Theory and Formulas

The Energy Consumption Calculator is a tool to compute either the energy consumed (in Wh) from power and time or the power consumed (in W) from energy and time. These calculations are fundamental in understanding energy usage, optimizing efficiency, and estimating energy costs.

Formula for Power to Energy:

The formula to calculate energy (\(E\)) is:
\[E = P \times T\]
Where:

• \(E\): Energy in watt-hours (Wh)
• \(P\): Power in watts (W)
• \(T\): Time in hours (h)

Formula for Energy to Power:

The formula to calculate power (\(P\)) is:
\[P = \frac{E}{T}\]
Where:

• \(P\): Power in watts (W)
• \(E\): Energy in watt-hours (Wh)
• \(T\): Time in hours (h)

Example Calculations

Example 1: Power to Energy

Given:

• Power = 2 kW
• Time = 5 hours

Calculation:

Convert power to watts:
\[2 \, \text{kW} = 2000 \, \text{W}\]
Calculate energy using the formula:
\[E = P \times T = 2000 \, \text{W} \times 5 \, \text{h} = 10000 \, \text{Wh}\]
Convert energy to kilowatt-hours:
\[10000 \, \text{Wh} = 10 \, \text{kWh}\]

Result: Energy consumed is \(10 \, \text{kWh}\).

Example 2: Power to Energy with Conversion

Given:

• Power = 500 mW
• Time = 2 minutes

Calculation:

Convert power to watts:
\[500 \, \text{mW} = 0.5 \, \text{W}\]
Convert time to hours:
\[2 \, \text{min} = \frac{2}{60} \, \text{h} = 0.0333 \, \text{h}\]
Calculate energy:
\[E = P \times T = 0.5 \, \text{W} \times 0.0333 \, \text{h} \approx 0.0167 \, \text{Wh}\]

Result: Energy consumed is \(0.0167 \, \text{Wh}\).

Example 3: Energy to Power

Given:

• Energy = 3000 Wh
• Time = 10 hours

Calculation:

Calculate power using the formula:
\[P = \frac{E}{T} = \frac{3000 \, \text{Wh}}{10 \, \text{h}} = 300 \, \text{W}\]

Result: Power required is \(300 \, \text{W}\).

Example 4: Energy to Power with Conversion

Given:

• Energy = 50 mWh
• Time = 30 seconds

Calculation:

Convert energy to watt-hours:
\[50 \, \text{mWh} = 0.05 \, \text{Wh}\]
Convert time to hours:
\[30 \, \text{s} = \frac{30}{3600} \, \text{h} = 0.00833 \, \text{h}\]
Calculate power:
\[P = \frac{E}{T} = \frac{0.05 \, \text{Wh}}{0.00833 \, \text{h}} \approx 6 \, \text{W}\]

Result: Power required is \(6 \, \text{W}\).