Authoritative Data Source & Methodology
- IEEE Std 1459-2010 — Definitions for the Measurement of Electric Power Quantities Under Sinusoidal, Nonsinusoidal, Balanced, or Unbalanced Conditions. IEEE
- IEC 60038: IEC Standard Voltages — RMS definitions and nominal AC voltages. IEC
- NIST SP 811 — Guide for the Use of the International System of Units (SI). NIST
Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.
The Formula Explained
$ \text{AC 1-phase:}\quad P = V_{\mathrm{rms}} \cdot I_{\mathrm{rms}} \cdot \mathrm{PF} $
$ \text{AC 3-phase (LL):}\quad P = \sqrt{3}\, V_{\mathrm{LL}} \cdot I_{\mathrm{rms}} \cdot \mathrm{PF} $
$ \text{From resistance:}\quad P = \dfrac{V^2}{R} $
Glossary of Variables
| Symbol | Meaning | Units |
|---|---|---|
| P | Real (active) power | W (watts), kW |
| V | Voltage (RMS for AC) | V (volts) |
| I | Current (RMS for AC) | A (amperes) |
| PF | Power factor (cos φ) | 0–1 |
| R | Resistance | Ω (ohms) |
| VLL | Line-to-line voltage (3-phase) | V |
How It Works: A Step-by-Step Example
Scenario: AC single-phase, $V=120\,$V, $I=2.0\,$A, $\mathrm{PF}=0.95$.
- Identify formula: $P = V I \mathrm{PF}$ (AC 1-phase).
- Compute: $P = 120 \times 2.0 \times 0.95 = 228\ \mathrm{W}$.
- Convert to kW: $228\ \mathrm{W} = 0.228\ \mathrm{kW}$.
- If you only had $R$ and $V$, use $P=V^2/R$ instead.
Frequently Asked Questions
Do I need power factor for DC?
No. DC uses $P=VI$ and PF is implicitly 1.
What PF should I use for typical motors?
Small induction motors often range 0.7–0.9. Use the nameplate or datasheet when available.
For three-phase, which voltage should I enter?
Enter line-to-line RMS voltage (e.g., 400 V in EU, 480 V in US industrial). Formula uses $\sqrt{3}\,V_{LL}I\mathrm{PF}$.
Can I calculate watts from resistance?
Yes, for resistive loads: $P=V^2/R$. For non-resistive AC loads, prefer $VI\mathrm{PF}$.
What’s the difference between W and VA?
VA is apparent power ($S$), while W is real power ($P$). Relationship: $P = S \cdot \mathrm{PF}$.
Does this assume balanced three-phase loads?
Yes. For unbalanced systems or harmonics, refer to IEEE Std 1459-2010 measurement definitions.
How accurate is the result?
For standard sinusoidal systems and correct inputs, results are engineering-grade. Always verify against equipment nameplates and standards.
Tool developed by Ugo Candido. Content reviewed by the CalcDomain Engineering Editorial Board.
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