Three-Phase Power Calculator
Calculate real (kW), apparent (kVA), and reactive (kVAR) power for balanced three-phase loads from line voltage, line current, and power factor. Covers both wye and delta configurations.
How to Use
- Enter line-to-line voltage (e.g., 208V, 400V, 480V industrial).
- Enter line current from the motor nameplate or clamp meter.
- Enter power factor (motors typically 0.8–0.9).
- See the three-phase waveforms shifted 120° apart on the visualization.
Show Work
Formulas
History of Three-Phase Power
Three-phase AC was pioneered independently by Nikola Tesla, Galileo Ferraris, and Mikhail Dolivo-Dobrovolsky in the late 1880s. Tesla patented his polyphase induction motor in 1888; Dolivo-Dobrovolsky, working for AEG in Germany, built the first practical three-phase system and, in 1891, demonstrated long-distance transmission from Lauffen to Frankfurt — 175 km over three-phase lines at 15 kV — cementing the technology's viability at scale.
The key insight is that three sinusoidal voltages offset by 120° sum to zero at every instant, so a balanced three-phase load consumes constant power rather than the pulsing 120 Hz power of a single-phase load. That constant-power property is what makes three-phase motors self-starting, smoother, and more efficient than single-phase equivalents — and why virtually every industrial motor above a few horsepower is three-phase.
Two winding topologies dominate: wye (star) connects one end of each winding to a common neutral, with phase voltage = VLL / √3; delta connects the windings end-to-end in a triangle, with phase current = IL / √3. The √3 factor is just the geometry of adding vectors 120° apart. Its practical gift to engineers: the total-power formula P = √3 × VLL × IL × PF works for both topologies, as long as you plug in line measurements.
About This Calculator
Enter line-to-line voltage (e.g. 208V, 400V, 480V), line current from a motor nameplate or clamp meter, and the load's power factor. The calculator returns total three-phase real power (kW), apparent power (kVA), reactive power (kVAR), and per-phase real power. The visualization plots the three phase voltages offset by 120° so you can see why instantaneous total power is constant.
Balanced-load assumption applies — for grossly unbalanced systems (a large single-phase load on one leg), you need per-phase voltmeter and ammeter readings and should sum real power across phases individually. Everything runs client-side; no nameplate data leaves your browser.
About the Three-Phase Power Calculator
The Three-Phase Power Calculator is a free tool for electronics and circuit design. It runs right in your web browser, so there is nothing to download. Calculate real (kW), apparent (kVA), and reactive (kVAR) power for balanced three-phase loads from line voltage, line current, and power factor. Covers both wye and delta configurations.
How it works
Type your numbers into the boxes. The answer shows up right away — you do not have to press a button. If you change a number, the answer changes too. So you can try different numbers and watch what happens, or check an answer you worked out yourself. Just make sure each box has the right kind of number in it.
Want the deeper story? The Knowledge Base explains the ideas behind the tools in more detail.
Frequently Asked Questions
What is the √3 factor?
It's the ratio between line-to-line and line-to-neutral voltage in a balanced 3-phase system. P_total = √3 × V_LL × I_L × PF (three phases combined). Without this factor you'd be off by ~73%.
Wye vs. delta — does the formula change?
No, as long as you use line-to-line voltage and line current. P = √3 × V_LL × I_L × PF works for both. The internal phase voltages and phase currents differ, but the line measurements give you the same total power.
How does this differ from single-phase?
Single-phase: P = V × I × PF. Three-phase: P = √3 × V_LL × I_L × PF. Three-phase has more uniform power delivery (the three phases sum to constant power instead of pulsing at 2× the line frequency), which is why motors run smoother on 3-phase.
What voltages are common?
208V (US wye, 120/208V), 230/400V (European), 480V (US industrial), 600V (Canadian industrial), 11kV/33kV/132kV (transmission). Higher voltage reduces current and wire losses at the same power level.
How do I use the Three-Phase Power Calculator?
Just type your numbers. The answer shows up right away — there is no button to press. Change anything and it updates by itself.
Is it free? Does it work without internet?
Yes to both. It is free with no sign-up, and once the page has loaded it keeps working even with no internet.
Where does my data go?
Nowhere — every calculation runs on your own device. Nothing you enter is uploaded, logged, or stored.
Common Use Cases
Motor Sizing
A 10HP motor at 480V 3-phase pulls ~14A nameplate at 0.85 PF → 7.5kW, 8.8kVA. Size breakers + wiring for the line current.
Industrial Panel Design
Total load kVA determines transformer and panel sizing. Calculate each feeder individually and sum VA (not W) for the main.
HVAC Compressor Selection
Rooftop unit nameplate: 480V 3ph, 25A, PF 0.9 → 18.7kW, 20.8kVA. Feeder ampacity must cover starting inrush (typically 6× running current).
Generator Rating
A 100kVA generator at 0.8 PF delivers 80kW. Loading to full nameplate kVA requires strictly resistive load.
Data Center Distribution
Rack PDUs rated in kVA; IT equipment consumes kW. PF near 1.0 for modern switched-mode supplies means kVA ≈ kW.
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