Electrical energy is the total work done or energy transferred by an electrical system over time. It equals power multiplied by time, measured in joules, watt-hours or kilowatt-hours.
Learning objectives
- Calculate energy from power and time
- Convert between joules, watt-hours and kilowatt-hours
- Estimate the energy stored in a battery
- Calculate running cost from energy and tariff
- Account for efficiency in energy conversions
Progressive explanation
Start with the plain-language idea, then move into the engineering detail. Each level stands on its own, so you can stop at the depth you need.
Beginner The core idea
Batteries store energy too. A 12 V, 60 Ah battery stores about 720 Wh, because voltage multiplied by amp-hours gives watt-hours. That is 0.72 kWh.
Intermediate How it behaves in a circuit
Cost = energy × tariff. Efficiency must be included when converting between forms: a charger that is 90 % efficient draws more from the mains than it delivers to the battery.
Advanced Limits, assumptions, engineering detail
Formulas and variables
Units of measurement
| Quantity | Symbol | Unit |
|---|---|---|
| Energy | E | joule (J) |
| Energy | E | watt-hour (Wh) or kilowatt-hour (kWh) |
| Battery capacity | Ah | ampere-hour (Ah) |
| Power | P | watt (W) |
Worked examples
Heater energy and cost
Problem. A 2000 W heater runs for 3 hours. How much energy does it use, and what does it cost at 0.20 per kWh?
Solution. E = 2000 W × 3 h = 6000 Wh = 6 kWh. Cost = 6 × 0.20.
Battery energy and runtime
Problem. A 12 V battery is rated 60 Ah. What energy does it store nominally, and how long can it supply a 100 W load at 80 % usable depth of discharge?
Solution. E = 12 × 60 = 720 Wh. Usable energy = 0.80 × 720 = 576 Wh. Runtime = 576/100 = 5.76 h.
Converting to joules
Problem. Express 1 kWh in joules.
Solution. 1 kWh = 1000 W × 3600 s.
Practical applications
- Electricity billing
- Battery runtime estimation
- Solar and storage sizing
- Electric-vehicle consumption
- Uninterruptible power supplies
- Industrial energy management
Automotive applications
Battery capacity, electric-vehicle consumption in kWh per 100 km, charging energy and parasitic drain are all energy calculations. The alternator must replace the energy taken from the battery, and charging losses mean the engine supplies more than the battery receives.
Industrial applications
Energy audits record consumption over time to find inefficiencies, while demand charges depend on the peak power drawn rather than total energy. Load profiles and power logging turn instantaneous measurements into the energy figures used for costing and carbon reporting.
Measurement procedure
- Use an energy meter or a power logger that integrates power over time.
- For a battery, a capacity test measures the ampere-hours delivered under a defined load.
- Do not estimate energy from a single instantaneous power reading on a varying load.
- Include charger and inverter losses when comparing measured energy at different points.
Common mistakes
- Confusing amp-hours with energy without multiplying by voltage.
- Ignoring efficiency and depth-of-discharge limits.
- Using peak power to estimate energy consumption.
- Forgetting to convert minutes to hours or watts to kilowatts.
Safety considerations
- Batteries store a large amount of energy and can deliver it at high current; insulate terminals and tools.
- Do not deep-discharge lead-acid batteries repeatedly, and charge them in a ventilated area.
- Use fuses and disconnects rated for the battery energy and prospective current.