Complex Power One Harmonic Cross Term Tool

Description

apparent = their product; active = apparent*cos(phaseDifference); reactive = apparent*sin(phaseDifference), with phaseDifference in radians.

Sinusoidal electrical calculations need a common frequency, phase reference and RMS or peak convention. Phasor sums, complex power and composite RMS describe different operations; a sign label alone does not establish a physical connection or waveform.

apparent = their product; active = apparent*cos(phaseDifference); reactive = apparent*sin(phaseDifference), with phaseDifference in radians.

When to use this tool

Use Complex Power One Harmonic Cross Term when checking a stated phasor, power or RMS convention.

How to use the tool and how it works

Enter voltageMagnitude, currentMagnitude, phaseDifference. Use the units and conventions below.
Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
Read active, reactive. Use the output convention below.

Require nonnegative voltageMagnitude and currentMagnitude. apparent = their product; active = apparent*cos(phaseDifference); reactive = apparent*sin(phaseDifference), with phaseDifference in radians.^[1]

Input field	Meaning and units	Accepted input
voltageMagnitude	Voltage Magnitude	Required. Finite number; minimum 0.
currentMagnitude	Current Magnitude	Required. Finite number; minimum 0.
phaseDifference	Voltage phase minus current phase in radians.	Required. Finite number.

Output field	Interpretation	Returned shape
active	Active	Required. Finite number.
reactive	Reactive	Required. Finite number.

json

{
  "input": {
    "voltageMagnitude": 10,
    "currentMagnitude": 2,
    "phaseDifference": 0
  },
  "output": {
    "active": 20,
    "reactive": 0
  }
}

Limitations and assumptions

For W and var use RMS magnitudes and voltage phase minus current phase. This is one harmonic contribution without cross-frequency effects or a complete distorted-waveform power analysis.
Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.

Alternative or Complementary methods

Use compatible measured waveforms and a complete circuit or harmonic model when signals are distorted, references differ or practical limits matter.

References

Calculation and input contract: electricity/complex-power-one-harmonic-cross-term — tool.io

Similar or alternative tools

Electricity: Complex Power Real Imaginary Pair
Return realPower = voltageReal*currentReal+voltageImaginary*currentImaginary and reactivePower = voltageImaginary*currentReal-voltageReal*currentImaginary.
Electricity: Ac Power Leading Lagging Quadrant
Return quadrant 1-4 from realPower/reactivePower signs, or zero on either axis.