Motor and VFD Equations Reference

Page review information

Edition covered: Motor and drive engineering practice — vendor documentation governs application — n/a — practice module
Content status: Reviewed
Coverage: Training module: Motor and VFD Equations Reference — educational treatment; sizing and application decisions follow vendor data and the governing standards.
Last reviewed: August 2026
Primary reference: The official published standard — required for final decisions

Confirm the governing edition, jurisdiction, and project-specific requirements before applying anything on this page.

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 an independent educational reference for industrial automation standards. It paraphrases and organizes guidance in original language; it is not a substitute for the official published standards, professional engineering judgment, or legal review, and content has not been independently verified against current published editions.

Items marked Review pending await technical review against the identified edition. Items marked Planned have no reviewed source material behind them. Do not rely on this site for compliance determinations, safety-critical design decisions, or legal interpretation.