Energy and Cost Formulas: kWh and Payback
Energy and cost formulas for kWh from power and hours, running cost, efficiency and payback of an upgrade, with worked examples and a table of yearly energy.
The formulas
| To find | Formula |
|---|---|
| Energy | E (kWh) = P (kW) × t (h) |
| Energy from watts | E (kWh) = P (W) × t (h) / 1000 |
| Running cost | Cost = E × tariff |
| Efficiency | η = Pout / Pin |
| Input power from output | Pin = Pout / η |
| Simple payback | Payback (years) = cost of the upgrade / saving per year |
The tariff is the price of one kWh in your own currency. A bill may also include fixed charges, demand charges and taxes that these formulas leave out.
Worked example: running cost of a 7.5 kW load
The load runs 8 hours a day for 26 days in the month, at a tariff of 0.10 per kWh.
- E = 7.5 × 8 × 26 = 1,560 kWh
- Cost = 1,560 × 0.10 = 156
Worked example: payback of a lighting upgrade
100 fittings of 150 W are replaced by fittings of 60 W, each costing 40. They run 10 hours a day, every day, at 0.10 per kWh.
- Power saved = 100 × (150 − 60) / 1000 = 9 kW
- Energy saved = 9 × 10 × 365 = 32,850 kWh a year
- Saving = 32,850 × 0.10 = 3,285 a year
- Payback = 100 × 40 / 3,285 = 1.218 years
Energy per year by load and daily hours
| Load | 4 h a day | 8 h a day | 12 h a day | 24 h a day |
|---|---|---|---|---|
| 1 kW | 1,460 kWh | 2,920 kWh | 4,380 kWh | 8,760 kWh |
| 5 kW | 7,300 kWh | 14,600 kWh | 21,900 kWh | 43,800 kWh |
| 10 kW | 14,600 kWh | 29,200 kWh | 43,800 kWh | 87,600 kWh |
Frequently asked questions
Is kWh the same as kW?
No. kW is a rate of using energy (power) and kWh is the amount of energy used over time. A 1 kW heater running for one hour uses 1 kWh.
Why is my real bill higher than this?
The bill can add a fixed charge, a charge for maximum demand, a low power factor penalty and taxes. Add them to the energy cost.
Does a motor use its rated power all the time?
Not usually. It draws power in line with its load. Use the real average load, or a measured figure, in place of the nameplate rating.
What does simple payback leave out?
It ignores the cost of money, the life of the equipment, changes in the tariff and maintenance. For a large investment use a full life-cycle cost.
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