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Power Calculator: AC Power Triangle, Mechanical Power and a Proper Unit Converter, All Together

Most power calculators pick a lane, either pure electrical or pure mechanical or just a unit converter and leave you jumping between three different sites for one project. This power calculator covers all three. It’s electrical side works as a genuine power triangle calculator, real power, reactive power and apparent power tied together by power factor, solve for whichever one your missing from any two others, with a single-phase/three-phase toggle that gets the √3 factor right, leaving it out is a surprisingly common mistake and it understates three-phase power by more then forty percent. As a proper three-phase power calculator, the geometry gets drawn out too, so the relationship between the three power values is something you can actually see, not just something the formula asserts. Mechanical mode covers the other side entirely, work over time, force times velocity or torque times angular velocity from RPM. The unit converter then keeps units that get lumped together elsewhere genuinely apart, mechanical horsepower and metric PS differ by about ten watts and that difference matters more then people think. Two extras tie the whole thing to something practical, power and duration give you energy in kWh, the number that actually shows up on a bill, and an efficiency chain multiplies successive stages, motor, gearbox, belt, together to show what actually comes out the other end after real losses.

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How to Use

This tool has three tabs: Electrical (AC), Mechanical and Unit Converter.

Using Electrical (AC) mode

• Choose your System: Single-phase or Three-phase (√3). A small hint appears explaining exactly which formula applies to your choice.
• Fill in any two or three of Voltage (V), Current (A), Power Factor (cosφ), and Real Power P (W) and leave whatever you want solved blank. The power factor field already has a default value in it, but treat it as editable, not fixed, since your actual load’s power factor is what matters here.
• Tap Calculate. You’ll get real, reactive and apparent power together, plus a drawn power triangle showing how they relate geometrically.

Using Mechanical mode

• Switch to the Mechanical tab and pick your Mechanical Formula: P = Work ÷ time, P = Force × velocity, or P = Torque × angular velocity.
• Fill in whichever fields show up for your chosen formula, Work (J) and Time (s) or Force (N) and Velocity (m/s) or Torque (N·m) and Speed (RPM).
• Tap Calculate to get mechanical power in watts.

Using Unit Converter mode

• Switch to the Unit Converter tab. Enter your Value and pick it’s From Unit, watts, kW, MW, mechanical hp, metric PS, BTU/hr, ft-lb/s or kcal/hr, each with it’s own genuine, distinct constant.
• Want your own unit? Type a Custom Unit Name and how many watts it equals, then tap Add, it’ll show up right alongside the built-in units from then on.
• Tap Calculate to convert.

Adding the shared extras (work with any of the three tabs)

• Under Energy over Time, enter a Duration (hours) if you want to know the energy consumed, this uses whatever power value you just calculated and gives you the result in kWh, the number your electricity bill actually cares about. Leave it blank to skip.
• Under Efficiency Chain, tap Add Stage for each stage of loss in your drivetrain, motor efficiency, then gearbox, then belt, whatever applies and enter each one’s efficiency percentage. This multiplies through your calculated power to show what actually reaches the output and the cumulative loss across the whole chain.
• Tap Calculate Power once everything’s filled in.

Exporting your result

• Use Print / PDF for a clean printable copy or Copy to paste the numbers elsewhere.

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Key Features

• AC power triangle, real, reactive, and apparent power solved from any two known values, with the geometric relationship actually drawn out
• Correct three-phase √3 handling, a toggle that applies the right factor instead of leaving it out, which is a genuinely common and costly mistake
• Mechanical power in three forms, work over time, force times velocity, or torque times angular velocity from RPM
• Distinct, exact power unit constants, mechanical horsepower and metric PS kept genuinely separate, along with BTU/hr, ft-lb/s and kcal/hr
• Unlimited custom power units, defined against watts and usable right alongside the built-in list
• Energy-over-time (kWh), turning your calculated power straight into a billing-relevant figure
• Multi-stage efficiency chain, multiplying successive losses, motor, gearbox, belt, to show real output power and cumulative loss

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Formula / Logic Used

AC Power (Single-Phase and Three-Phase)

$$S = V \times I \ \text{(1φ)}, \qquad S = \sqrt{3} \times V_L \times I_L \ \text{(3φ)}$$

$$P = S \times \cos\phi, \qquad Q = S \times \sin\phi, \qquad P^2 + Q^2 = S^2$$

Leaving out the √3 factor on a three-phase system and using the plain single-phase formula understates real power by more then forty percent, which is exactly the kind of mistake this toggle exists to prevent.

Mechanical Power

$$P = \frac{W}{t}, \qquad P = F \times v, \qquad P = T \times \omega, \qquad \omega = \frac{2\pi N}{60}$$

Power Unit Constants

$$1\ Mechanical\ HP = 745.699872\ W, \qquad 1\ Metric\ PS = 735.49875\ W$$

BTU/hr, ft-lb/s and kcal/hr each get there own exact conversion factor too, none of them treated as roughly-equal stand-ins for each other.

Energy over Time

$$Energy\ (kWh) = \frac{Power\ (W)}{1000} \times Hours$$

Efficiency Chain

$$P_{output} = P_{input} \times \prod_i \eta_i$$

Efficiencies multiply, not add, which is exactly why three individually decent stages, say 90%, 92% and 95%, can still combine into a noticeably lower overall figure, about 79% here, then any single stage on it’s own would suggest.

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Who Should Use This Tool

Electrical and mechanical engineers and engineering students, who need to move between electrical power, mechanical power and plain unit conversion without switching between three separate tools. Also useful for anyone sizing a drivetrain who wants to see real output power after every stage of loss or checking the actual energy cost of running something for a set number of hours.

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Frequently Asked Questions (FAQs)

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Related Tools

• Ohm’s Law Calculator – for basic voltage, current, and resistance relationships feeding into this power calculation
• Engineering Unit Calculator – for broader unit conversion needs beyond power
• Motor-to-Transformer Sizing Calculator – size the transformer supplying the power calculated here