Three-Phase Power Calculator

Three-Phase Power Calculator: equations, variables, units and worked solution

The three-phase power calculator calculates Real power, Apparent power, Reactive power, Power-factor angle, Phase voltage, Phase current from Line-to-line voltage, Line current, Power factor. It does not hide the arithmetic: the result panel shows the governing formula, canonical-unit conversion, numeric substitution, unrounded evaluation and final rounded answer for every output.

Variables and measurement units

For the Three-Phase Power Calculator, Line-to-line voltage, Line current, and Power factor are normalized to V, A, and ratio before Math.sqrt(3)*voltage*current*powerFactor/1000 is evaluated. The unrounded value used for wye, Math.sqrt(3)*voltage*current*powerFactor/1000, and Real power is retained internally; formatting is applied only to the result cards.

Formula model

For balanced three-phase line quantities, P = √3 × V_L × I_L × PF; S = √3 × V_L × I_L; Q = √(S² − P²). Wye and delta selections determine phase voltage and current.

Formula-based worked derivation

1. Real power
   1. Formula: Real power = Math.sqrt(3) × voltage × current × powerFactor ÷ 1000
   2. Default substitution: Real power = Math.sqrt(3) × (480) × (100) × (0.9) ÷ 1000
   3. Unrounded evaluation: 74.824594887 kW
   4. Displayed answer: 74.8246 kW
2. Apparent power
   1. Formula: Apparent power = Math.sqrt(3) × voltage × current ÷ 1000
   2. Default substitution: Apparent power = Math.sqrt(3) × (480) × (100) ÷ 1000
   3. Unrounded evaluation: 83.1384387633 kVA
   4. Displayed answer: 83.1384 kVA
3. Reactive power
   1. Formula: Reactive power = Math.sqrt(apparentPower^2-realPower^2)
   2. Default substitution: Reactive power = Math.sqrt(apparentPower^2-realPower^2)
   3. Unrounded evaluation: 36.2392052893 kVAR
   4. Displayed answer: 36.2392 kVAR
4. Power-factor angle
   1. Formula: Power-factor angle = Math.acos(powerFactor) × 180 ÷ Math.PI
   2. Default substitution: Power-factor angle = Math.acos((0.9)) × 180 ÷ Math.PI
   3. Unrounded evaluation: 25.8419327632 degrees
   4. Displayed answer: 25.842 degrees
5. Phase voltage
   1. Formula: Phase voltage = connection === "wye" ? voltage ÷ Math.sqrt(3) : voltage
   2. Default substitution: Phase voltage = wye === "wye" ? (480) ÷ Math.sqrt(3) : (480)
   3. Unrounded evaluation: 277.128129211 V
   4. Displayed answer: 277.1281 V
6. Phase current
   1. Formula: Phase current = connection === "delta" ? current ÷ Math.sqrt(3) : current
   2. Default substitution: Phase current = wye === "delta" ? (100) ÷ Math.sqrt(3) : (100)
   3. Unrounded evaluation: 100 A
   4. Displayed answer: 100 A

In the Three-Phase Power Calculator, changing Line-to-line voltage, Line current, and Power factor rebuilds the numeric substitution for Math.sqrt(3)*voltage*current*powerFactor/1000. The engine converts selected measurements to V, A, and ratio, retains unrounded values, and, when reverse solving is available, inserts the solved variable back into the same equation to verify wye, Math.sqrt(3)*voltage*current*powerFactor/1000, and Real power with a numerical residual.

Input and output interpretation

Use measured or documented values for Line-to-line voltage, Line current, Power factor. The calculated outputs are Real power, Apparent power, Reactive power, Power-factor angle, Phase voltage, Phase current. Check each intermediate line before relying on the final value; an implausible intermediate quantity usually identifies a unit, range or assumption error.

Algorithm and verification

The Three-Phase Power Calculator uses its own `three-phase-power` JavaScript engine to calculate wye, Math.sqrt(3)*voltage*current*powerFactor/1000, and Real power from Line-to-line voltage, Line current, and Power factor with Math.sqrt(3)*voltage*current*powerFactor/1000. Calculator-owned boundary and mode tests check that workflow; an external frozen-reference oracle checks the numeric outputs, and physical source mutation testing confirms that a changed `three-phase-power` engine is rejected.

Visual interpretation

In the Three-Phase Power Calculator, this guidance applies to Line-to-line voltage, Line current, and Power factor and the reported wye, Math.sqrt(3)*voltage*current*powerFactor/1000, and Real power. The `three-phase-power` workflow evaluates Math.sqrt(3)*voltage*current*powerFactor/1000 in V, A, and ratio; This model assumes a balanced sinusoidal three-phase system. Harmonics, unbalance, motor starting and code-required conductor sizing need separate analysis.. Verification context: d3197e.

Dimensional formula audit

The three-phase power calculator normalizes voltage (Line-to-line voltage, V), current (Line current, A), powerFactor (Power factor, ratio) before evaluating the equations. Its reported quantities are Real power in kW, Apparent power in kVA, Reactive power in kVAR, Power-factor angle in degrees, Phase voltage in V, Phase current in A. This separation matters because a numerical value without its measurement dimension can produce a plausible-looking but physically or financially incorrect answer. Conversion factors are applied before substitution, and output conversion occurs only after the canonical result has been calculated at full precision.

• Real power = sqrt(3) × voltage × current × powerFactor ÷ 1000
• Apparent power = sqrt(3) × voltage × current ÷ 1000
• Reactive power = sqrt(apparentPower^2-realPower^2)
• Power-factor angle = acos(powerFactor) × 180 ÷ π
• Phase voltage = connection = "wye" ? voltage ÷ sqrt(3) : voltage
• Phase current = connection = "delta" ? current ÷ sqrt(3) : current

Formula sensitivity and boundary verification

To verify the three-phase power calculator, hold all other inputs fixed and change voltage within its permitted range. The live substitution line shows exactly where that value enters the equation for Real power. Repeat the check with current. The result must follow the displayed algebra, remain finite, and retain the stated output unit. At minimum and maximum boundaries, the validator rejects undefined domains, impossible denominators and nonphysical values rather than silently returning a number.

Manual reproduction of the result

For an independent hand check, first convert every selected unit to the canonical units shown in the variable table. Next copy the governing equation, replace each symbol with the canonical value shown in the live derivation, and calculate the intermediate expression without early rounding. Finally round only once to the displayed precision and compare both the numerical value and unit with the calculator card. This process makes the three-phase power calculator reproducible instead of relying on an unexplained result.

Limitations

This model assumes a balanced sinusoidal three-phase system. Harmonics, unbalance, motor starting and code-required conductor sizing need separate analysis.