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Electrical Formulas Cheat Sheet

The electrical formulas instrument and electrical engineers use daily, on one printable page: Ohm's law, power, three phase, motors, voltage drop and power factor correction.

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Ohm's law and power

Ohm's law	V = I × R
Power	P = V × I = I² × R = V² ÷ R
Series	R = R1 + R2 + …
Parallel	1/R = 1/R1 + 1/R2 + …

AC power

Single phase	P = V × I × cos φ
Three phase	P = √3 × V_L × I_L × cos φ
Apparent power	S = √3 × V_L × I_L (kVA)
Power triangle	S² = P² + Q²
RMS	V_rms = V_peak ÷ √2

Star and delta

	Star (Y)	Delta (Δ)
Line voltage	√3 × V_ph	V_ph
Line current	I_ph	√3 × I_ph
Star delta starting	Current and torque ÷ 3

Motors

Full load current	I = P ÷ (√3 × V × η × cos φ)
Synchronous speed	N_s = 120 × f ÷ poles
Slip	s = (N_s − N) ÷ N_s
Torque	T (N·m) = 9549 × P (kW) ÷ N (rpm)
Rule of thumb	415 V motor: about 1.8 A per kW

Voltage drop

Single phase	ΔV = 2 × I × L × (R cos φ + X sin φ)
Three phase	ΔV = √3 × I × L × (R cos φ + X sin φ)
Limits (typical)	3 % lighting, 5 % power

Power factor correction

Capacitor	Q_c = P × (tan φ₁ − tan φ₂) kVAR
Example	100 kW from 0.8 to 0.95: 42 kVAR

Copper and cables

Item	Value
Copper resistivity (20 °C)	0.0172 Ω·mm²/m
Aluminium resistivity	0.0282 Ω·mm²/m
Copper temperature coefficient	0.00393 per °C
1.5 mm² copper	about 12.1 Ω/km (IEC 60228 class 2)
2.5 mm² copper	about 7.41 Ω/km

Reactance and resonance

Inductive	X_L = 2π f L
Capacitive	X_C = 1 ÷ (2π f C)
Resonance	f₀ = 1 ÷ (2π √(L C))
Time constant	τ = R C or L ÷ R

Energy

Energy	E (kWh) = P (kW) × t (h)
Battery	Backup (h) ≈ Ah × V × η ÷ load (W)

Related Calculators and Tools

Ohm's Law CalculatorFree on instrumentationblog.in Voltage Drop CalculatorFree on instrumentationblog.in Motor Full Load Current CalculatorFree on instrumentationblog.in Power Factor Correction CalculatorFree on instrumentationblog.in

Frequently Asked Questions

What is the formula for three phase power?

P = √3 × line voltage × line current × power factor.

How many amps is a 1 kW motor at 415 V?

Roughly 1.8 A, depending on efficiency and power factor.

What is the line voltage in star?

√3 times the phase voltage, for example 415 V line for 240 V phase.

Learn more on the blog

Basics of Ohm's law

A practical guide on instrumentationblog.in that explains the theory behind this cheat sheet.

Read Full Article

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