Energy From Power: Kilowatt-Hours From a Day of Readings or a Power Curve, and What They Cost

Home › Calculators › Energy From Power

Opens on Chapter 21’s example: a home’s day, P(t) = 0.5 + 0.15t − 0.00625t² kilowatts (t in hours after 6 a.m.), over 24 hours, at 16¢ a kWh.

1. A smooth power model

Power (kW) t in hours

From hour

To hour

Load another example from the book

2. Or readings

Readings (kW), evenly spaced separate with commas

Hours between

Load readings from the book

3. The price

Price per kWh

Days like this in a month

Units helper

Multiply the total by 60 if the rate is per minute and the time in hours

Enter your numbers, then press Work it out.

How it works

Energy is the integral of power over time: kilowatts × hours, the area under the curve. For a polynomial model the reverse power rule (Chapter 20) gives it exactly; for readings, trapezoids give it to a close estimate: spacing × (all the readings − half of the first and last). The cost is the kilowatt-hours × the price. A month of days like this is the day × the number of days, if every day really is like it.

From the book, Chapter 21. The home uses 26.4 kWh, $4.22 a day at 16¢, about $127 for a month of such days; peaking at 1.4 kW. The roof’s panels made 21.05 kWh, worth $3.37. The heat pump used 12 kWh ($1.92). Every chapter and its calculator →

Numbers can be typed as 1,450, $38, 0.40, 12%, 1/6 or 2 3/8. Functions can be typed as 16t², 6 + 48t − 16t^2, 1000e^(0.05t) or √x; answers are rounded half up, the way the book rounds. Everything stays in your browser: no sign-up, nothing stored or sent.