Kilowatt-Hour & Electricity Cost

Every time you switch on a kettle, charge your phone, or leave a light on, you are consuming electrical energy. Energy companies don't sell you watts — they sell you energy, and the unit they use is the kilowatt-hour (kWh). One kilowatt-hour is the amount of energy transferred when a device with a power rating of one kilowatt operates for exactly one hour. It is simply a unit of energy, just like the joule, but chosen because joules are inconveniently small for everyday electricity bills. Understanding kilowatt-hours lets you make real financial decisions: which appliances are expensive to run, how much a streaming session costs, whether switching off standby devices actually saves money. The calculation is straightforward — multiply the device's power rating in kilowatts by the number of hours it runs, then multiply by the price per kWh charged by your energy supplier. This connects the physics of power and energy directly to economics, making it one of the most practically useful calculations in the entire electricity unit. The kilowatt-hour is not an SI unit, but it is a legal unit of measurement in the UK and across the EU for energy billing. Its relationship to the joule is exact: 1 kWh = 3,600,000 J = 3.6 × 10⁶ J. This large conversion factor explains why energy bills use kWh rather than joules — a typical UK household uses roughly 8–10 kWh per day, which would be an unwieldy 30,000,000 joules.

Key takeaways
  • Power vs Energy — the key distinction
  • Defining the kilowatt-hour precisely
  • Calculating energy consumed in kWh
  • Calculating electricity cost
  • Reading an electricity meter

Power vs Energy — the key distinction

Power is the rate of energy transfer, measured in watts (W) or kilowatts (kW). Energy is the total amount transferred over a period of time. Think of power as the speed of a tap flowing water, and energy as the total volume of water collected in a bucket. A 2 kW heater running for 3 hours transfers 6 kWh of energy — exactly like a tap running at 2 litres per minute for 3 hours would fill a 360-litre container.

Defining the kilowatt-hour precisely

1 kilowatt-hour = 1 kW × 1 hour = 1000 W × 3600 s = 3,600,000 J = 3.6 MJ. To convert any energy in kWh to joules, multiply by 3.6 × 10⁶. Conversely, to express a large number of joules as kWh, divide by 3.6 × 10⁶. The kWh is a convenient unit because power ratings on appliances are given in watts or kilowatts, and usage is naturally measured in hours.

Calculating energy consumed in kWh

The formula is: Energy (kWh) = Power (kW) × Time (hours). You must ensure the power is in kilowatts (divide watts by 1000) and time is in hours (divide minutes by 60). For example, a 600 W microwave used for 20 minutes: Power = 0.6 kW, Time = 20/60 = 0.333 hours, Energy = 0.6 × 0.333 = 0.2 kWh.

Calculating electricity cost

Once you have the energy in kWh, multiply by the unit cost (price per kWh) charged by the supplier. Cost = Energy (kWh) × Price per kWh. In the UK, typical prices are around 24–29 pence per kWh (as of 2024). If your 0.2 kWh microwave session costs 25p/kWh, the cost is 0.2 × 25 = 5 pence. This framework works for any appliance: find power rating, convert to kW, multiply by hours of use, multiply by unit cost.

Reading an electricity meter

Domestic electricity meters record cumulative energy used in kWh. Your bill is calculated as: Units used = current reading − previous reading (in kWh). The total cost equals units used multiplied by the unit rate, plus a daily standing charge. Smart meters now send readings automatically, but understanding the kWh unit means you can verify any bill yourself — a powerful example of physics knowledge having direct financial value.

The Key Equation

EkWh=PkW×th,Cost=EkWh×cE_{\text{kWh}} = P_{\text{kW}} \times t_{\text{h}}, \quad \text{Cost} = E_{\text{kWh}} \times c
  • E_{\text{kWh}} — Electrical energy consumed (kilowatt-hour (kWh)): Total energy transferred by the appliance; 1 kWh = 3.6 × 10⁶ J
  • P_{\text{kW}} — Power rating (kilowatt (kW)): Rate of energy transfer; divide the wattage by 1000 to get kW
  • t_{\text{h}} — Time of operation (hour (h)): Duration the appliance is in use; divide minutes by 60 to convert to hours
  • c — Unit cost of electricity (pence per kWh (p/kWh) or £/kWh): Price charged by the energy supplier per kilowatt-hour of energy used
  • \text{Cost} — Electricity cost (pence (p) or pounds (£)): Total monetary cost of running the appliance for the given time period

Worked Example

Problem. A household uses the following appliances in one day: a 2500 W electric shower for 8 minutes, a 1200 W hair dryer for 15 minutes, and a 55 W television for 4 hours. The electricity tariff is 28 p/kWh. Calculate (a) the total energy consumed in kWh, and (b) the total cost in pence.

Etotal=0.853 kWh,Cost=0.853×28≈24 pE_{\text{total}} = 0.853 \text{ kWh}, \quad \text{Cost} = 0.853 \times 28 \approx 24 \text{ p}

Answer. Total energy consumed ≈ 0.853 kWh; total cost ≈ 24 pence.

Figure
Diagram
Kilowatt-Hour: Energy = Power × Time0.3330.3000.2200.853Shower2.5 kW, 8 minHair Dryer1.2 kW, 15 minTelevision0.055 kW, 4 hTOTALall appliancesEnergy (kWh)0.350.150Cost Calculation at 28 p/kWhCost = 0.853 kWh × 28 p/kWh ≈ 24 pence
Origins · 1 minJames Prescott Joule and how this was discovered
JP
James Prescott Joule
1818–1889 · British

Joule established the equivalence of mechanical work and heat, leading to the first law of thermodynamics and the conservation of energy. He also quantified the heating effect of electric current — now known as Joule heating — showing that the heat produced is proportional to the square of the current, the resistance, and the time. This foundational work underpins every calculation of electrical energy and is why the SI unit of energy bears his name. The kilowatt-hour is simply a scaled, practical unit of the same quantity Joule so painstakingly measured. Joule was largely a self-taught amateur scientist who ran his family's brewery. He conducted many of his famous experiments in his personal laboratory and even took temperature measurements during his honeymoon in the Swiss Alps, attempting to detect the slight warming of water at the base of a waterfall due to its loss of gravitational potential energy.

  • Electric Power — Electric power (P = IV = I²R = V²/R) is the rate of energy transfer that you must know in kilowatts before you can calculate energy in kWh.
  • Current and Charge — Electric current is the flow of charge that drives energy transfer in circuits; understanding current is foundational to calculating power and hence electricity costs.
  • Potential Difference and Voltage — Voltage (potential difference) combined with current gives power (P = IV), which feeds directly into the kWh energy calculation.
  • Resistance and Ohm's Law — Resistance determines how much current flows for a given voltage, setting the power consumption of devices and therefore their running costs.