Watts to Joules Calculator

E = P × t, and since 1 W = 1 J/s the two are already in the same system so no conversion factor appears

P

The power the appliance draws, in watts — normally the figure on its nameplate. It is a rate: joules per second, energy flowing rather than energy stored. On this page it is held constant for the whole period, which is exact for a resistive load on a steady supply and an average for anything that cycles on and off, such as a refrigerator or a thermostat-controlled heater. A value of zero is accepted and gives zero energy, which is correct rather than degenerate

t

How long the power is sustained, in seconds. This is the input that makes the page necessary: without it there is no answer at all, because a rate only becomes an amount once you say for how long. The same 2000 W is 2000 J over one second and 7,200,000 J over an hour. The field takes seconds, minutes or hours, and it must be greater than zero — a zero duration is not an instant of enormous power, it is the absence of any process, and the page refuses it rather than returning a flat 0 J

3600000

The number of joules in one kilowatt hour, and it is a definition rather than a conversion: 1 W for 1 h, written out. It is the only constant in the page, and it is what lets the energy be restated in the unit an electricity bill is written in. Every published figure for a battery, a domestic appliance or an electric vehicle is quoted in this unit, which is why the row is on the panel at all — the joules are the answer to the question asked, the kilowatt hours are the answer to the question that follows

Use it whenever a device is described by its wattage and you want to know how much energy it actually consumes: an appliance rating checked against a daily or monthly figure, a battery bank sized from a continuous load, or the running cost worked out from a meter reading. It is energy from power and time, a single multiplication, and it is also the reverse of the joules to watts calculator — that page divides energy by time to get power, this one multiplies power by time to get energy, and the same pair of quantities is on both. The one thing to settle first is the period, because a wattage with no duration is not an answer to anything

1. The defaults: 1000 W left on for an hour

   1. Power 1000 W sustained for 3600 seconds
   2. Multiply: 1000 × 3600 = 3,600,000 J
   3. Divide by 1000 for kilojoules: 3600 kJ
   4. Divide by 3,600,000 for kilowatt hours: exactly 1 kWh

   The three rows are the same number in three sizes, and the third one is the reason the unit is named the way it is — one kilowatt sustained for one hour. This is also the pair of defaults on the joules to watts page read backwards: there, 3.6 MJ spread over an hour gives 1000 W; here, 1000 W held for an hour gives 3.6 MJ. Coming from either page, the other one agrees to the digit, which is what makes the pair worth having separately.

2. A 2000 W kettle boiled for one minute

   1. Power 2000 W for 60 seconds
   2. Multiply: 2000 × 60 = 120,000 J
   3. In kilojoules that is 120 kJ
   4. In kilowatt hours: 120,000 / 3,600,000 = 0.033333 kWh

   A tenth of a kilowatt hour is not what most people expect a kettle to use, and the two figures behind it are both true: 2 kW is a large rate, one minute is a short period, and energy is the product. This is the everyday shape of the mistake the page guards against — a high wattage sounds expensive, but cost is energy, and energy is what a rate does over time. Boiling the same kettle for an hour would be 7.2 MJ, sixty times as much, from the same appliance.

3. 1200 W held for 60 seconds, the reverse of the joules to watts case

   1. Power 1200 W for 60 seconds
   2. Multiply: 1200 × 60 = 72,000 J
   3. In kilojoules: 72 kJ
   4. In kilowatt hours: 72,000 / 3,600,000 = 0.02 kWh

   The joules to watts page contains the mirror image of this case — the same 72,000 J over the same 60 seconds, entered there as an energy and returned as 1200 W. The two pages are inverses of one another, and a reader who has both open should get the same third number back after going around the loop. If the two ever disagreed, one of them would be wrong about the arithmetic rather than about the physics.

4. A 10 W router left on for a full day

   1. Power 10 W held for 86,400 seconds, which is 24 hours
   2. Multiply: 10 × 86,400 = 864,000 J
   3. In kilojoules: 864 kJ
   4. In kilowatt hours: 864,000 / 3,600,000 = 0.24 kWh

   This is the question small always-on devices actually raise, and the answer is a quarter of a kilowatt hour a day — under a tenth of what a refrigerator uses, and about a hundredth of what a single electric vehicle charge draws. Reading it in kilowatt hours rather than joules is what makes that comparison possible at all: 864 kJ means nothing next to a monthly bill, while 0.24 kWh sits directly beside the other figures on it.

5. A milliwatt held for one second, the small end of the range

   1. Power 0.001 W for 1 second
   2. Multiply: 0.001 × 1 = 0.001 J
   3. In kilojoules: 0.000001 kJ, the same quantity six places down
   4. In kilowatt hours: 2.778 × 10⁻¹⁰, which is past the point where fixed decimals stop being readable

   Nothing in the physics changes at this end of the range, and the page still needs the row to behave. Two decimals on the joules row would print this as 0.00 J — a wrong answer and an indistinguishable one — which is why that row carries three. The kilowatt-hour row has left the ordinary-decimal window altogether and switches to scientific notation, the same switch the joules to watts page makes for the same reason: the two pages span fourteen orders of magnitude between a milliwatt-second and a megawatt-day.

The power is held constant across the whole period, which is exact for a resistive load on a steady supply and only an average for anything that cycles: a refrigerator, a thermostat-controlled heater or a device with a standby state draws a varying current, and the energy it really uses depends on its duty cycle rather than on its rating. A nameplate figure is a maximum, not a typical draw — the measured consumption of an appliance is often well below it, and a rating taken at one supply voltage shifts when the voltage does. The page gives energy at the point of consumption, so it says nothing about efficiency: how much of that energy came out as heat, light or motion is a separate question and a separate set of pages. The energy is not priced, because a tariff is not an input here. Nothing here converts energy into a temperature rise, either, which needs a mass and a specific heat capacity.

How many joules are in one kilowatt hour?

Exactly 3,600,000, and by definition rather than by measurement: one kilowatt hour is one watt sustained for one hour, so it is 1 × 3600 seconds of joules, or 3.6 MJ. That is why the third row of the panel is not a redundant restatement of the first — the joules answer the question the page is named after, and the kilowatt hours put the same quantity into the unit an electricity meter, a battery datasheet and a car's range estimate all use.

Why does the page need a time as well as a power?

Because a watt is a rate, and a rate only becomes an amount once it has been sustained for something. There is no way around this: 2000 W for one second is 2000 J, for one hour it is 7.2 MJ, and those are the same appliance on the same supply with the same nameplate. A wattage on its own is not a small answer to this question, it is not an answer to it at all, which is why the duration field is required and the page refuses zero seconds rather than returning a flat zero.

What is the difference between this and the joules to watts calculator?

They are the same relationship read in opposite directions. Here you know the power and the time and you want the energy, so the page multiplies. There you know the energy and the time and you want the power, so the page divides. The fields overlap because the quantities are identical, and the outputs do not overlap at all because one page answers in watts and the other in joules. If you know which of the three you are missing, that decides which page you want.

Is a watt really one joule per second?

Yes, and it is a definition rather than a rule of thumb, which is why the multiplication on this page needs no conversion factor. It is also the reason the kilojoule and the kilowatt hour rows are simple divisions by 1000 and 3,600,000: every one of those factors is a definition. The one thing the definition does not do is tell you how long — a joule per second describes an ongoing transfer, and the total transferred is that rate multiplied by the period it ran for.

Does this tell me what the appliance costs to run?

Not by itself. The page stops at energy, which is the quantity a bill is computed from, and the missing input is the price per unit — a tariff that varies by country, by time of day and by contract. The output to carry forward is the kilowatt hour figure: passing it to the electricity cost calculator together with your rate turns it into money. Doing that division here would mean asking for a price on a page about physics.

Why do the three rows show such different numbers of decimals?

Because they are three segments of one ruler and each segment has a different useful width. The joules row carries three decimals so that a milliwatt-second reads as 0.001 J rather than 0.00; the kilojoule row carries six because a kilojoule is a thousand joules, so six places there is the same precision as three there; and the kilowatt-hour row switches to scientific notation because the range reaches from 2.778 × 10⁻¹⁰ to 24000 kWh, and fixed decimals print zeros at one end or the other.

Should I enter the nameplate power or a measured one?

Either, as long as you know which you have. A nameplate rating is the maximum the appliance draws, so entering it gives an upper bound on the energy, which is the right figure for sizing cable or a battery. A measured figure, from a plug-in meter, is what it actually used, and it will be lower for anything that cycles — often far lower. The arithmetic is identical either way, and the difference between the two answers is information rather than an error.

• Joule — the definition of the joule as one watt-second, and why a watt is a rate of energy transfer rather than an amount of it — Wikipedia
• Kilowatt-hour — the definition of the unit as 3.6 million joules, and why it is the unit electricity is metered and billed in — Wikipedia
• NIST Special Publication 811, Guide for the Use of the International System of Units (SI), section 4.1 — the SI treatment of quantity calculus, and the watt as a special name for the joule per second — National Institute of Standards and Technology