Understanding Real, Apparent and Reactive Power in a Three-Phase System
A three-phase power calculator works out how much power flows in a balanced three-phase circuit, the kind used for industrial motors, large HVAC plant, and most commercial distribution. Three-phase supplies deliver power more smoothly and use conductor material more efficiently than single-phase, which is why factories and big buildings rely on them. This tool takes the line voltage, the line current, and the power factor and returns the three quantities engineers care about: real power in watts, apparent power in volt-amperes, and reactive power in volt-amperes reactive.
The governing equations all share the √3 factor that comes from the geometry of three phases spaced 120 degrees apart. Real power is P = √3 × V_L × I × cos φ, apparent power is S = √3 × V_L × I, and reactive power is Q = √3 × V_L × I × sin φ. Power factor is the ratio cos φ = P ÷ S, and the three powers form a right triangle where S is the hypotenuse, P is the base and Q is the height. The calculator also handles the connection detail that trips people up: in a star (wye) connection the line-to-line voltage is √3 times the phase voltage, so 230 volts per phase gives 398 volts line to line, while in a delta connection line and phase voltage are equal.
A concrete example shows the flow. Feed a balanced load 400 volts line to line at 10 amps with a power factor of 0.8. Apparent power is √3 × 400 × 10 = 6928 VA, or 6.93 kVA. Real power is that times 0.8, giving 5543 watts, about 5.54 kW, which is the useful power that does work. Reactive power is √3 × 400 × 10 × sin(cos⁻¹ 0.8) = 4157 VAR, the power that sloshes back and forth energising the magnetic fields of motors without doing net work. The power triangle drawn on screen makes the relationship visual, and you can solve backwards too — give the calculator the kilowatts, voltage and power factor and it returns the current the load will draw.
These numbers matter in daily engineering. A plant electrician sizing a cable and breaker for a 5.5 kW motor needs the current, which depends on voltage and power factor, not just the kilowatt rating on the nameplate. A facilities manager comparing a 6.93 kVA transformer against a 5.54 kW load checks there is enough apparent-power headroom. An energy auditor looking at a poor 0.8 power factor calculates the reactive burden and decides whether capacitor correction is worthwhile. The built-in kilowatt-to-horsepower conversion, using 1 HP = 746 watts, helps when a motor is rated in one unit and specified in the other.
The model assumes a balanced load, meaning the three phases carry equal current, which is the normal design case; genuinely unbalanced loads need per-phase analysis this tool does not attempt. Power factor is strictly between 0 and 1, and the calculator rejects anything outside that range rather than returning a meaningless result, because a value above 1 or below 0 is not physically possible for this model. A common error is confusing line and phase voltage, so use the built-in converter and note whether your figure is line-to-line or line-to-neutral before entering it; on a 400 volt line-to-line system each phase sits at only 230 volts, and swapping the two throws every power figure out by the √3 factor. Another slip is reading a motor nameplate power factor for a lightly loaded motor, whose real power factor at part load is often much lower, which understates the current the supply must actually carry. Every result is an engineering estimate; any wiring work must follow local code and be done by a qualified electrician. All calculation happens locally in your browser and nothing you type is uploaded or stored.
