Electric Motor Calculations Formulas List

Basic Electrical Formulas:

\[ P = V \times I \text{ (DC Power)} \] \[ P = V \times I \times PF \text{ (AC Single Phase)} \] \[ P = \sqrt{3} \times V \times I \times PF \text{ (AC Three Phase)} \]

Common Motor Formulas:

Power (P): \( P = \frac{T \times N}{9.5488} \) (Watts)

Torque (T): \( T = \frac{9.5488 \times P}{N} \) (Nm)

Speed (N): \( N = \frac{9.5488 \times P}{T} \) (RPM)

Current (I): \( I = \frac{P}{V \times \eta \times PF} \) (Amps)

Efficiency (η): \( \eta = \frac{P_{out}}{P_{in}} \times 100\% \)

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1. Basic Electrical Formulas

Fundamental equations for electrical power calculations in DC and AC systems.

\[ P = V \times I \text{ (DC Power)} \] \[ P = V \times I \times PF \text{ (AC Single Phase)} \] \[ P = \sqrt{3} \times V \times I \times PF \text{ (AC Three Phase)} \]

Where:

\( P \) — Power in watts (W)
\( V \) — Voltage in volts (V)
\( I \) — Current in amperes (A)
\( PF \) — Power factor (unitless, 0-1)

2. Motor Power Calculations

Formulas relating mechanical power to electrical power in motors.

\[ P = \frac{T \times N}{9.5488} \]

Where:

\( T \) — Torque in newton-meters (Nm)
\( N \) — Rotational speed in revolutions per minute (RPM)
9.5488 — Conversion factor (30/π)

3. Torque and Speed Relationships

Fundamental relationships between torque, speed, and power in electric motors.

\[ T = \frac{9.5488 \times P}{N} \] \[ N = \frac{9.5488 \times P}{T} \]

Note: These relationships show the inverse proportion between torque and speed at constant power.

4. Efficiency and Power Factor

Formulas for motor efficiency and power factor calculations.

\[ \eta = \frac{P_{out}}{P_{in}} \times 100\% \] \[ PF = \frac{P}{S} = \frac{P}{V \times I} \]

Where:

\( \eta \) — Efficiency in percent (%)
\( P_{out} \) — Output mechanical power
\( P_{in} \) — Input electrical power
\( PF \) — Power factor
\( S \) — Apparent power in volt-amperes (VA)

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between real, apparent, and reactive power?
A: Real power (P) does actual work, apparent power (S) is the product of V×I, and reactive power (Q) is stored and returned to the system.

Q2: How does motor efficiency affect power consumption?
A: Higher efficiency means more input power is converted to mechanical work rather than lost as heat.

Q3: Why is power factor important?
A: Low PF increases current for the same real power, requiring larger conductors and generating more losses.

Q4: How do you calculate motor slip?
A: \( Slip = \frac{N_s - N}{N_s} \times 100\% \) where Nₛ is synchronous speed.

Q5: What's the relationship between HP and watts?
A: 1 HP = 746 watts (electrical HP) or 735.5 watts (metric HP).