Electrical

Power Calculator

Electrical power formulas. Fast, accurate, and completely free.

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Real Power

2,300 W

P = V × I

⚡ Power Conversions

Kilowatts (kW)

2.300

Horsepower (HP)

3.08

BTU/hr

7,849

kWh per day (24h)

55.20

📊 AC Power Components

Apparent Power (VA)

2,300

Reactive Power (VAR)

0.00

Mathematical Formula

P_{DC} = V \times I \quad | \quad P_{1\phi} = V \times I \times PF \quad | \quad P_{3\phi} = \sqrt{3} \times V \times I \times PF

P = Real Power in Watts (W)

V = Voltage in Volts (V)

I = Current in Amperes (A)

PF = Power Factor (cos φ, 0 to 1)

S = Apparent Power = V × I (VA)

Q = Reactive Power = S × sin(arccos(PF)) (VAR)

How to Use this Calculator

Select the circuit type — DC, Single-Phase AC, or Three-Phase AC.
Enter the Voltage in Volts and Current in Amperes.
For AC circuits, set the Power Factor (1.0 = purely resistive, 0.8 = typical motor).
View real power in multiple units (W, kW, HP, BTU/hr) and AC power components (VA, VAR).

Understanding Electrical Power

Electrical power is the rate at which electrical energy is transferred by an electric circuit. Measured in Watts (W), it's one of the most fundamental quantities in electrical engineering. Whether you're sizing a generator, designing a power distribution system, or simply estimating your electricity consumption, understanding power calculations is essential.

DC Power

In Direct Current (DC) circuits, power calculation is straightforward: P = V × I. A 12V battery supplying 5A delivers exactly 60W of power. DC power is purely real — there are no reactive components. Applications include battery systems, solar panels (before the inverter), automotive electronics, and LED drivers.

Single-Phase AC Power

Alternating Current (AC) power is more complex due to the sinusoidal nature of the waveform. In single-phase AC circuits, the formula is P = V × I × PF, where PF is the Power Factor. The power factor represents the cosine of the phase angle between the voltage and current waveforms. A power factor of 1.0 means voltage and current are perfectly in phase (purely resistive load), while a lower power factor indicates reactive components (inductive or capacitive loads).

Three-Phase AC Power

Three-phase power is used in industrial and commercial settings for its efficiency. The formula P = √3 × V × I × PF (using line voltage and line current) accounts for the 120-degree phase separation between the three phases. Three-phase systems deliver constant power (unlike single-phase which pulsates), making them ideal for motors and heavy machinery.

The Power Triangle: Real, Apparent & Reactive

In AC circuits, three types of power exist. Real Power (P) in Watts is the actual power consumed and converted to useful work or heat. Apparent Power (S) in Volt-Amps (VA) is the product of RMS voltage and current — it represents the total power flowing in the circuit. Reactive Power (Q) in VAR is the power oscillating between the source and reactive components (inductors, capacitors); it performs no useful work but is necessary for maintaining magnetic and electric fields.

These three form a right triangle: S² = P² + Q². The ratio P/S equals the power factor. Improving power factor (closer to 1.0) reduces wasted reactive power, lowers current draw, and decreases energy losses. Many industrial facilities install power factor correction capacitors to achieve this.

Power Unit Conversions

Common conversions include: 1 kW = 1,000 W, 1 HP (mechanical) = 745.7 W, and 1 W = 3.412 BTU/hr. Understanding these conversions is crucial when specifying motors (rated in HP), generators (rated in kVA), and HVAC systems (rated in BTU/hr).

Frequently Asked Questions (FAQ)

What is power factor and why does it matter?

Power factor is the ratio of real power (W) to apparent power (VA). A low power factor means more current is required to deliver the same real power, leading to higher energy losses, larger cables, and utility penalties. Most utilities charge commercial customers extra for power factors below 0.9.

What power factor should I use for common loads?

Incandescent bulbs and heaters: PF = 1.0. LED lights: PF = 0.5–0.95. Electric motors: PF = 0.7–0.9. Computer power supplies: PF = 0.6–0.99. Air conditioners: PF = 0.8–0.95.

How is Three-Phase power different from Single-Phase?

Three-phase power uses three AC waveforms offset by 120°, delivering √3 (≈1.732) times more power than single-phase for the same voltage and current. It provides constant power delivery, is more efficient for transmission, and is essential for large motors and industrial equipment.

What is the difference between kW and kVA?

kW (kilowatt) measures real power that does actual work. kVA (kilovolt-amp) measures apparent power, which is the vector sum of real and reactive power. kW = kVA × Power Factor. Generators and UPS systems are rated in kVA because they must handle both real and reactive loads.

How do I convert Watts to Horsepower?

Divide Watts by 745.7 to get mechanical Horsepower. For example, a 1,500W motor is approximately 2.01 HP. Note that motor nameplate HP refers to output shaft power, while input electrical power is higher due to motor efficiency losses (typically 80-95% efficient).

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