The electrical power calculator above derives power from the electrical quantities you can measure, rather than pricing electricity you have already used. Give it a voltage and a current, or a voltage and a resistance, or a current and a resistance, and it returns real power together with the apparent and reactive power that go with it. It covers DC, single-phase AC and three-phase AC, and the three-phase case is the one most calculators either omit or get subtly wrong.
Arb Digital builds free tools that pick one job and do it completely. This one solves P = VI and every rearrangement of it, including the power-factor and three-phase forms. It is deliberately not a billing tool: the boundary against the site's existing electricity pages is that this derives power from circuit quantities, while a bill calculator prices consumption you already know and a converter simply rescales watts into other units.
What This Electrical Power Calculator Does
It computes real power in watts — the figure a wattmeter shows and the figure that turns into heat, motion or light. Alongside it the grid gives apparent power in volt-amperes, reactive power in volt-amperes reactive, the equivalent mechanical horsepower, and the energy consumed over a run time you specify. Those five numbers between them answer nearly every practical question about a load.
The supply-type selector matters more than it looks. In DC there is no phase angle, so real and apparent power are identical and power factor does not exist. In single-phase AC, real power is voltage times current times power factor. In three-phase AC with a line-to-line voltage, the same product picks up a factor of the square root of three. Choosing the wrong one produces an answer that is out by 73 per cent, which is large enough to matter and small enough to look plausible.
The three input routes let you work from whatever you have. Voltage and current is the direct measurement route. Voltage and resistance suits a known heating element. Current and resistance suits a measured current through a known conductor, and is the form used to calculate losses in a cable run. The resistive routes force power factor to 1 because a pure resistance has no phase shift by definition.
How to Use It
- Choose the supply type. DC, single-phase or three-phase. If you are looking at a nameplate that quotes a line-to-line voltage such as 400 V or 480 V and three conductors, you want three-phase.
- Choose what you know. The tool reads only the fields relevant to that route, so you never have to invent a number you do not have.
- Enter the power factor if the load is not resistive. Motors, transformers, fluorescent ballasts and switched-mode supplies all draw current out of phase with voltage, and ignoring that overstates real power.
- Read apparent power as well as real power. Cables, breakers and transformers are sized on apparent power, because they carry the full current regardless of its phase.
- Set a run time for the energy figure. Watts describe a rate; kilowatt-hours describe a quantity. The energy converter handles joules, BTU and other units if you need them.
The Formula: How Electrical Power Is Calculated
For DC, power is simply P = VI. Substituting Ohm's law gives the two other forms, P = I2R and P = V2 ÷ R. OpenStax University Physics Volume 2, section 9.5 on electrical energy and power, states that the power gained or lost by any device has the form P = IV and that the power dissipated by a resistor has the form I squared R, equal to V squared over R.
For single-phase AC the real power becomes P = VI cos φ, where cos φ is the power factor, using root-mean-square voltage and current. Apparent power S = VI, and reactive power Q = √(S2 − P2). Those three form a right triangle, which is why they are conventionally drawn as one.
For three-phase AC quoted line-to-line, P = √3 × VLL × Iline × cos φ. Work the default values: √3 × 400 × 20 = 13,856 VA of apparent power, times a power factor of 0.85 gives 11,778 W of real power, and the reactive component is √(13,8562 − 11,7782) = 7,299 VAR. The same load on a wattmeter would read 11.78 kW while the supply cable carries the current implied by 13.86 kVA.
Where the Square Root of Three Comes From
This is the step that trips people up, and it is worth understanding rather than memorising. A three-phase supply has three conductors carrying voltages 120 degrees apart in phase. The voltage measured between any two lines is not twice the voltage from line to neutral — vector addition of two waveforms 120 degrees apart gives a magnitude of √3 times the phase voltage. A 400 V line-to-line system is a 230 V line-to-neutral system, because 230 × √3 is very close to 400.
Total power is three times the per-phase power, which is Vphase × Iphase × cos φ. Substituting Vphase = VLL ÷ √3 turns three into √3, and the familiar formula falls out. If your voltage figure is line-to-neutral rather than line-to-line, use the single-phase formula and multiply by three instead — mixing the two conventions is the most common source of three-phase errors.
Real, Apparent and Reactive Power
Real power in watts is the part that does work. Reactive power in VAR is the part that flows back and forth between the source and the load's magnetic or electric fields, doing no net work but occupying capacity in every cable and transformer on the way. Apparent power in volt-amperes is the vector sum of the two, and it is what determines the current that actually flows. All three share the same dimensions and, in SI terms, the same coherent derived unit; the SI Brochure published by the BIPM defines the watt as the coherent unit of power, with the volt-ampere and the var used by convention to signal which component is meant.
The practical consequence is that a load with a poor power factor draws more current for the same useful output. At a power factor of 0.85, the default here, the supply carries about 18 per cent more current than a purely resistive load of the same wattage would need. That extra current heats cables, consumes transformer capacity and, in commercial tariffs, is frequently billed for separately. This is why power-factor correction capacitors exist: they supply the reactive component locally so the upstream network does not have to.
Note that a wattmeter reads real power and an ammeter reads the current corresponding to apparent power. If you multiply an ammeter reading by a voltmeter reading on an AC circuit, you get apparent power, not watts. The gap between those two numbers is precisely the power factor.
Input Power, Output Power and Nameplate Ratings
A motor nameplate that says 11 kW is almost always quoting mechanical output at the shaft, not electrical input at the terminals. The two differ by the efficiency of the machine, which for an industrial induction motor is typically somewhere between 85 and 95 per cent. Electrical input is mechanical output divided by efficiency, so an 11 kW motor at 90 per cent efficiency draws around 12.2 kW from the supply, and that larger figure is what this calculator returns when you feed it measured voltage and current.
Efficiency and power factor are frequently confused because both are dimensionless numbers between zero and one that appear on the same nameplate. They describe different losses. Power factor describes how much of the current does useful work; efficiency describes how much of the real power that reaches the load emerges as the output you wanted. A motor can have an excellent power factor and poor efficiency, or the reverse, and correcting one does nothing for the other.
That distinction matters when reading a result here. The horsepower figure in the grid is the electrical power expressed in mechanical units, not the shaft output. To get shaft output, multiply by the efficiency. To go the other way from a nameplate rating to an expected supply current, divide the rated output by efficiency, then by power factor, then by the voltage and by the square root of three for a three-phase machine.
Where the Power Actually Goes
Resistive loss in a conductor is one of the few places the I squared R form of the equation is used directly rather than as a rearrangement. Because loss scales with the square of current, halving the current for the same delivered power cuts cable losses to a quarter. That single relationship is why transmission networks run at high voltage and low current, and why a long low-voltage run needs disproportionately thick cable.
You can see this on the current-and-resistance route in the tool. Enter the current flowing in a cable and the cable resistance, and the result is the power being dissipated as heat in the cable itself — energy that leaves the system as warm copper rather than reaching the load. On a long run this is not a rounding error. It is also, incidentally, the mechanism behind every electric heater, where the same physics is the intended outcome rather than a loss.
How This Differs From the Site's Other Electricity Tools
Arb Digital already publishes tools that touch electricity, and each does a different job. The power converter rescales an existing power figure between watts, kilowatts, horsepower and BTU per hour; it derives nothing. The electricity bill calculator takes consumption you already know and applies a tariff to it, which is a pricing question rather than a physics one. This page sits before both of them: it derives the power figure in the first place from voltage, current, resistance and phase.
The natural sequence is to work out power here, convert units with the watts to horsepower converter if you need mechanical equivalents, and only then move to consumption and cost. For sizing work, the breaker size calculator uses the current implied by apparent power, and the resistance converter handles ohm-scale unit changes. For off-grid design the solar panel calculator and the battery life calculator take the energy figure from this page as their starting input.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Mixing line-to-line and line-to-neutral voltages — using a phase voltage in the three-phase formula understates power by a factor of the square root of three.
- Assuming power factor is 1 — motors, transformers and electronic supplies draw current out of phase, so real power is lower than volts times amps.
- Sizing cables on watts — conductors carry the full current, which corresponds to apparent power, not to the real power a meter records.
- Using peak instead of RMS values — every AC formula here expects root-mean-square voltage and current, and a peak reading is higher by roughly 41 per cent for a sine wave.
- Applying power factor to a DC circuit — DC has no phase angle, so the concept does not exist and the tool ignores it in DC mode.
Related Free Tools From Arb Digital
Rescale results with the power converter, the energy converter or the watts to horsepower converter, and handle component values with the resistance converter. For downstream questions, the electricity bill calculator prices consumption, the breaker size calculator covers protection, and the solar panel calculator and battery life calculator cover generation and storage. The full free online tools hub lists everything Arb Digital publishes.
Frequently Asked Questions
Watts measure real power, the part that does useful work. Volt-amperes measure apparent power, the product of voltage and current regardless of phase. They are equal only when the power factor is 1, and the ratio between them is the power factor itself.
Because the line-to-line voltage of a three-phase supply is the square root of three times the line-to-neutral voltage, a consequence of adding two waveforms 120 degrees apart. Total power is three times per-phase power, and substituting the phase voltage turns that three into a square root of three.
Use 1 only for genuinely resistive loads such as heaters and incandescent lamps. Motors and transformers are typically between 0.7 and 0.9 at rated load and lower at part load, and the equipment nameplate usually states the figure the manufacturer measured.
Root-mean-square. Every AC quantity in these formulas is an RMS value, and mains voltages quoted as 120, 230 or 400 volts are already RMS. A peak value is about 1.41 times larger for a sine wave and will overstate the answer if entered directly.
No. It derives power and energy from circuit quantities. Pricing that consumption against a tariff is a separate job handled by the electricity bill calculator, and this page deliberately stays on the physics side of that line.
Because a purely resistive load has no phase shift, so all the apparent power is real power and nothing is exchanged with a magnetic or electric field. The resistance input routes force this condition, and DC has no reactive component at all.
The power converter rescales a power figure between watts, kilowatts, horsepower and other units. This calculator derives a power figure that was never entered, from voltage, current, resistance and phase relationships. One changes units, the other computes a quantity.
This tool is provided for educational and estimating use. It is not a substitute for design calculations to an applicable wiring standard, and nothing on this page is electrical installation or safety guidance.
