Does this calculator assume balanced three-phase load?

Yes. It uses the balanced three-phase relationship from entered line voltage, line current and PF.

Can I use 400 V as the voltage?

Use 400 V only when it matches the Australian three-phase line-to-line basis for the project record being reviewed.

What does the current cross-check show?

It recalculates current from the calculated kW, entered voltage and PF so the relationship stays visible.

Does this check voltage unbalance?

No. Use a separate voltage-unbalance record when phase voltages are materially different.

Does this size cables or protection?

No. It gives a power relationship record that may feed later cable, protection, demand or equipment checks.

Three-phase power matrix calculator

S = sqrt(3) x V_LL x I / 1000; P = S x PF; Q = S x sin(arccos(PF)); I_check = P x 1000 / (sqrt(3) x V_LL x PF)

Voltage is entered as line-to-line voltage.
Current is entered as balanced line current.
PF must be above 0 and not greater than 1.
The calculator does not assess voltage unbalance, current unbalance, harmonic content or metering uncertainty.

Formula variables
Variable	Meaning	Unit	Use
S	Apparent power	kVA	Three-phase apparent power from line voltage and current.
V_LL	Line voltage	V	Entered line-to-line voltage.
I	Line current	A	Entered balanced three-phase line current.
PF	Power factor	ratio	Entered power factor for the operating point.
P	Real power	kW	Apparent power multiplied by PF.
Q	Reactive power	kVAr	Reactive component from the power triangle.
I_check	Current cross-check	A	Current recalculated from kW, voltage and PF.

Three-phase power matrix calculator technical guide

Calculate Australian three-phase kVA, kW, kVAr and current cross-check values from entered voltage, current and power factor.

Use this calculator when a three-phase load needs one visible relationship record: line voltage, line current, power factor, apparent power, real power and reactive power. It is useful for Australian switchboard notes, plant load records, estimating checks and handoffs into demand, cable or power-factor workflows.

The calculator is intentionally narrow. It assumes the entered values represent a balanced three-phase operating point and does not check voltage unbalance, current unbalance, harmonic distortion, instrument uncertainty, protection settings or equipment suitability.

Power Matrix Use Cases

Three-phase power matrix use cases
Work situation	Entered basis	Useful output	Outside the result
Switchboard load note	Line voltage, line current and PF	kVA, kW, kVAr and current cross-check	Cable size or protection decision
Plant estimate	Nominal 400 V, current and expected PF	Power matrix for an estimating record	Metering confirmation or load balance proof
Metering summary	Measured current and measured PF	Consistent relationship values	Instrument accuracy or data logging analysis
Demand handoff	kW and kVA context from current	Values for demand or tariff worksheets	Tariff interpretation
Correction planning	Reactive component visible beside real power	kVAr context before correction worksheet	Capacitor equipment selection

A matrix record is strongest when the voltage, current and PF are all from the same operating condition. Mixing a design current with a measured PF from another period can make the relationship look more precise than it is.

Three-Phase Boundary

Three-phase matrix boundary
Included in this calculator	Not included in this calculator
Line-to-line voltage	Phase-by-phase voltage unbalance
Balanced line current	Current unbalance or neutral current
Entered PF	Harmonic distortion or waveform quality
kVA, kW, kVAr and PF angle	Cable, protection or transformer selection
Current cross-check	Meter calibration or instrument uncertainty

The boundary matters because the formula is only a relationship between entered values. A real installation may need separate measurement, balancing, protection, harmonic or manufacturer checks before design decisions are made.

Input Checklist

Values to collect before using the matrix
Input	Strong basis	Weak basis
Matrix reference	Switchboard, meter, load or estimate record	Generic note with no traceable load
Line voltage	Measured or documented line-to-line value	Assumed value that does not match the site
Line current	Balanced current basis for the same load condition	One phase current used as if all phases match
Power factor	Measured, calculated or documented PF for the same period	PF copied from a different load or tariff note
Review context	Project note naming how the matrix will be used next	Output copied into another worksheet with no source

If each phase has materially different current or voltage, keep a separate load-balancing or unbalance record instead of reducing the condition to one balanced matrix.

Review Workflow

Name the switchboard, load, meter or estimate being represented.
Confirm the line-to-line voltage basis for the Australian project context.
Enter the balanced line current value for the same operating condition.
Enter the power factor value that belongs with that current and voltage.
Read kVA, kW, kVAr, PF angle and current cross-check together.
If PF is very low, check the metering basis and load condition before relying on the reactive result.
Send the output to the next calculator only when the source values and assumptions are recorded.
Use separate records for unbalance, harmonics, cable sizing, protection, correction equipment or tariff interpretation.

The workflow makes the three-phase relationship visible without pretending the matrix is a full electrical design review.

Worked Australian Examples

Three-phase power examples
Situation	Entered values	Output reading	Practical note
400 V plant load	400 V, 180 A, PF 0.86	124.71 kVA, 107.25 kW and 63.64 kVAr	Keep the load condition with the result.
Planning record	400 V, 95 A, PF 0.90	Compact matrix for an early estimate	Nominal voltage is a worksheet basis only.
Low PF matrix review	400 V, 140 A, PF 0.64	Matrix is calculated with a PF review note	Check metering before using the reactive value.

These examples use common Australian three-phase context, but the entered voltage should always match the actual project record.

Related Tools

Use the kVA, kW and power factor calculator when the task is a smaller two-value conversion. Use the reactive power kVAr calculator when the kVAr side of the power triangle needs its own record. Use the power-factor relationship chart when the task is explanation rather than calculation.

Next tool selection
Next question	Use next
Convert kVA, kW and PF without current	kVA, kW and power factor calculator
Derive kVAr from kW and PF or kW and kVA	Reactive power kVAr calculator
Explain the power triangle	Power-factor relationship chart
Review low PF correction need	Power factor correction calculator

Stop Points

The load is materially unbalanced across phases.
Voltage values are phase-to-neutral while the calculator expects line-to-line voltage.
Current and PF come from different operating conditions.
Harmonics or waveform distortion are material to the decision.
The matrix is being used as a cable, protection or equipment selection result.

Export the matrix only with the voltage, current, PF source and intended next use. The result is a relationship record, not a complete design decision.

Reference: TPM-1
Line voltage: 400 V
Current: 180 A
Power factor: 0.86

Apparent power124.71 kVA
Real power107.25 kW
Reactive power63.64 kVAr

Three-phase power matrix107.25 kW

124.71 kVA and 63.64 kVAr.

The matrix keeps apparent, real and reactive power together so downstream power-factor and tariff checks use the same basis.

Line voltage is entered as the three-phase line-to-line voltage.
The current is the balanced three-phase line current.
The power factor is entered by the user.

Reference: TPM-2
Line voltage: 400 V
Current: 95 A
Power factor: 0.9

Apparent power65.82 kVA
Real power59.24 kW
Reactive power28.69 kVAr

Three-phase power matrix59.24 kW

65.82 kVA and 28.69 kVAr.

The result gives a compact power triangle record before cable, demand or equipment worksheets are used.

The voltage value is a nominal worksheet input.
The load is treated as balanced for this calculation.
Measured unbalance and harmonics need separate records.

Reference: TPM-3
Line voltage: 400 V
Current: 140 A
Power factor: 0.64

Apparent power96.99 kVA
Real power62.08 kW
Reactive power74.53 kVAr

Three-phase power matrix62.08 kW

96.99 kVA and 74.53 kVAr.

The matrix can be calculated, but low power factor should be checked before relying on the reactive component.

The entered PF reflects the operating condition being reviewed.
The calculator does not size correction equipment.
Reactive power records should be paired with metering context.