Principle: Electrical energy is the total work done or energy used by electrical power over time. If power is the rate (watts), energy is the accumulation (watt-hours or joules). One watt for one hour equals one watt-hour (Wh); 1000 Wh make 1 kWh (kilowatt-hour), a common billing unit. The fundamental relation is E = P × t, i.e. energy (in joules or Wh) is power multiplied by time. For example, a 60 W lightbulb running for 5 hours consumes 60 × 5 = 300 Wh, which is 0.3 kWh.
In general, if power varies over time, energy is the area under the power-vs-time curve (E = ∫ P(t) dt). For steady loads or stepwise changes, we sum each segment’s P × t. Engineers distinguish between:
Formulas: For constant power usage: For example, running a 1500 W appliance for 3 hours: E = 1500 × 3 / 1000 = 4.5 kWh. If multiple devices are used, sum their individual P × t contributions. Energy can also be computed from current and voltage: since P = V × I, then E = V × I × t (in joules) for DC or resistive AC circuits. In practice, energy meters perform this integration electronically and display kWh.
Suppose an office has four 100 W lights for 8 hours a day, and a 2 kW heater used for 2 hours. The daily energy is calculated as follows:
4 × 100 W × 8 h = 3200 Wh = 3.2 kWh2000 W × 2 h = 4000 Wh = 4 kWhTotal = 7.2 kWh per day. Over a 30-day month, this amounts to 7.2 × 30 = 216 kWh. If electricity costs £0.15 per kWh, the monthly cost is 216 × 0.15 = £32.40.
We can also calculate backwards: if an appliance used 5 kWh in a day and ran for 10 hours, its average load was P = E / t = 5 kWh / 10 h = 0.5 kW = 500 W.
Energy consumption calculation is crucial for:
48 / 12 = 4 Ah, factoring in discharge limits).5 W × 24 h = 120 Wh/day ≈ 43.8 kWh/year).In less common contexts, energy might be measured in BTU (British Thermal Units) or toe (ton of oil equivalent) for cross-disciplinary work, but conversion is always possible (1 kWh = 3412 BTU).
Energy consumption drives operational cost and efficiency. Building regulations and standards (such as ASHRAE, IEC 60364-8-1 for energy efficiency, or the EU Energy Performance of Buildings Directive) mandate calculations of expected kWh usage for compliance. Utility companies install smart meters that record kWh to bill customers and manage load. In industry, ISO 50001 Energy Management systems require organizations to track and improve energy use, which starts with accurate consumption calculations. Data such as annual kWh per square meter is used to benchmark buildings. On a larger scale, national grids rely on aggregate kWh forecasts to schedule fuel for power plants.
While the basic energy formula E = P × t is simple, standards ensure consistent measurement. The IEC 62053 series defines how electricity meters measure and classify kWh accuracy. BS 7671 Appendix L (informative) discusses energy efficiency in electrical installations, encouraging the minimization of wasted kWh. International building codes often require a load calculation or energy model—essentially a detailed kWh calculation for a typical year (taking into account occupancy schedules, weather, etc.). For appliances, the EU energy label shows annual kWh consumption based on standardized usage patterns, allowing consumers to compare efficiency. All these guidelines rest on the fundamental integration of power over time.
Managing energy calculations for complex systems is made easier with software:
Ultimately, whether via a sophisticated simulation or a manual summation, accurate energy consumption calculation is key to designing efficient systems and estimating operating costs.