1,200
W
1.2
kW
1,200
VA
0
VAR
1,200
W
1,200
W
120
V
10
A
12
Ω
28.8
kWh
1,200
W
1.2
kW
1,200
VA
0
VAR
1,200
W
1,200
W
120
V
10
A
12
Ω
28.8
kWh
The Electrical Power Calculator computes real, apparent, and reactive power in DC and AC circuits using multiple power formulas. Power is the rate at which electrical energy is transferred or converted, measured in watts (W). Understanding power calculations is fundamental to every aspect of electrical engineering, from designing household circuits to sizing industrial equipment and managing power grids.
For DC circuits and purely resistive AC loads, power is simply the product of voltage and current: $$P = V \cdot I$$. Two equivalent formulas derived from Ohm’s law are equally useful: $$P = \frac{V^2}{R} \quad \text{and} \quad P = I^2 R$$
In AC circuits with reactive components (inductors and capacitors), not all the power delivered is consumed as useful work. The power factor (PF) describes the ratio of real (useful) power to apparent power: $$P_{real} = V \cdot I \cdot PF$$. The apparent power $$S = V \cdot I$$ is measured in volt-amperes (VA), while the reactive power $$Q = V \cdot I \cdot \sin(\phi)$$ is measured in volt-amperes reactive (VAR), where φ is the phase angle between voltage and current.
These three quantities form the power triangle: $$S^2 = P^2 + Q^2$$. A power factor of 1.0 means all power is real (resistive load). A power factor less than 1.0 means some power oscillates between the source and reactive components without doing useful work. Utilities may charge penalties for low power factor because it increases current demand on the grid without delivering useful energy.
This calculator provides all three power forms (real, apparent, reactive), the alternative V²/R and I²R calculations for resistance-based analysis, and a kilowatt conversion for practical applications. Whether you are sizing a circuit breaker, estimating your electricity bill, or designing a power factor correction system, this tool gives you the complete power picture.
The calculator uses the fundamental power equations:
Apparent Power:
$$S = V \cdot I \quad \text{(VA)}$$
Real (Active) Power:
$$P = V \cdot I \cdot PF = S \cdot \cos\phi \quad \text{(W)}$$
Reactive Power:
$$Q = V \cdot I \cdot \sin\phi = S \cdot \sqrt{1 - PF^2} \quad \text{(VAR)}$$
Power Triangle relation:
$$S^2 = P^2 + Q^2$$
Alternative formulas (resistive loads):
$$P = \frac{V^2}{R} \quad \text{and} \quad P = I^2 R$$
For DC circuits or purely resistive AC loads, set PF = 1 and all power is real (P = S, Q = 0).
Real power (W) is the actual energy consumed by the load per second. Apparent power (VA) is what the source must deliver, including reactive components. Reactive power (VAR) oscillates between source and load, increasing current without doing useful work. The V²/R and I²R results apply to purely resistive loads and should match the real power when PF = 1. For a typical household, a 1200 W device at 120 V draws 10 A. Industrial motors with PF = 0.85 draw more current than the real power alone would suggest.
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A 2400 W electric heater at 240 V draws 10 A with PF = 1. All three power formulas (VI, V²/R, I²R) agree at 2400 W. No reactive power is present in a purely resistive load.
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A motor drawing 25 A at 480 V with PF = 0.85 consumes 10.2 kW of real power but requires 12 kVA of apparent power. The 6.3 kVAR of reactive power increases the current demand by 18% over a unity PF load.
Watts (W) measure real power—the actual energy consumed per second that does useful work (heat, light, motion). Volt-amperes (VA) measure apparent power—the total power the source must deliver, including reactive components. Volt-amperes reactive (VAR) measure the power that oscillates between source and reactive components (inductors, capacitors) without doing useful work. For DC or purely resistive loads, W = VA and VAR = 0.
Power factor is the ratio of real power to apparent power (PF = P/S), ranging from 0 to 1. A PF of 1 means all delivered power does useful work. Low PF means the circuit draws more current than necessary, increasing line losses, requiring larger conductors, and potentially incurring utility penalties. Common PF values: resistive heaters = 1.0, LED lights = 0.5–0.95, motors = 0.75–0.90, computers = 0.6–0.75 (without PFC).
Use P = V²/R when you know the voltage across a component and its resistance. Use P = I²R when you know the current through a component and its resistance. Both give the same result for the same component. V²/R is often more convenient for parallel circuits (same voltage), while I²R is more convenient for series circuits (same current).
Simply divide watts by 1000 to get kilowatts: 1 kW = 1000 W. Your electricity bill is typically in kilowatt-hours (kWh), which is power (kW) multiplied by time (hours). A 2400 W heater running for 3 hours consumes 7.2 kWh.
This calculator is for single-phase or DC circuits. For three-phase power, the formulas include an additional factor of √3: P = √3 × Vₗₗ × I × PF (for line-to-line voltage) or P = 3 × Vₚₕ × I × PF (for phase voltage). The power triangle relationship (S² = P² + Q²) remains the same.
Power factor correction (PFC) typically involves adding capacitors in parallel with inductive loads (motors, transformers) to cancel the reactive power. Active PFC circuits in electronics use switching converters to shape the input current. Improving PF from 0.7 to 0.95 reduces the apparent power demand by 26%, significantly reducing current draw, conductor losses, and utility penalties.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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