Kilowatt-hours, energy conversion and costs

What you will learn

E(kWh) = P(kW)t(h); convert to joules; use supplied unit prices.

Specification mapping: C3.3

Prerequisites: C3.1

Physical principles

A kilowatt-hour is a unit of energy, the energy transferred at one kilowatt for one hour. Since 1 kW = 1000 W and 1 h = 3600 s, 1 kWh = 3.60 × 10⁶ J = 3.60 MJ. It is not kW per hour; that would describe a rate of change of power.

For domestic energy use, E in kWh equals power in kW multiplied by duration in hours. Convert watts to kilowatts by dividing by 1000 and minutes to hours by dividing by 60. For variable loads add each interval’s energy or use a measured average.

To estimate a usage charge, multiply energy by a supplied price per kWh. A standing charge is separate and depends on the billing duration. State whether costs include it. Illustrative prices in worked examples are supplied data rather than claims about current tariffs. Compare actual energy saved, not just changes in peak power.

Scientific diagram and interpretation

A cell drives a resistor with an ammeter in series. A voltmeter connects across the resistor through a separate parallel branch. The cell’s longer plate is positive.

Equations and relationships

E(kWh) = P(kW)t(h); 1 kWh = 3.60 × 10⁶ J

Worked examples and applications

Energy calculation

A 1.5 kW heater runs for 40 min. t = 40/60 = 0.6667 h. E = 1.5×0.6667 = 1.0 kWh = 3.6 MJ.

Supplied price

At an illustrative 25 p per kWh, 2.4 kWh costs 2.4×25 = 60 p = £0.60, excluding standing charges.

Mixed loads

A 50 W device on for 10 h and a 2.0 kW device on for 0.25 h each use 0.50 kWh. Combined energy is 1.00 kWh.

Common misconceptions

kWh measures energy; kW measures power. Neither is “kilowatts per hour”.

Examination technique

Write units into each stage and convert pence to pounds only once.

For an explanation, connect the physical cause to its effect. For a calculation, state the model, rearrange before substitution, retain intermediate digits, and finish with units. For a data question, refer to the actual readings and distinguish a trend from proof of a cause.

Check your understanding

Five questions. Choose an option, then Check Answer. Read the feedback and use Try Again to reset. Use Tab between controls, arrow keys within radio groups, and Enter or Space on buttons. These local practice answers are not saved.