Three-Phase Power Calculator

Parameters

Every field on the form is listed below with its unit, its accepted range, and the behaviour that is easy to get wrong. Three of the six fields appear and disappear depending on the calculation mode, so the form only ever asks for the two quantities it needs to solve for the third.

Calculation mode

Selects which quantity is solved for. Power from V and I gives active power from a measured voltage and current. Current from V and P gives line current from a known kW rating. Voltage from I and P gives the line voltage implied by a measured current and a known kW. Unitless selection, three options. Gotcha. The two input fields the mode does not need are hidden and are not sent to the calculation at all, so a value you typed in an earlier mode has no effect once you switch away from it.

Connection type

Star (Y) or delta. Unitless selection. In star, phase voltage is the line voltage divided by 1.732 and phase current equals line current. In delta, phase voltage equals line voltage and phase current is the line current divided by 1.732. Gotcha. This field changes the phase voltage and phase current outputs only. Active power, apparent power, reactive power and line current are identical for star and delta, because the line quantities are what the formulas work with.

Power factor

The cosine of the angle between phase voltage and phase current. Dimensionless, accepted range 0.1 to 1.0, default 0.85. Used in every calculation mode and in the reactive power result. Typical values are 0.80 to 0.90 for a loaded induction motor, 0.95 to 1.0 for resistive heating, and 0.90 or better for a corrected site. Gotcha. The value is treated as lagging. There is no way to enter a leading power factor, and reactive power is always reported as a positive number, so an over corrected site will read the same as an under corrected one.

Line voltage

The line-to-line voltage of the supply, in volts. Form range 100 to 50000 V, default 415 V. Shown in the Power from V and I and Current from V and P modes. Standard Australian values are 400 V nominal and 415 V as commonly measured at the switchboard. Gotcha. This is line-to-line, not phase-to-neutral. Entering 230 V here does not model a single-phase circuit. It models a three-phase system whose line-to-line voltage happens to be 230 V, which is not a supply you will meet in an Australian installation.

Line current

The current in one line conductor, in amperes. Form range 0.1 to 10000 A, default 50 A. Shown in the Power from V and I and Voltage from I and P modes. Gotcha. The calculation assumes all three lines carry this same current. If your clamp meter gives three different readings, the load is unbalanced and this calculator does not model it. Use the highest reading only if you want a worst case figure, and treat the result as approximate.

Active power

Real power drawn by the load, in kilowatts. Form range 0.1 to 10000 kW, default 30 kW. Shown in the Current from V and P and Voltage from I and P modes. Gotcha. This is kW, not kVA. A motor nameplate kW is the mechanical shaft output, so the electrical input is higher by the motor efficiency. If you want the current a motor actually draws, use the Full Load Current calculator, which divides by efficiency as well as power factor.

Assumptions and limits

The arithmetic here is the textbook balanced three-phase relationship and nothing more. Knowing what it leaves out matters more than knowing what it includes.

What the tool assumes

• A perfectly balanced load. All three lines carry equal current at equal phase displacement, so neutral current is zero. Real installations with single-phase loads spread across phases are never exactly balanced.
• A pure sine wave at fundamental frequency. No harmonic content is modelled, so displacement power factor and true power factor are treated as the same number. On a site with variable speed drives, rectifiers or LED drivers, the true power factor is lower than the displacement value and the apparent power result will read optimistically.
• Lagging power factor. Reactive power is computed as apparent power multiplied by the square root of one minus the power factor squared, and is always positive. Nothing in the result distinguishes a lagging load from a leading one.
• Voltage measured at the load. No cable impedance, no voltage drop and no losses are modelled anywhere. The voltage you enter is the voltage the load sees.
• Star and delta as an output relationship only. The connection type is applied at the end, to convert line quantities into phase quantities. It does not change the power or current results.

What the compliance checks actually check

Two checks run on every calculation. The first flags a power factor below 0.80. The second flags a line current above 630 A. The 630 A figure is a generic distribution ceiling coded into this tool as a sanity check. It is not a limit taken from AS/NZS 3000, and it says nothing about your cable, your protective device or the capacity of your supply. A pass on both checks is not a compliance result.

What this must not be used for

• Single-phase circuits. The formulas all carry the 1.732 factor and there is no single-phase mode.
• Unbalanced loads, neutral current sizing, or any calculation where the three phases differ.
• Sites with significant harmonic distortion, where kVA and neutral loading both need a harmonic study rather than a fundamental frequency calculation.
• Cable sizing or protective device selection. Those require the derating and installation method work in AS/NZS 3008.1.1, not a line current figure on its own.
• Fault level, arc flash, protection grading or earthing design. None of that is modelled here.
• Evidence of compliance. This calculator is not validated or certified. Check every result against the current edition of AS/NZS 3000 and AS/NZS 3008.1.1, and have it signed off by the person responsible for the installation before it is used in design or on site.

Worked examples

Three examples covering all three calculation modes and both connection types. Every figure below comes from the same formulas the calculator runs, so you can reproduce them by typing the inputs into the form.

Three-Phase Power Guide

Three-phase power is the standard for commercial, industrial, and utility electrical systems worldwide, including Australia and New Zealand. It delivers power using three conductors carrying alternating current waveforms that are offset by 120 degrees from each other. Compared to single-phase, three-phase supply provides approximately 73 percent more power using the same conductor cross section, produces a constant power output (no pulsating torque in motors), and enables more efficient transmission over long distances. The standard Australian three-phase supply is 400 V line-to-line and 230 V phase-to-neutral at 50 Hz. This calculator converts between voltage, current, real power, apparent power, and reactive power for both star and delta connected loads.

Key concepts

• Real power (P). The active power that performs useful work, measured in watts (W) or kilowatts (kW). In a balanced three-phase system, P = 1.732 x V_line x I_line x cos(phi). This is the power that appears on the electricity bill and converts to heat, motion, or light.
• Apparent power (S). The total power in the circuit, combining both real and reactive components. Measured in volt-amperes (VA) or kilovolt-amperes (kVA). Cables, transformers, and generators are all rated in kVA because their thermal limits depend on the total current they carry, regardless of power factor.
• Power factor (cos phi). The ratio of real power to apparent power, ranging from 0 to 1. A power factor of 1.0 means all current is doing useful work. Low power factor (below 0.90) means the supply is carrying more current than necessary, increasing cable losses, transformer loading, and supply authority demand charges. Most Australian supply authorities penalise consumers with power factor below 0.90.
• Star (Y) vs delta (triangle) connection. In a star connected system, each load is connected between a phase and the neutral point. Line voltage is 1.732 times phase voltage, and line current equals phase current. In a delta connected system, each load is connected between two phases directly. Line voltage equals phase voltage, and line current is 1.732 times phase current. Star connection provides a neutral for single-phase loads. Delta connection is common for motors and transformers.

Common scenarios

1. Sizing a three-phase cable for a motor. A 30 kW three-phase motor with a power factor of 0.85 on a 400 V supply draws approximately 51 A per phase. The cable must be sized to carry this current continuously, with allowances for installation conditions (grouping, ambient temperature, insulation type) per AS/NZS 3008.1.1. The calculator gives the line current directly from the kW rating, voltage, and power factor.
2. Checking transformer loading. A 500 kVA distribution transformer supplies a mixed load of motors and lighting. The total real power demand is 380 kW at 0.82 power factor. The apparent power is 380 / 0.82 = 463 kVA, which is within the transformer rating. If additional load is added, the power factor must be improved (capacitor bank) or a larger transformer specified.
3. Balancing single-phase loads across three phases. A commercial kitchen has twelve 2.4 kW single-phase ovens to distribute across a three-phase supply. Placing four ovens on each phase gives a balanced load of 9.6 kW per phase. The calculator can verify the per-phase and total current draw, helping identify whether the existing supply can handle the connected load before additional circuits are installed.