Three-Phase Power Calculator

Three-Phase Power is evaluated from Line Voltage, Line Current and Power Factor. The calculation reports Real Power, Apparent Power and Reactive Power.

Results

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About the Three-Phase Power Calculator

Three-Phase Power is treated here as a quantitative relation between Line Voltage, Line Current, Power Factor and Real Power and Real Power, Apparent Power, Reactive Power and Line Current.

The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.

Formula basis:
P (kW) = sqrt3 x VL x IL x PF / 1,000
S (kVA) = sqrt3 x VL x IL / 1,000
Q (kVAR) = sqrt3 x VL x IL x sin(φ) / 1,000
Solving for current: IL = P x 1,000 / (sqrt3 x VL x PF)
Phase voltage: Vφ = VL / sqrt3 approximately VL / 1.7321

Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.

Formula & How It Works

The calculation applies the following relations exactly as recorded in the metadata:

P (kW) = sqrt3 x VL x IL x PF / 1,000
S (kVA) = sqrt3 x VL x IL / 1,000
Q (kVAR) = sqrt3 x VL x IL x sin(φ) / 1,000
Solving for current: IL = P x 1,000 / (sqrt3 x VL x PF)
Phase voltage: Vφ = VL / sqrt3 approximately VL / 1.7321

Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.

Worked Examples

Example 1: Industrial Motor — 480V, 3-Phase

Inputs

line_voltage: 480 line_current: 65 pf: 0.85
Real Power: 45.934 kW. Apparent Power: 54.04 kVA. Reactive Power: 28.467 kVAR. Phase Voltage: 277.13 V

With Line Voltage = 480, Line Current = 65 and Power Factor = 0.85 as the stated inputs, the result is Real Power = 45.934 kW, Apparent Power = 54.04 kVA and Reactive Power = 28.467 kVAR. Each value corresponds to the declared output fields.

Example 2: Find Current — 75 HP Motor

Inputs

line_voltage: 480 pf: 0.88 real_kw: 55.93
Apparent Power: 63.557 kVA. Line Current: 76.45 A. Phase Voltage: 277.13 V

With Line Voltage = 480, Power Factor = 0.88 and Real Power = 55.93 as the stated inputs, the result is Apparent Power = 63.557 kVA, Line Current = 76.45 A and Phase Voltage = 277.13 V. Each value corresponds to the declared output fields.

Example 3: Data Center 208V Distribution

Inputs

line_voltage: 208 line_current: 200 pf: 0.95
Real Power: 68.451 kW. Apparent Power: 72.053 kVA. Reactive Power: 22.499 kVAR. Phase Voltage: 120.09 V

With Line Voltage = 208, Line Current = 200 and Power Factor = 0.95 as the stated inputs, the result is Real Power = 68.451 kW, Apparent Power = 72.053 kVA and Reactive Power = 22.499 kVAR. Each value corresponds to the declared output fields.

Example 4: Transformer Sizing — Retail Store

Inputs

line_voltage: 480 pf: 0.9 real_kw: 150
Apparent Power: 166.667 kVA. Line Current: 200.47 A. Phase Voltage: 277.13 V

With Line Voltage = 480, Power Factor = 0.9 and Real Power = 150 as the stated inputs, the result is Apparent Power = 166.667 kVA, Line Current = 200.47 A and Phase Voltage = 277.13 V. Each value corresponds to the declared output fields.

Common Use Cases

  • Size a 3-phase transformer for a factory floor
  • Calculate current draw of a 3-phase motor
  • Convert between single-phase and three-phase power ratings