Three Phase Power Calculator

Calculate real (kW), apparent (kVA), and reactive (kVAR) power for a three-phase system in one tool. Use Balanced for a normal evenly-loaded supply, Unbalanced Current when a shared supply voltage feeds uneven single-phase loads across the three phases, or Unbalanced Voltage for fully independent per-phase values. Choose Wye (Star) or Delta to see the matching phase voltage and current alongside your line values. Unbalanced modes include a current or voltage unbalance percentage check, and results include a per-phase power breakdown, a power comparison chart, and a print view that captures the chart and results exactly as they appear on screen. Built for electricians, electrical engineers, facility managers, and students studying for licensing exams.

Pick a calculation mode, choose the connection type, enter your known values, and click Calculate.

Connection

Quick Presets

Line-to-Line Voltage (select or enter custom)

Line Current (amps)

Power Factor (0.10 – 1.00)

Phase A

Current (A)

Power Factor

Phase B

Current (A)

Power Factor

Phase C

Current (A)

Power Factor

Phase A

Voltage (V)

Current (A)

Power Factor

Phase B

Voltage (V)

Current (A)

Power Factor

Phase C

Voltage (V)

Current (A)

Power Factor

⚠️ Measurable voltage imbalance across phases is not a normal operating condition on a healthy three-phase supply. Even a few percent can meaningfully increase motor heating and reduce insulation life. Treat this as a signal to check connections and verify with a meter — not as a routine design input like current imbalance.

Results

Real Power (P)

—

Apparent Power (S)

—

kVA

Reactive Power (Q)

—

kVAR

Phase Angle (φ)

—

Formula: —

Power Triangle — P / Q / S

Real (P), reactive (Q), and apparent (S) power form the power triangle: S² = P² + Q². A lower power factor means a larger reactive-power slice for the same real-power output.

Real (P) Reactive (Q) Apparent (S)

💵 Want to know what this load costs to run? The Electrical Cost Calculator turns your kW result into an estimated daily, monthly, or annual energy bill.

🌀 Sizing the breaker or conductor for a three-phase motor? Use the Circuit Breaker Sizing Calculator (Motor Circuit mode) or the Motor Starting Current Estimator for locked-rotor/inrush behavior.

🔲 Feeding this load through a transformer? Use the Transformer Sizing Calculator to size the kVA rating from this same power result.

Results are engineering estimates. Balanced three-phase formulas, Wye/Delta phase relationships, and the current/voltage-unbalance percentage definition have been confirmed against IEEE references and the National Electrical Code (NFPA 70). Actual system behavior varies with real-world conditions. Verify with a licensed electrician before any electrical work.

How to Use the Three Phase Power Calculator

Choose a Calculation Mode

Pick Balanced for a normal evenly-loaded three-phase supply, Unbalanced Current for a shared supply voltage with uneven loading per phase, or Unbalanced Voltage for fully independent per-phase values.

Select the Connection Type

Choose Wye (Star) or Delta. This determines how line and phase voltage/current relate for the derived values shown with your results.

Enter Voltage, Current, and Power Factor

Enter a single line voltage, current, and power factor for Balanced mode, or independent values per phase (A/B/C) for either unbalanced mode. Or tap a Quick Preset.

Calculate, Review, and Print

Click Calculate to see real (kW), apparent (kVA), and reactive (kVAR) power, the phase angle, and — in unbalanced modes — the current or voltage unbalance percentage. Use Print to capture the results and chart exactly as they appear on screen.

Comprehensive Guide to Three-Phase Power

The balanced three-phase power formula

Using line quantities, real power P = √3 × line-to-line voltage × line current × power factor. Apparent power S = √3 × line-to-line voltage × line current (no power factor applied), and reactive power Q = S × sin(φ), where φ is the angle whose cosine is the power factor. These three values form the power triangle: S² = P² + Q². This relationship holds for both Wye and Delta connections when using line (not phase) voltage and current.

Wye (Star) vs. Delta

In a Wye connection, the three phase windings share a common neutral point; phase voltage is the line-to-line voltage divided by √3, while phase current equals line current. In a Delta connection, the windings form a closed loop with no neutral; phase voltage equals line-to-line voltage, while phase current equals line current divided by √3. Wye is common in commercial/industrial distribution (e.g. 277/480V), where the neutral supplies single-phase loads; Delta is common in some industrial and utility contexts and in motor winding configurations.

Power factor and the power triangle

Power factor is the ratio of real power to apparent power, and reflects how much of the supplied current does useful work versus how much is exchanged with the system's magnetic fields (reactive power) without being consumed. Resistive loads run near unity power factor; inductive loads like motors and transformers pull the power factor below 1.0, increasing the apparent power (and therefore the current) needed to deliver the same real power. A lower power factor means a wider angle φ and a larger reactive-power leg of the triangle.

Understanding current vs. voltage imbalance

Current imbalance across phases is common and usually benign in origin — it simply means single-phase loads (lighting, receptacles, small equipment) aren't perfectly evenly distributed across the three phases of an otherwise healthy, balanced supply. NEMA/IEEE guidance treats meaningful current unbalance (commonly flagged above roughly 5–10%) as worth correcting because it increases losses and uneven heating, but it is not itself evidence of a supply fault. Voltage imbalance is different in kind: it means the supply voltage itself differs measurably from phase to phase, which points to a wiring, connection, or utility-side issue rather than normal load distribution, and is generally treated as a condition to investigate and verify with a meter before relying on the circuit as designed.

When to use each mode

Use Balanced for planning and sizing work where the supply and load are both assumed even — the normal case for new circuit design. Use Unbalanced Current when auditing an existing panel or feeder where you've measured different currents per phase but the supply voltage itself is sound. Use Unbalanced Voltage only after a meter has confirmed the supply voltage itself differs by phase — most often during troubleshooting, not routine design.

Worked Examples

Three real-world scenarios, one per mode. Click "Load This Example" to run it in the calculator above.

1. Balanced — 480V Industrial Motor Load

A balanced 480V three-phase Wye supply feeds a motor load drawing 45A per line at 0.90 power factor.

S = √3 × 480V × 45A ÷ 1000 = 37.4 kVA. P = 37.4 × 0.90 = 33.6 kW. Q = 37.4 × sin(25.8°) = 16.3 kVAR.

2. Unbalanced Current — Uneven Panel Loading, 480V

A balanced 480V supply feeds a panel with uneven single-phase loads: Phase A 40A/0.90 PF, Phase B 52A/0.88 PF, Phase C 35A/0.91 PF.

P_total = P1+P2+P3 ≈ 30.0 kW. Current unbalance = (52 − 42.3) / 42.3 × 100 ≈ 22.9% — well above the 5–10% caution range.

3. Unbalanced Voltage — Sagging Phase C

A meter reads 475V, 480V, and 460V line-to-line across the three phases of a nominally 480V Wye supply, each carrying 40A at 0.90 PF.

Voltage unbalance = (480 − 471.7) / 471.7 × 100 ≈ 1.8% — a supply condition worth investigating, not a routine design input.

Quick Reference — Voltages & Typical Power Factors

Common North American three-phase line-to-line voltages, and typical power factor ranges by load type — starting points only, always prefer a nameplate or measured value.

Common Line Voltage	Typical Context
208 V	Commercial buildings (Wye, 120/208V)
240 V	Small commercial (Delta, 120/240V)
480 V	Industrial motors and equipment (Wye, 277/480V)
600 V	Heavy industrial, some Canadian standard

Load Type	Typical Power Factor
Resistive heating / incandescent lighting	≈1.00
Fully loaded induction motor	0.85 – 0.90
Lightly loaded induction motor	0.60 – 0.80
Mixed industrial/commercial (unknown)	0.85 (common placeholder)

Frequently Asked Questions

What is the three-phase power formula?

For a balanced three-phase system using line quantities: real power P (kW) = √3 × line-to-line voltage × line current × power factor ÷ 1000. Apparent power S (kVA) = √3 × line-to-line voltage × line current ÷ 1000, and reactive power Q (kVAR) = S × sin(φ), where φ is the angle whose cosine is the power factor. Together P, Q, and S form the power triangle, with S² = P² + Q².

What is the difference between Wye (Star) and Delta connections?

In a Wye (Star) connection, phase voltage equals line-to-line voltage divided by √3, while phase current equals line current. In a Delta connection, phase voltage equals line-to-line voltage, while phase current equals line current divided by √3. The total power formula using line quantities is identical for both configurations — the difference only affects the internal phase (winding) voltage and current values shown alongside your results.

What is the difference between unbalanced current and unbalanced voltage, and why does it matter?

Current unbalance happens when a still-balanced three-phase supply feeds uneven single-phase loads across its phases — a common, normal condition on branch-circuit panels that this calculator's Unbalanced Current mode models directly. Voltage unbalance means the supply itself is delivering measurably different voltages phase to phase, which is not a normal operating condition — it usually points to a loose connection, an overloaded neutral, or a utility-side supply problem, and is generally treated as a fault to investigate and verify with a meter rather than a routine design input.

What power factor should I use if I don't know the exact value?

Purely resistive loads (heating elements, incandescent lighting) run near 1.0. General-purpose induction motors commonly fall between 0.80 and 0.90 depending on load. Lightly loaded motors and older equipment can run lower. When the exact nameplate or measured power factor isn't available, 0.85 is a common placeholder for mixed industrial/commercial loads, but a nameplate or measured value is always more accurate.

Are these results confirmed against a recognized standard?

Yes. The balanced and per-phase power formulas, the Wye/Delta phase-voltage and phase-current relationships, and the current/voltage-unbalance percentage definition used in this calculator have been confirmed against IEEE references and the National Electrical Code (NFPA 70). Results remain engineering estimates for reference and planning — see the disclaimer below for what is and isn't modeled.

Three Phase Power Calculator

How to Use the Three Phase Power Calculator

Comprehensive Guide to Three-Phase Power

The balanced three-phase power formula

Wye (Star) vs. Delta

Power factor and the power triangle

Understanding current vs. voltage imbalance

When to use each mode

Worked Examples

Quick Reference — Voltages & Typical Power Factors

Frequently Asked Questions

What is the three-phase power formula?

What is the difference between Wye (Star) and Delta connections?

What is the difference between unbalanced current and unbalanced voltage, and why does it matter?

What power factor should I use if I don't know the exact value?

Are these results confirmed against a recognized standard?

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