outputs are in watts and kilowatts, not watt-hours.

Is this the same as converting watts to joules?

It is the same equation read in the other direction. Power is energy divided by time, so energy is power multiplied by time; this page takes energy and time and returns power, and the reverse conversion takes power and time and returns energy. Either way the time is a required third quantity, which is why neither an energy unit nor a power unit can be converted into the other by a factor alone — a watt is a joule per second, and that per second has to come from somewhere.

• NIST Guide for the Use of the International System of Units (SI), §4 — the watt as one joule per second, and the kilowatt-hour as 3.6 megajoules — NIST
• Watt — the definition as a rate of energy transfer, and its relation to the joule, the kilowatt-hour and the horsepower — Wikipedia
• Estimating Appliance and Home Electronic Energy Use — working from a rated wattage and hours of use to the kilowatt-hours a meter will charge for — U.S. Department of Energy