Engineering-Grade Accuracy

Power Engineering
Tools Hub

Rigorous, transparent calculations for electrical power systems. Built for professionals and students who demand accuracy and explainability.

Available Tools
⚡
AC Power & Current Calculator
1φ / 3φ balanced systems. Solve P, Q, S, V, I, pf from any known subset.
Live
📉
Voltage Drop Calculator
Conductor impedance, %VD, cable sizing per NEC / IEC.
Coming Soon
🔄
Per-Unit Converter
Base conversion, MVA base change, multi-voltage systems.
Coming Soon
⚠️
3φ Symmetrical Fault
Bolted fault current, X/R ratio, interrupting duty.
Coming Soon
🔌
Transformer Sizing
kVA sizing, derating factors, loading analysis.
Coming Soon
🌡️
Cable Ampacity
Thermal rating, derating per NEC 310 / IEC 60287.
Coming Soon
🔋
Capacitor Bank Sizing
PF correction, Mvar required, resonance check.
Coming Soon

About Accuracy

Every tool in this hub is built on peer-reviewed formulas from standard power engineering textbooks and IEEE standards. Key principles:

  • All intermediate calculations use full IEEE 754 double precision. Display values are rounded for readability; internal precision is never reduced early.
  • Unit conversions are handled by a centralized conversion module to prevent silent unit bugs.
  • Overdetermined systems are detected and flagged — the tool will never silently hide inconsistencies.
  • The "Show Steps" feature reveals every formula and intermediate value, enabling independent verification.
Disclaimer: This hub is an educational and professional reference tool. Results must be independently verified by a licensed Professional Engineer before use in safety-critical, life-safety, or code-compliance applications. The authors assume no liability for errors in design decisions based on this tool.
AC Power & Current Calculator
Balanced steady-state AC analysis · 1φ and 3φ systems · Solves for any unknown from given subset of P, Q, S, V, I, pf, φ
Configuration
System Type
? Single-phase uses one voltage/current pair. Three-phase (balanced) uses line current and either line-to-line (V_LL) or line-to-neutral (V_LN) voltage. Assumes balanced, sinusoidal steady-state operation.
Voltage Reference
? Line-to-Line (V_LL): voltage between two phases. Line-to-Neutral (V_LN): voltage from phase to neutral. For balanced 3φ: V_LL = √3 × V_LN ≈ 1.732 × V_LN.
Power Factor Type
? Lagging (inductive): current lags voltage; Q positive — motors, inductors. Leading (capacitive): current leads voltage; Q negative — capacitors, lightly loaded synchronous generators.
Known Values — enter any 2 or more
P Real (Active) Power
? Real power P (watts) is the average rate of energy transfer that does actual work. P = |S|·pf = V·I·cos(φ). Also called "true power" or "active power".
Q Reactive Power
? Reactive power Q (VAR) represents energy oscillating between source and reactive elements. It does no real work but is needed to maintain voltage. Q = |S|·sin(φ). Positive for lagging, negative for leading.
S Apparent Power
? Apparent power |S| (VA) is the vector magnitude of P + jQ. Equipment ratings (transformers, generators, UPS) are given in VA or kVA. |S|² = P² + Q².
V Voltage
? For 1φ: RMS voltage across the load. For 3φ: V_LL (line-to-line) or V_LN (line-to-neutral) per the Voltage Reference setting. Always enter RMS (not peak) values.
I Current
? For 1φ: RMS current through the load. For 3φ: line current (I_line). Always enter RMS (not peak) values. I_peak = I_rms × √2.
pf Power Factor
? Power factor = cos(φ) where φ is the angle between voltage and current phasors. Range: 0 (pure reactive) to 1 (pure resistive). pf = P / |S|. Leave blank if entering φ (angle) instead.
φ Phase Angle
? Phase angle between voltage and current phasors, in degrees. |φ| ≤ 90°. φ = arccos(pf). You may enter either pf or φ — both fields are equivalent. If both are entered, they must be consistent.
°
Results
Enter values and press Calculate to see results.
Power Triangle
🧪 Built-in Validation Tests — click to run

Accuracy & Assumptions

Steady-state, balanced, sinusoidal operation is assumed throughout. All calculations use IEEE 754 double-precision floating point internally.

  • Three-phase results assume a perfectly balanced system (equal phase voltages, equal line currents, 120° spacing). For unbalanced systems, symmetrical component analysis is required.
  • Power factor sign convention follows IEEE Std 1459-2010: lagging = positive Q (inductive), leading = negative Q (capacitive).
  • Voltage inputs must be RMS values, not peak. I_peak = I_RMS × √2.
  • Waveforms assumed purely sinusoidal — harmonic distortion (THD) is not accounted for.
Disclaimer: Educational / professional reference only. Verify all results before use in design, commissioning, or safety-critical work. Always engage a licensed Professional Engineer for code-compliance and safety-critical decisions.

References

[1] J.D. Glover, T.J. Overbye & M.S. Sarma, Power Systems Analysis and Design, 6th ed., Cengage Learning, 2017. — Core relationships for phasor power, P, Q, S.
[2] S.J. Chapman, Electric Machinery Fundamentals, 5th ed., McGraw-Hill, 2011. — Sign conventions, three-phase power formulas.
[3] IEEE Std 1459-2010, IEEE Standard Definitions for the Measurement of Electric Power Quantities Under Sinusoidal, Nonsinusoidal, Balanced, or Unbalanced Conditions. — Formal definitions of P, Q, S.
[4] B.M. Weedy et al., Electric Power Systems, 5th ed., Wiley, 2012. — Three-phase power: S = √3 · V_LL · I_line · (pf + j·sin φ).
[5] W.H. Kersting, Distribution System Modeling and Analysis, 3rd ed., CRC Press, 2012. — V_LN / V_LL relationships, line current conventions.

Sign Conventions

  • pf = cos(φ) where φ = ∠V − ∠I
  • Lagging / Inductive: Current lags voltage, φ > 0, Q > 0. Absorbs reactive power. Typical: motors, transformers.
  • Leading / Capacitive: Current leads voltage, φ < 0, Q < 0. Supplies reactive power. Typical: capacitor banks, over-excited synchronous machines.
  • S = P + jQ where |S| = √(P² + Q²)
  • 3φ V_LL ↔ V_LN: V_LL = √3 · V_LN

Key Formulas

  • 1φ: |S| = V · I
  • 3φ V_LL: |S| = √3 · V_LL · I_line
  • 3φ V_LN: |S| = 3 · V_LN · I_line
  • P = |S| · pf
  • Q = |S| · sin(arccos(pf)) · ±1
  • pf = P / |S| = cos(φ)
  • sin(φ) = √(1 − pf²)
  • φ = arccos(pf)
  • V_LN = V_LL / √3 (balanced 3φ)

Known Limitations & Assumptions

  • Balanced 3φ only. Unbalanced systems (sequence components, unequal loading) are not supported.
  • Fundamental frequency only. Harmonic power (IEEE 1459 non-fundamental apparent power) is not computed. Results are valid only for clean sinusoidal waveforms.
  • RMS values required. Peak or average values will give incorrect results.
  • No impedance model. This tool does not compute line drop, fault currents, or impedance-dependent quantities.
  • Floating-point precision. Results near pf = 1.0000 may show very small non-zero Q due to arccos/sqrt floating-point behavior; guard logic limits this to < 1 ppm error.
  • No frequency dependency. Reactance and susceptance values are not computed; enter measured P/Q/S directly.