Enter the maximum voltage (volts), the maximum current (amps), voltage phase angle, current phase angle, time, and the angular frequency (rad/s) into the calculator to determine the Instantaneous Power.

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## Instantaneous Power Formula

The following formula is used to calculate the Instantaneous Power.

P(t) = Vm*Im*cos(wt+av)*cos(wt+ai)

- Where P(t) is the Instantaneous Power (amps)
- Vm is the maximum voltage (volts)
- Im is the maximum current (amps)
- w is the angular frequency (rad/s)
- t is the time (s)
- av is the voltage phase angle (rad)
- ai is the current phase angle (rad)

## How to Calculate Instantaneous Power?

The following example problems outline how to calculate Instantaneous Power.

**Example Problem #1**

- First, determine the maximum voltage (volts). In this example, the maximum voltage (volts) is determined to be 15.
- Next, determine the maximum current (amps). For this problem, the maximum current (amps) is 40.
- Next, determine the angular frequency (rad/s). In this case, the angular frequency (rad/s) is found to be 12.
- Next, determine the time. For this problem, the time is 5 seconds.
- Next, determine the voltage and current phase angle. These are 2 and 3 rad, respectively.
- Finally, calculate the Instantaneous Power using the formula above:

P(t) = Vm*Im*cos(wt+av)*cos(wt+ai)

Inserting the values from above and solving yields:

P(t) = 15*40*cos(12*5+2)*cos(12*5+3) = 398.405 (amps)

**Example Problem #2**

Using the same method as above, determine the variables required by the formula. For this example problem, these are:

maximum voltage (volts) = 15

maximum current (amps) = 412

angular frequency (rad/s) = 2

time (s) = 15

phase angles (rad) = 14 & 5

Enter these given values into the calculator or above yields:

P(t) = 15*412*cos(2*15+14)*cos(2*15+5) = -5583.94** **(amps)