Electrical energy in joules:
formula and worked example

Power and energy are not the same thing

Power tells you how fast energy is being used right now. Energy tells you how much has been used in total. A 65 W laptop charger and a 65 W soldering iron draw power at the same rate, but a charger left on for a day uses far more energy than an iron used for a minute. The joule is the unit that captures that total.

One joule is the energy used by one watt over one second. That is a very small quantity by household standards: a phone screen burns through thousands of joules every minute. Joules are most useful in physics, battery and capacitor problems and short bursts of activity, where seconds are the natural time scale.

• Power w: the rate of energy use, in watts.
• Seconds: how long that power is sustained, in seconds.
• Result: energy in joules, where 1 J = 1 W × 1 s.

The formula and the one assumption inside it

The calculation is a straight product, but it carries one assumption: the power stays roughly constant for the whole time. A laptop that draws 65 W while charging at full speed and 15 W when nearly full does not fit a single multiplication, and you need to split the period into stretches.

When power varies, add up the segments. Ten minutes at 60 W and twenty minutes at 20 W is 600 × 60 + 1,200 × 20 = 60,000 J, not an average that hides the difference.

Worked example: a 65 W charger for two minutes

A laptop charger delivers 65 W for 2 minutes while the battery is quickly topped up. How much energy moves?

1. 1Convert time to seconds: 2 minutes × 60 = 120 s.
2. 2Multiply power by time: 65 × 120 = 7,800 J.
3. 3Convert for a feel of scale: 7,800 ÷ 3,600 = 2.17 Wh, or about 0.0022 kWh.

So a two-minute burst at charger power is about 2.2 watt-hours, a tiny part of a laptop battery that holds tens of watt-hours.

From joules to the units on a bill

Utilities bill in kilowatt-hours, not joules. The conversion factor is worth memorising: one kilowatt-hour is 1,000 W for 3,600 s, which is 3,600,000 J, or 3.6 MJ. To move from joules to kilowatt-hours, divide by 3.6 million.

• 7,800 J is about 2.17 Wh, which is 0.00217 kWh.
• A 1,500 W heater running for an hour is 5.4 million J, or exactly 1.5 kWh.
• A 10 W LED bulb on for 10 hours is 360,000 J, or 0.1 kWh.

Using joules for appliances over hours yields enormous numbers that are hard to compare. Switch to watt-hours or kilowatt-hours as soon as the time runs into minutes or hours.

Power or time: which input matters

Energy is directly proportional to both inputs. A 10% increase in power gives 10% more energy: 65 W becomes 71.5 W, and 7,800 J rises to 8,580 J. Doubling the time doubles it again. There is no hidden curvature, unlike the squared terms in resistor heating.

The practical consequence is that saving energy is symmetrical: trimming power by 20% or cutting the run time by 20% gives the same saving. In practice, time is easier to control, since turning something off beats redesigning it.

Mistakes with energy calculations

• Leaving time in minutes or hours, which turns joules into a meaningless mix of units.
• Using the rated power of an appliance when it actually cycles, such as a fridge compressor that runs a third of the time.
• Confusing power in kW with energy in kWh, a slip that appears even in published comparisons.
• Mixing up Wh and J: 1 Wh is 3,600 J, so reading a watt-hour figure as joules understates the energy by a factor of 3,600.

A scenario: how long can a battery sustain a load

A 10 Wh battery holds 36,000 J. Feed it to a 65 W load and it lasts 36,000 ÷ 65, about 554 seconds, just over nine minutes, before it is empty, assuming an ideal battery with no conversion losses. Real conversion losses and battery ageing make the figure shorter.

Run the same calculation backwards when sizing a supply: required energy divided by available power gives the minimum time, and required energy divided by the allowed time gives the minimum power.