Formula & Calculator
Power in kW (Single Phase)
Calculates real power in kilowatts for a single-phase AC circuit from voltage, current, and power factor.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| P | Real power (active power) | kW |
| V | RMS voltage (line-to-neutral) | V |
| I | RMS current | A |
| pf | Power factor = cos θ (phase angle between V and I) | dimensionless |
| θ | Phase angle between voltage and current | ° |
What it means
The real power in a single‑phase AC circuit is given by P(kW) = (V × I × cosθ) / 1000, where V is RMS voltage, I is RMS current, and cosθ is the power factor. This formula calculates the actual power consumed, which is the product of apparent power and power factor. It is used for sizing fuses, wires, and circuit breakers. Example: A 230V, 10A resistive heater (cosθ=1) draws P = 230 × 10 × 1 / 1000 = 2.3 kW. If the load is a motor with power factor 0.8, the real power is 230×10×0.8/1000 = 1.84 kW, though the current remains 10A. This is why power factor correction is important to reduce current and losses.
Worked example
Single‑Phase Power – Practical Example
Real‑World| Parameter | Value |
|---|---|
| V | 230 V |
| I | 10 A |
| cos θ | 0.85 |
| Formula | P(kW) = (V × I × cos θ) / 1000 |
Common mistakes
Watch for unit mismatches (W vs kW, single- vs three-phase) and remember to include power factor or efficiency where the formula requires it.Applications
Power in kW (single‑phase): P(kW) = (V × I × cosθ)/1000 calculates real power for single‑phase AC circuits. This is used to determine the active power consumption of single‑phase loads, such as lighting and small appliances. Engineers use it for load calculations, circuit design, and energy auditing.
- Residential and commercial load calculation
- Circuit breaker and cable sizing for single‑phase
- Energy consumption estimation
- Power factor analysis and correction
- Educational understanding of single‑phase power