Electrical Energy and the Kilowatt-Hour

From power to energy

Power P indicates how fast a device consumes energy, but it does not say how much energy has actually been consumed in total. For that, you also need to know the operating time t. The electrical energy consumed (or supplied) is calculated as:

E = P x t

where:

• E is the energy in joules (J) if P is in watts and t in seconds
• P is the power in watts (W)
• t is the duration in seconds (s)

The kilowatt-hour: a more practical unit

The joule is a unit suited to physics, but too small for an electricity bill. We therefore use the kilowatt-hour (kWh), which corresponds to the energy consumed by a 1 kW device operating for 1 hour:

1 kWh = 1000 W x 3600 s = 3,600,000 J

To calculate an energy in kWh directly, we use P in kW and t in hours:

E (in kWh) = P (in kW) x t (in h)

Concrete example

An oven of power P = 2000 W = 2 kW operates for t = 1.5 h.

E = 2 x 1.5 = 3 kWh

If we wanted the result in joules: E = 2000 x (1.5 x 3600) = 2000 x 5400 = 10,800,000 J, which indeed confirms 3 kWh (3 x 3,600,000 = 10,800,000 J).

Common pitfall

Never mix units within the same formula: if P is in watts, t must be in seconds to obtain E in joules; if P is in kilowatts, t must be in hours to obtain E in kWh. Forgetting to convert minutes to hours (or hours to seconds) is the most common mistake in this type of calculation.