Authoritative Content Ecosystem
Data Source and Methodology
Authoritative Source: IEEE Standard 1459-2010 — Definitions for the Measurement of Electric Power Quantities Under Sinusoidal, Nonsinusoidal, Balanced, or Unbalanced Conditions. IEEE, 2010. View on IEEE Xplore.
Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.
The Formula Explained
DC: $$ P = V \\times I $$
Single-phase AC: $$ P = V_{\\mathrm{rms}} \\times I_{\\mathrm{rms}} \\times PF $$
Three-phase AC (balanced): $$ P = \\sqrt{3} \\times V_{LL} \\times I_{L} \\times PF $$
Apparent power: $$ S = V \\times I \\quad (\\text{1-\\!phase}), \\qquad S = \\sqrt{3} \\times V_{LL} \\times I_{L} \\quad (\\text{3-\\!phase}) $$
Relation: $$ P = PF \\times S $$
Glossary of Variables
- I (A): RMS current.
- V (V): RMS voltage; for 3‑phase, line‑to‑line RMS.
- PF (unitless): Power factor, 0–1, ratio of real to apparent power.
- P (W): Real power delivered to the load.
- S (VA): Apparent power (volt‑amperes).
- kW, kVA: P and S expressed in kilounits (÷ 1000).
How It Works: A Step‑by‑Step Example
Scenario: Single‑phase AC heater draws I = 5 A at V = 230 V with PF = 0.90.
- Apply single‑phase real power: P = V × I × PF.
- Compute: P = 230 × 5 × 0.90 = 1035 W = 1.035 kW.
- Apparent power: S = V × I = 230 × 5 = 1150 VA = 1.15 kVA.
- Check: P = PF × S = 0.90 × 1150 = 1035 W (matches).
Frequently Asked Questions (FAQ)
Do I need power factor for DC?
No. PF = 1 for DC, so P = V × I.
What PF should I use if I don’t know it?
Many general‑purpose loads lie between 0.8 and 0.95. Motors under light load may have lower PF. Use the nameplate or datasheet when available.
Which voltage do I use for 3‑phase systems?
Use the line‑to‑line RMS voltage and line current per conductor in the √3 formula to get total three‑phase power.
Why does the calculator show both W and VA?
Watts are real power used by the load; VA is apparent power used to size sources like generators and UPS. In AC, W = PF × VA.
Can this tool convert watts back to amps?
Yes, rearrange: I = P / (V × PF) for AC, and I = P / V for DC. A dedicated Watts to Amps tool is recommended for convenience.
Does frequency (50/60 Hz) change the result?
Not directly in the formula; however, frequency can influence PF and load behavior, which indirectly affects P.
Is this valid for unbalanced 3‑phase?
The √3 formula assumes a balanced load. For unbalanced systems, compute per phase and sum, or use instrumentation per IEEE 1459.