Volts to Joules Calculator

What a volt is and what a joule is

A volt and a joule answer two different questions. A volt describes how hard electricity pushes: it is the electric potential at one point in a circuit compared with another. A joule describes how much energy gets delivered once that push moves charge through the circuit. The two are tied together by the coulomb, which counts the amount of charge.

The formal definitions come from the SI system. NIST's Special Publication 811, the agency's guide to SI units, defines one volt as one joule of energy per coulomb of charge, and the BIPM SI Brochure sets the same definition worldwide. That single relationship is all you need to move between volts and joules.

A water analogy helps. Voltage works like water pressure, charge works like the amount of water that flows, and energy is what the flowing water does when it turns a wheel. High pressure with no water moves nothing, and lots of water with no pressure moves nothing either. Energy only shows up when a push moves charge.

Keeping the two ideas separate matters for real decisions. A watch battery and a car battery differ by a factor of eight in voltage, but the car battery also moves far more charge, so the gap in stored energy is much wider than eight. Whenever a spec sheet quotes volts, ask what the charge or current is before drawing any conclusion about the energy involved.

The formula that connects volts and joules

The conversion is one multiplication:

Energy (joules) = volts x charge (coulombs)

One volt pushing one coulomb of charge delivers exactly one joule. Double the voltage and you double the energy for the same charge. Double the charge and the energy doubles too. You can also run it backward: charge in coulombs equals energy in joules divided by volts.

The catch is that volts alone never contain energy. A 9 volt battery sitting in a drawer holds no joules for you until charge flows through something. That is why every real volts-to-joules conversion needs a second number: either the charge in coulombs, or the current and the time it flowed.

Worked examples you can check by hand

Here are four examples you can verify with one multiplication each:

The charge column comes from the current and the run time, which the next section covers. Notice the range: a few hundred joules for a quick battery test, more than two hundred thousand for a light bulb over an hour. Joules are small units, so everyday numbers get big fast.

When you know current and time instead of charge

Most of the time you will not know the charge in coulombs. You will know the current in amps and how long it flowed in seconds. Charge is just current multiplied by time, because one amp delivers one coulomb each second:

Energy (joules) = volts x amps x seconds

That also equals watts multiplied by seconds, since volts x amps = watts. Take the 9 volt phone charger drawing 2 amps for 300 seconds: 9 x 2 = 18 watts, and 18 W x 300 s = 5,400 J. The AA battery works the same way: 2,500 mAh of capacity is 2.5 amp-hours, 2.5 A flowing for 3,600 seconds is 9,000 coulombs, and 1.5 V x 9,000 C = 13,500 J.

Keep the time unit in seconds. If your device ran for minutes, multiply by 60 first; for hours, multiply by 3,600. A charge time typed in minutes straight into the formula will come out 60 times too small.

The reverse direction works the same way. If a motor drew 0.5 amps at 24 volts for 20 seconds, it used 24 x 0.5 x 20 = 240 joules. If you only know the watts, multiply them by the seconds: a 45 watt soldering iron running for two minutes uses 45 x 120 = 5,400 joules, the same figure as the 9 volt charger earlier because watts and seconds already contain the voltage.

Joules, watt-hours and kilowatt-hours

Joules are the SI unit of energy, but American households buy electricity in kilowatt-hours, so the two need a bridge. A watt is one joule per second, a watt-hour is 3,600 joules, and a kilowatt-hour is 3,600,000 joules, which the EIA's units and calculators page treats as the standard household billing unit.

To turn joules into kilowatt-hours, divide by 3,600,000. The 5,400 J from the phone charger is about 0.0015 kWh, and the 216,000 J from the bulb is 0.06 kWh. At 15 cents per kilowatt-hour, that bulb hour costs a bit under one cent, which is why utilities bill in kilowatt-hours instead of joules.

Capacitor energy: 0.5 C V squared

Capacitors store energy in an electric field, and their formula is different because the charge they hold depends on the voltage. A capacitor with capacitance C farads charged to V volts stores:

Energy = 0.5 x C x V x V

The squared voltage is the part people miss. Going from 5 V to 12 V is 2.4 times the voltage but 5.76 times the energy, because 12 x 12 = 144 and 5 x 5 = 25. This is also why camera flash circuits and defibrillators, which need a burst of energy, charge capacitors to high voltages rather than using bigger capacitance alone.

Why the numbers get big so fast

One joule is a tiny amount: roughly the work of lifting an apple one meter. That is why a single hour of ordinary household life runs into millions of joules. A 1,500 watt space heater on for one hour uses 1,500 x 3,600 = 5,400,000 J, which is 1.5 kilowatt-hours.

The same scaling shows up in battery specs. A phone battery rated at 4,000 mAh and 3.85 V holds 4 A x 3,600 s = 14,400 coulombs, and 3.85 V x 14,400 C = 55,440 J, or about 15.4 watt-hours. Car batteries look smaller in amp-hours but run at 12 volts or more, so each coulomb carries roughly three times the energy of one in a phone cell.

When a spec sheet lists energy directly, it may appear in joules, kilojoules (1,000 J), megajoules (1,000,000 J) or watt-hours. One kilojoule is about 0.278 watt-hours, so a 3,600,000 J snack label is 1 kWh of food energy, give or take rounding.

Sources agree on these bridges because they are definitions rather than measurements. The NIST conversion tables in Special Publication 811 list 1 joule per second as 1 watt and the kilowatt-hour as an accepted unit outside the SI proper, which is why a page can move between joules and kilowatt-hours without ever touching a measured constant. The only judgment call is rounding: carrying three or four significant figures is plenty for household math, while lab work keeps more.

Mistakes people make with volts and joules

These four slips cause most wrong answers:

One more nuance: amp-hours on a battery are charge, not energy. Two batteries with the same amp-hour rating hold different amounts of energy if their voltages differ, which is why the 1.5 V AA and a 3.7 V lithium cell with the same mAh rating do different amounts of work. The calculator above keeps volts, charge, current, time and capacitance in separate boxes so each formula gets the inputs it needs.