# Induction Motor Torque-Speed Characteristic (Kloss)

Build the torque-speed curve of a three-phase induction motor using the Kloss equation T/T_max = 2/(s/s_max + s_max/s). Returns rated torque, breakdown (max) torque, starting torque, breakdown slip, and a sampled T-n curve with configurable point count.

> Canonical page: https://elysiatools.com/en/tools/motor-torque-speed

- **Category:** Math & Numbers

- **Keywords:** torque-speed, induction motor, Kloss equation, breakdown torque, starting torque, pull-out slip, T-n curve, motor characteristic, electrical engineering

## Overview

This induction motor torque-speed characteristic calculator allows you to model and analyze the mechanical performance of a three-phase induction motor using the Kloss equation. By entering basic motor nameplate data such as frequency, pole pairs, rated power, and rated speed, the tool computes critical parameters including rated torque, breakdown (maximum) torque, starting torque, and breakdown slip, while generating a detailed, sampled torque-speed (T-n) curve.

## Inputs

- **Frequency f (Hz)** (number): Supply frequency in Hz.
- **Pole Pairs p** (number): Number of POLE PAIRS p (a 4-pole motor has p=2).
- **Power Unit** (select)
- **Rated Power** (number): Rated shaft output power in the selected unit.
- **Rated Speed n_rated (rpm)** (number): Rated rotor speed (must be less than synchronous speed n_s).
- **Max Torque T_max (Nm)** (number): Optional. If provided, overload factor is computed from it; otherwise λ is used.
- **Overload Factor λ (T_max/T_rated)** (number): Used only when T_max is not given. Typical 2.0–3.0.
- **Curve Sample Points** (number): Number of points sampled on the T-n curve (11–41).
- **Decimal Places** (number)

## When to use

- When designing or selecting a three-phase induction motor and you need to estimate its torque-speed curve from nameplate data.
- When analyzing motor startup behavior and verifying if the starting torque is sufficient for a specific load.
- When calculating the breakdown slip and maximum overload capacity of an induction motor under varying frequency or pole configurations.

## How it works

- Enter the supply frequency, number of pole pairs, rated power, and rated rotor speed from the motor's nameplate.
- Specify either the maximum torque directly or provide an overload factor to determine the breakdown torque.
- The tool calculates the synchronous speed, rated slip, rated torque, breakdown slip, and starting torque.
- It applies the Kloss equation to generate a sampled torque-speed curve containing your preferred number of data points.

## Use cases

- Generating torque-speed data points to plot motor characteristics in external engineering reports or simulation software.
- Verifying motor overload margins by comparing rated torque against breakdown torque using the overload factor.
- Estimating the starting torque (at zero speed/slip of 1) to ensure the motor can start under heavy load conditions.

## Frequently asked questions

### What is the Kloss equation used for?

The Kloss equation is an analytical formula used to approximate the torque-speed (or torque-slip) relationship of an induction motor based on its maximum torque and breakdown slip.

### How is the number of pole pairs related to the number of poles?

The pole pairs parameter (p) is half the total number of poles. For example, a standard 4-pole motor has 2 pole pairs.

### What is breakdown slip?

Breakdown slip (or pull-out slip) is the slip value at which the induction motor produces its maximum (breakdown) torque.

### Can I input the maximum torque directly?

Yes, you can enter the maximum torque in Nm. If left blank, the tool will automatically calculate it using the provided overload factor.

### What range of sample points can I generate for the curve?

You can configure the tool to sample between 11 and 41 points along the torque-speed curve.

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