Motor and VFD Equations Reference

Intermediate Time: 10 min Type: Reference Focus: Motor / Drive Engineering

After this module: Quick-reference equations for speed, torque, slip, power, and VFD sizing — formatted for fast lookup during design or commissioning.

Purpose

This module collects the most useful motor and VFD equations into one reference note for training and first-pass engineering review.

Use these as working relationships, not as a substitute for detailed manufacturer data or standards-based design methods.

Mechanical power and torque

Core relationship:

P = T x omega

Where:

P = mechanical power
T = torque
omega = angular velocity

Common engineering form:

P(kW) = T(Nm) x rpm / 9550

Horsepower form:

HP = T(lb-ft) x rpm / 5252

Synchronous speed

For AC machines:

N_s = 120 x f / poles

Where:

N_s = synchronous speed in rpm
f = electrical frequency
poles = number of poles

This is why changing VFD output frequency changes motor speed.

Slip

For induction motors:

s = (N_s - N_r) / N_s

Where:

N_s = synchronous speed
N_r = rotor speed

Slip is required for induction-motor torque production.

Efficiency

eta = P_out / P_in

Efficiency is a ratio between useful mechanical output and electrical input.

Power factor

PF = Real Power / Apparent Power

In simple terms, power factor indicates how effectively current is being converted into useful power.

Three-phase power reminder

For quick review:

P = sqrt(3) x V_LL x I_L x PF

This is a useful relationship when estimating the electrical side of a motor system.

VFD speed relationship

A VFD changes motor speed mainly by changing output frequency.

First-pass rule:

lower output frequency → lower synchronous speed
higher output frequency → higher synchronous speed until voltage and control limits are reached

Practical cautions

Equations alone do not select a motor or drive correctly.
Real design still depends on nameplate data, load profile, duty cycle, and manufacturer ratings.
Do not use simplified equations as a substitute for conductor, protection, or thermal review.

← Motor Efficiency, Power Factor, and Losses ↑ Motors, Drives, and Motion Servo Feedback and Inertia Matching →

Trust Boundary — Engineering Judgment Required

This site is a personal-use paraphrase and navigation reference for industrial automation standards. It is not a substitute for authoritative standards documents, professional engineering judgment, or legal review. All content is sourced from a local RAG corpus and has not been independently verified against current published editions.

Items marked TO VERIFY have limited or unconfirmed local coverage. Items marked NOT IN CORPUS are not covered in the local repository. Do not rely on this site for compliance determinations, safety-critical design decisions, or legal interpretation.