Fundamentals ReferenceUpdated 2026-08-15

Master Electrical Formulas & Equations Cheat Sheet

Complete engineering reference cheat sheet covering DC circuits, AC single-phase & three-phase formulas, Ohm's law, power, impedance, reactance, and transformer ratios.

Key Formulas: V = IR | P = VI = I²R = V²/R | S = √3 × V × I | X_C = 1/(2πfC) | X_L = 2πfL

1. DC Circuit Fundamentals

In direct current (DC) circuits, electric charge flows in a single constant direction. Purely resistive components govern current flow without frequency-dependent reactance.

•

Ohm's Law:

V = I \times R

I = V / R

R = V / I

•

Joule's Law of Power:

P = V \times I = I^2 R = V^2 / R

•

Series Resistance:

R_{\text{total}} = R_1 + R_2 + \dots + R_n

•

Parallel Resistance:

\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots + \frac{1}{R_n}

2. Single-Phase AC Formulas

Alternating current introduces time-varying sinusoidal waveforms where current and voltage can be out of phase due to reactive elements (inductors and capacitors).

•

Apparent Power:

S = V_{\text{rms}} \times I_{\text{rms}}

(Volt-Amps, VA)

•

Real / Active Power:

P = V_{\text{rms}} \times I_{\text{rms}} \times \cos(\theta)

(Watts, W)

•

Reactive Power:

Q = V_{\text{rms}} \times I_{\text{rms}} \times \sin(\theta)

(VAR)

•

Power Factor:

\text{PF} = \cos(\theta) = \frac{P}{S}

•

Total Impedance:

Z = \sqrt{R^2 + (X_L - X_C)^2}

(Ohms, Ω)

3. Three-Phase AC Systems (Balanced)

Three-phase electrical power utilizes three sinusoidal voltages spaced 120 electrical degrees apart, providing constant power delivery and high transmission efficiency.

•

Three-Phase Real Power:

P_{3\phi} = \sqrt{3} \times V_{\text{LL}} \times I_{\text{line}} \times \text{PF}

•

Three-Phase Apparent Power:

S_{3\phi} = \sqrt{3} \times V_{\text{LL}} \times I_{\text{line}}

•

Wye (Y) Connection:

V_{\text{LL}} = \sqrt{3} \times V_{\text{LN}}

I_{\text{line}} = I_{\text{phase}}

•

Delta (Δ) Connection:

V_{\text{line}} = V_{\text{phase}}

I_{\text{line}} = \sqrt{3} \times I_{\text{phase}}

4. Reactance & Resonance Formulas

•

Capacitive Reactance:

X_C = \frac{1}{2\pi f C}

(Ω)

•

Inductive Reactance:

X_L = 2\pi f L

(Ω)

•

Resonant Frequency:

f_0 = \frac{1}{2\pi \sqrt{LC}}

(Hz)

•

Capacitor Stored Energy:

E_C = \frac{1}{2} C V^2

(Joules)

•

Inductor Stored Energy:

E_L = \frac{1}{2} L I^2

(Joules)

Frequently Asked Questions

Why is the square root of 3 (√3 ≈ 1.732) used in 3-phase calculations?

The factor √3 arises geometrically from the vector difference between two phase voltages that are 120° apart in a balanced three-phase Wye system: 2 × cos(30°) = √3.

Related Calculators & Engineering Tools

Ohm's Law Calculator

Power Calculator

Power Factor Calculator