{"id":11101,"date":"2026-05-27T14:28:18","date_gmt":"2026-05-27T05:28:18","guid":{"rendered":"https:\/\/cik-ele.com\/?p=11101"},"modified":"2026-06-30T16:10:29","modified_gmt":"2026-06-30T07:10:29","slug":"moment-of-inertia","status":"publish","type":"post","link":"http:\/\/cxubw72.secure.ne.jp\/en\/column\/moment-of-inertia\/","title":{"rendered":"What Is Moment of Inertia? Calculation Formulas and Selection Criteria for Motor Design"},"content":{"rendered":"<p>Moment of inertia is a physical quantity that indicates how easily a rotating object can be set in motion or brought to a stop, and it is an essential factor in motor design calculations. During motor selection, it is necessary to correctly calculate the load\u2019s moment of inertia and estimate the required torque and acceleration\/deceleration performance.<\/p>\n<p>If the moment of inertia is estimated incorrectly, depending on the motor type and operating conditions, this can lead to overshoot or undershoot during startup and stopping, control instability, or even operational failure.<\/p>\n<p>In this article, we will explain step-by-step everything from the basic definition of moment of inertia and its relationship to torque, to calculation formulas for typical motor configurations, and key points to consider during motor selection. We hope this serves as a useful reference for engineers involved in motor design and equipment development.<\/p>\n<table style=\"height: 48px; border-color: #2470c7; background-color: #f0fdff;\" border=\"6\" width=\"551\">\n<caption>\u00a0<\/caption>\n<tbody>\n<tr style=\"height: 38.4141px;\">\n<td style=\"width: 541.504px; height: 38.4141px;\"><strong><u>Supervised by: C.I. TAKIRON Corporation Electronic Devices Sales Group<\/u><\/strong><\/p>\n<p>This article has been supervised based on the advanced technical expertise and insights we have cultivated since our founding in 1919 as a leading company in plastic processing. Our department continuously analyzes market trends and the latest technologies in ultra-compact, high-precision micro motors, focusing on providing high-value-added information to designers and developers. As a team of experts with in-depth knowledge of product characteristics, we support our customers\u2019 problem-solving and technological innovation by delivering accurate and practical content.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<h2 style=\"color: #fff; background: #437ae8; line-height: 70px; font-size: 30px; margin: 10; padding-left: 1em; padding: 1em;\"><strong>Basics of Moment of Inertia and Its Relationship to Torque<\/strong><\/h2>\n<p><img decoding=\"async\" class=\"alignnone size-medium wp-image-11144\" src=\"https:\/\/cik-ele.com\/wp-content\/uploads\/2026\/05\/c57d52f74a764f4bb61150235b695464-540x304.jpg\" alt=\"What Is Moment of Inertia? Calculation Formulas and Selection Criteria for Motor Design\" width=\"540\" height=\"304\" \/><\/p>\n<p>We will explain the definition, relationships, and units of the moment of inertia, comparing them to linear motion.<\/p>\n<p><strong>Contents of This Section<\/strong><\/p>\n<ul>\n<li>Definition of Moment of Inertia in Rotational Motion<\/li>\n<li>Relationship Between <a href=\"https:\/\/cik-ele.com\/en\/column\/torque-motors\/\">Torque<\/a> and Angular Acceleration<\/li>\n<li>The Difference Between the Units kg\u00b7m\u00b2 and GD\u00b2<\/li>\n<\/ul>\n<p>The moment of inertia J (sometimes denoted as I in academic literature, but we will use J consistently in this article) is a physical quantity that indicates how difficult it is to rotate or stop a rotating body. It corresponds to mass in linear motion and, in rotational motion, is described by the relationship between the moment of inertia, torque, and angular acceleration.<\/p>\n<p>In motor design calculations, accurately determining this value serves as the starting point for calculating the required torque and performing motor selection.<\/p>\n<p>&nbsp;<\/p>\n<h3 style=\"color: #fff; background: #c3effa; line-height: 20px; font-size: 23px; margin: 10; padding-left: 1em; padding: 1em;\"><span style=\"color: #000000; font-size: 18pt;\"><strong>Definition of Moment of Inertia in Rotational Motion<\/strong><\/span><\/h3>\n<p>The moment of inertia in rotational motion is defined as the sum of the products of the mass M of each particle and the square of its distance R from the axis of rotation. The basic equation is expressed as J = MR\u00b2, and even if the mass M is the same, the value increases as the mass is concentrated farther from the axis of rotation.<\/p>\n<p>In linear motion, there is a tendency that \u201cthe greater the mass, the harder it is to move\u201d; in rotational motion, the moment of inertia plays the same role. The larger the moment of inertia of a rotating body, the greater the torque required to start or stop its rotation. For a system of point masses, it is expressed as J = \u03a3MiRi\u00b2, and for a continuous body, as J = \u222bR\u00b2dm; however, in practice, it is common to use pre-derived formulas specific to different shapes.<\/p>\n<p>The more mass is concentrated away from the axis of rotation, the greater the value of the moment of inertia. For example, for disks of the same mass, if the diameter doubles, the moment of inertia quadruples.<\/p>\n<p>While linear motion is characterized by the principle that \u201cthe greater the mass, the harder it is to move,\u201d in rotational motion, the moment of inertia determines how difficult it is to rotate the object. In motor selection, accurately calculating the moment of inertia based on the shape and mass distribution of the object to be driven is the starting point of the design process.<\/p>\n<p>&nbsp;<\/p>\n<h3 style=\"color: #fff; background: #c3effa; line-height: 20px; font-size: 23px; margin: 10; padding-left: 1em; padding: 1em;\"><span style=\"color: #000000; font-size: 18pt;\"><strong>Relationship Between Torque and Angular Acceleration<\/strong><\/span><\/h3>\n<div>\n<p>The relationship between torque and angular acceleration is given by the equation of motion for rotational motion:<\/p>\n<p>T = J\u03b1 (T: torque [N\u00b7m], J: moment of inertia [kg\u00b7m\u00b2], \u03b1: angular acceleration [rad\/s\u00b2])<\/p>\n<p>.<\/p>\n<p>Equation of Motion for Linear Motion<\/p>\n<p>F = Ma<\/p>\n<p>.<\/p>\n<p>This equation shows that the larger the moment of inertia, the greater the torque required to achieve the same angular acceleration. For example, accelerating a rotating body with twice the moment of inertia in the same amount of time requires twice the torque.<\/p>\n<p>Understanding T = J\u03b1 is fundamental to design calculations when estimating the torque required for motor acceleration and deceleration. Correctly determining the load\u2019s moment of inertia and using this equation to calculate the required torque leads to motor selection.<\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<div>\n<h3 style=\"color: #fff; background: #c3effa; line-height: 20px; font-size: 23px; margin: 10; padding-left: 1em; padding: 1em;\"><span style=\"color: #000000; font-size: 18pt;\"><strong>The Difference Between kg\u00b7m\u00b2 and GD\u00b2<\/strong><\/span><\/h3>\n<\/div>\n<div>\n<p>\u00a0Let\u2019s clarify the difference between the units kg\u00b7m\u00b2 and GD\u00b2. In motor technical documentation, the moment of inertia may be expressed in the International System of Units (SI) as J (kg\u00b7m\u00b2) or in the gravitational unit system as GD\u00b2 (kgf\u00b7m\u00b2).<\/p>\n<table style=\"width: 100%; max-width: 100%; border-collapse: collapse;\">\n<tbody>\n<tr style=\"height: 23px;\">\n<td style=\"width: 20%; background-color: #f0fff8; padding-top: 2px; padding-bottom: 4px; border: 1px solid #999999; height: 23px;\">Unit<\/td>\n<td style=\"width: 38.2601%; background-color: #f0fff8; padding-top: 2px; padding-bottom: 4px; border: 1px solid #999999; height: 23px;\">\u00a0kg\u00b7m\u00b2 (International System of Units)<\/td>\n<td style=\"width: 21.7399%; background-color: #f0fff8; padding-top: 2px; padding-bottom: 4px; border: 1px solid #999999; height: 23px;\">GD\u00b2 (Gravitational Unit System)<\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 20%; background-color: #ffffff; padding-top: 2px; padding-bottom: 4px; border: 1px solid #999999; height: 28px;\">Symbol<\/td>\n<td style=\"width: 38.2601%; background-color: #ffffff; padding-top: 2px; padding-bottom: 4px; border: 1px solid #999999; height: 28px;\">J<\/td>\n<td style=\"width: 21.7399%; background-color: #ffffff; padding-top: 2px; padding-bottom: 4px; border: 1px solid #999999; height: 28px;\">GD\u00b2<\/td>\n<\/tr>\n<tr style=\"height: 37.1562px;\">\n<td style=\"width: 20%; background-color: #ffffff; padding-top: 2px; padding-bottom: 4px; border: 1px solid #999999; height: 37.1562px;\">\u00a0Definition<\/td>\n<td style=\"width: 38.2601%; background-color: #ffffff; padding-top: 2px; padding-bottom: 4px; border: 1px solid #999999; height: 37.1562px;\">J=M\u00d7R\u00b2<\/td>\n<td style=\"width: 21.7399%; background-color: #ffffff; padding-top: 2px; padding-bottom: 4px; border: 1px solid #999999; height: 37.1562px;\">GD\u00b2=W\u00d7D\u00b2<\/td>\n<\/tr>\n<tr style=\"height: 23px;\">\n<td style=\"width: 20%; background-color: #ffffff; padding-top: 2px; padding-bottom: 4px; border: 1px solid #999999; height: 23px;\">Units<\/td>\n<td style=\"width: 38.2601%; background-color: #ffffff; padding-top: 2px; padding-bottom: 4px; border: 1px solid #999999; height: 23px;\">kg\u00b7m\u00b2<\/td>\n<td style=\"width: 21.7399%; background-color: #ffffff; padding-top: 2px; padding-bottom: 4px; border: 1px solid #999999; height: 23px;\">kgf\u00b7m\u00b2<\/td>\n<\/tr>\n<tr style=\"height: 23px;\">\n<td style=\"width: 20%; background-color: #ffffff; padding-top: 2px; padding-bottom: 4px; border: 1px solid #999999; height: 23px;\">\u00a0Conversion Relationship<\/td>\n<td style=\"width: 38.2601%; background-color: #ffffff; padding-top: 2px; padding-bottom: 4px; border: 1px solid #999999; height: 23px;\">J=GD\u00b2\/4<\/td>\n<td style=\"width: 21.7399%; background-color: #ffffff; padding-top: 2px; padding-bottom: 4px; border: 1px solid #999999; height: 23px;\">GD\u00b2=4J<\/td>\n<\/tr>\n<tr style=\"height: 23px;\">\n<td style=\"width: 20%; background-color: #ffffff; padding-top: 2px; padding-bottom: 4px; border: 1px solid #999999; height: 23px;\">Applications<\/td>\n<td style=\"width: 38.2601%; background-color: #ffffff; padding-top: 2px; padding-bottom: 4px; border: 1px solid #999999; height: 23px;\">General current technical documentation<\/td>\n<td style=\"width: 21.7399%; background-color: #ffffff; padding-top: 2px; padding-bottom: 4px; border: 1px solid #999999; height: 23px;\">Legacy motor catalogs<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div>\n<p>\u00a0GD\u00b2 is also known as the \u201cflywheel effect\u201d and was once a widely used unit in motor design calculations. While the International System of Units (kg\u00b7m\u00b2) is now the standard, motor manufacturers\u2019 catalogs may still list both units. Since misidentifying the unit during selection can result in a fourfold error in the calculation results, it is essential to correctly apply the conversion formula J = GD\u00b2\/4.<\/p>\n<p>&nbsp;<\/p>\n<h2 style=\"color: #fff; background: #437ae8; line-height: 70px; font-size: 30px; margin: 10; padding-left: 1em; padding: 1em;\"><strong>Formulas for Calculating Moment of Inertia and Methods for Determining It by Shape<\/strong><\/h2>\n<\/div>\n<\/div>\n<div>\n<div>\n<p><img decoding=\"async\" class=\"alignnone size-medium wp-image-11176\" src=\"https:\/\/cik-ele.com\/wp-content\/uploads\/2026\/05\/a0de1c2411e18b31db0c409565613763-540x304.jpg\" alt=\"What Is Moment of Inertia? Calculation Formulas and Selection Criteria for Motor Design\" width=\"540\" height=\"304\" \/><\/p>\n<p>Although the moment of inertia is technically calculated using integration, in practice it is common to use pre-derived formulas specific to each shape.<\/p>\n<p><strong>Topics Covered in This Section<\/strong><\/p>\n<ul>\n<li>Calculating the Moment of Inertia for Cylinders and Discs<\/li>\n<li>Calculating the Moment of Inertia for Rods and Rectangular Prisms<\/li>\n<li>Calculation Procedure for Motor Shaft Equivalents, Including Deceleration Mechanisms<\/li>\n<\/ul>\n<p>Calculation formulas are available for typical rotating bodies such as cylinders, disks, rods, and rectangular prisms; the moment of inertia can be calculated once the mass, dimensions, and position of the rotation axis of the object are known.<\/p>\n<p>Furthermore, in actual mechanical systems\u2014such as belt conveyors and reduction mechanisms\u2014it is necessary to sum the moments of inertia of multiple rotating bodies and convert them to the motor shaft.<\/p>\n<p>&nbsp;<\/p>\n<h3 style=\"color: #fff; background: #c3effa; line-height: 20px; font-size: 23px; margin: 10; padding-left: 1em; padding: 1em;\"><span style=\"color: #000000; font-size: 18pt;\"><strong>Calculating the Moment of Inertia for Cylinders and Discs<\/strong><\/span><\/h3>\n<p>The moments of inertia for cylinders and disks are used in calculations for motor rotors, cylindrical parts, and similar components. If the mass M and diameter D (and inner diameter d) are known, they can be calculated using the following formulas.<\/p>\n<table style=\"width: 100%; max-width: 100%; border-collapse: collapse;\">\n<tbody>\n<tr style=\"height: 23px;\">\n<td style=\"width: 20%; background-color: #f0fff8; padding-top: 2px; padding-bottom: 4px; border: 1px solid #999999; height: 23px;\">Shape<\/td>\n<td style=\"width: 27.2214%; background-color: #f0fff8; padding-top: 2px; padding-bottom: 4px; border: 1px solid #999999; height: 23px;\">Formula<\/td>\n<td style=\"width: 31.7786%; background-color: #f0fff8; padding-top: 2px; padding-bottom: 4px; border: 1px solid #999999; height: 23px;\">Application Examples<\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 20%; background-color: #ffffff; padding-top: 2px; padding-bottom: 4px; border: 1px solid #999999; height: 28px;\">\u00a0Solid Cylinder (Disk)<\/td>\n<td style=\"width: 27.2214%; background-color: #ffffff; padding-top: 2px; padding-bottom: 4px; border: 1px solid #999999; height: 28px;\">J = 1\/8 \u00d7 M \u00d7 D\u00b2<\/td>\n<td style=\"width: 31.7786%; background-color: #ffffff; padding-top: 2px; padding-bottom: 4px; border: 1px solid #999999; height: 28px;\">Rotor, Flywheel<\/td>\n<\/tr>\n<tr style=\"height: 37.1562px;\">\n<td style=\"width: 20%; background-color: #ffffff; padding-top: 2px; padding-bottom: 4px; border: 1px solid #999999; height: 37.1562px;\">\u00a0Hollow Cylinder<\/td>\n<td style=\"width: 27.2214%; background-color: #ffffff; padding-top: 2px; padding-bottom: 4px; border: 1px solid #999999; height: 37.1562px;\">J = 1\/8 \u00d7 M \u00d7 (D\u00b2 + d\u00b2)<\/td>\n<td style=\"width: 31.7786%; background-color: #ffffff; padding-top: 2px; padding-bottom: 4px; border: 1px solid #999999; height: 37.1562px;\">Couplings, Pipes<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>As a calculation example, consider a hollow cylindrical part with mass M = 0.5 kg, outer diameter D = 60 mm (0.06 m),and an inner diameter d = 30 mm (0.03 m), the moment of inertia is calculated as J = 1\/8 \u00d7 0.5 \u00d7 (0.06\u00b2 + 0.03\u00b2) = 1\/8 \u00d7 0.5 \u00d7 0.0045 \u2248 2.8 \u00d7 10\u207b\u2074 kg\u00b7m\u00b2.<\/p>\n<p>These formulas are used to calculate the moment of inertia for cylindrical components such as rotors and <a href=\"https:\/\/cik-ele.com\/en\/column\/coupling\/\">couplings.<\/a><\/p>\n<p>&nbsp;<\/p>\n<h3 style=\"color: #fff; background: #c3effa; line-height: 20px; font-size: 23px; margin: 10; padding-left: 1em; padding: 1em;\"><span style=\"color: #000000; font-size: 18pt;\"><strong>Calculating the Moment of Inertia for Rods and Rectangular Prisms<\/strong><\/span><\/h3>\n<p>The moment of inertia for rods and rectangular prisms is necessary when calculating rod-shaped or rectangular prism-shaped components included in rotational mechanisms, such as arms and sliders. The moment of inertia of a rod varies depending on the position of the rotation axis, so the following two formulas are used as appropriate.<\/p>\n<p><strong>\u00a0[Formulas for the Moment of Inertia of a Rod]<\/strong><\/p>\n<ul>\n<li>When the rotation axis is at one end: J = 1\/3 \u00d7 M \u00d7 L\u00b2<\/li>\n<li>When the rotation axis is at the center: J = 1\/12 \u00d7 M \u00d7 L\u00b2<\/li>\n<\/ul>\n<p>The value is four times larger when the rotation axis is at the end. In cases where the center of rotation differs from the component\u2019s center of mass\u2014such as at the joints of a robot arm\u2014it is necessary to accurately determine where the mechanism\u2019s rotation axis is located and select the corresponding formula.<\/p>\n<p>&nbsp;<\/p>\n<h3 style=\"color: #fff; background: #c3effa; line-height: 20px; font-size: 23px; margin: 10; padding-left: 1em; padding: 1em;\"><span style=\"color: #000000; font-size: 18pt;\"><strong>Calculation Procedure for Motor-Shaft Equivalence Including a Reduction Gear<\/strong><\/span><\/h3>\n<p>Calculations for motor-shaft equivalent values involving a reduction gear are necessary for mechanical systems where a reduction gear is interposed between the motor and the load. The formula for converting the load\u2019s moment of inertia to the motor shaft is Jm = JL\/i\u00b2 (where Jm is the motor-shaft equivalent load moment of inertia, JL is the load moment of inertia, and i is the reduction ratio).<\/p>\n<p>For example, if the load moment of inertia is 1.0 \u00d7 10\u207b\u00b3 kg\u00b7m\u00b2 and the reduction ratio is 2, the value converted to the motor shaft is Jm = 1.0 \u00d7 10\u207b\u00b3 \/ 4 = 2.5 \u00d7 10\u207b\u2074 kg\u00b7m\u00b2. When the reduction ratio is 2, the load moment of inertia converted to the motor shaft is one-fourth of the load-side value.Note that since the definition of the reduction ratio i varies by manufacturer, both Jm = JL \/ i\u00b2 and Jm = JL \u00d7 i\u00b2 represent the same concept expressed differently. Care must be taken regarding the basis for the reduction ratio i.<\/p>\n<p>You must check the notation for the reduction ratio in each catalog and apply the conversion formula according to the definition provided by each manufacturer.<\/p>\n<p>&nbsp;<\/p>\n<h2 style=\"color: #fff; background: #437ae8; line-height: 70px; font-size: 30px; margin: 10; padding-left: 1em; padding: 1em;\"><strong>Three Steps for Motor Selection Based on Moment of Inertia<\/strong><\/h2>\n<p><img decoding=\"async\" class=\"alignnone size-medium wp-image-11178\" src=\"https:\/\/cik-ele.com\/wp-content\/uploads\/2026\/05\/b82ee1d32c20543af5b66f7e4fca0ad3-540x304.jpg\" alt=\"What Is Moment of Inertia? Calculation Formulas and Selection Criteria for Motor Design\" width=\"540\" height=\"304\" \/><\/p>\n<p>After correctly calculating the value of the moment of inertia, the next step is motor selection based on that value.<\/p>\n<p><strong>\u00a0Topics Covered in This Section<\/strong><\/p>\n<ul>\n<li>Calculating Load Inertia and Required Torque<\/li>\n<li>Verifying the Inertia Ratio and Ensuring Control Stability<\/li>\n<li>Addressing Load Inertia by Utilizing Geared Motors<\/li>\n<\/ul>\n<p>When performing motor selection, you must proceed through the following three steps in order: calculating the load moment of inertia, calculating the required torque, and verifying the inertia ratio or allowable load moment of inertia. In applications where the rotational speed varies, it is necessary to consider not only the torque during steady-state operation but also the torque associated with acceleration and deceleration; therefore, following these steps in order leads to an appropriate selection<\/p>\n<p>&nbsp;<\/p>\n<h3 style=\"color: #fff; background: #c3effa; line-height: 20px; font-size: 23px; margin: 10; padding-left: 1em; padding: 1em;\"><span style=\"color: #000000; font-size: 18pt;\"><strong>Calculating Load Inertia and Required Torque<\/strong><\/span><\/h3>\n<p>Calculating the load moment of inertia and the required torque is the first step in motor selection. To determine the total load moment of inertia of the entire mechanism to be driven, calculate the moments of inertia for each mechanism component (such as pulleys and tables) and the load itself, then sum them to calculate the total load moment of inertia, JL.<\/p>\n<p>Once the total load moment of inertia JL has been determined, calculate the angular acceleration \u03b1 based on the acceleration time and target rotational speed, and then use the equation T = J\u03b1 to determine the acceleration torque. The total torque required of the motor is the sum of the acceleration torque and the load torque required during steady-state operation, such as friction torque. For operations involving startup and acceleration, the required torque must be calculated by taking into account both the load torque and the acceleration torque.<\/p>\n<p>&nbsp;<\/p>\n<h3 style=\"color: #fff; background: #c3effa; line-height: 20px; font-size: 23px; margin: 10; padding-left: 1em; padding: 1em;\"><span style=\"color: #000000; font-size: 18pt;\"><strong>Verification of the Inertia Ratio and Ensuring Control Stability<\/strong><\/span><\/h3>\n<p>The inertia ratio is the load moment of inertia divided by the motor rotor\u2019s moment of inertia. If this ratio exceeds the motor\u2019s recommended range, the motor may be unable to follow acceleration commands, potentially leading to loss of synchronization or unstable operation.<\/p>\n<p>Since the recommended inertia ratio and the upper limit of allowable moment of inertia vary depending on the motor type, the basic principle of motor selection is to check the recommended values listed in the catalog or technical documentation for the motor to be used and ensure that the system remains within those limits.<\/p>\n<p>Even if there is a margin in acceleration and deceleration torque, exceeding the recommended inertia ratio may lead to loss of synchronization or unstable operation. On the other hand, setting the <a href=\"https:\/\/cik-ele.com\/en\/column\/safety-factor\/\">safety factor<\/a> too high results in overspecification, which is disadvantageous in terms of motor size and cost. It is essential to select a motor within the appropriate range for the specific application.<\/p>\n<p>&nbsp;<\/p>\n<h3 style=\"color: #fff; background: #c3effa; line-height: 20px; font-size: 23px; margin: 10; padding-left: 1em; padding: 1em;\"><span style=\"color: #000000; font-size: 18pt;\"><strong>Addressing Load Inertia Through the Use of Geared Motors<\/strong><\/span><\/h3>\n<p>Using Geared motors is an effective solution when the load\u2019s moment of inertia exceeds the motor\u2019s allowable limit. By incorporating a reduction gear, the moment of inertia on the motor shaft is reduced by the square of the reduction ratio, enabling even compact motors to drive heavy loads. For example, with a reduction ratio of 2, the load\u2019s moment of inertia, as calculated relative to the motor shaft, becomes one-fourth of that on the load side.<\/p>\n<p>However, increasing the reduction ratio lowers the motor\u2019s output speed, so the design must strike a balance with the target speed. When the load inertia moment is large, incorporating a reduction mechanism is also a viable option.<\/p>\n<p>Product specifications and application conditions must be verified on each manufacturer\u2019s product page or through their customer service department. C.I. Takiron Corporation offers Geared motors that combine gearheads with Coreless or Brushless motors, and we can also propose configurations tailored to specific applications and requirements.<\/p>\n<p>&nbsp;<\/p>\n<h2 style=\"color: #fff; background: #437ae8; line-height: 70px; font-size: 30px; margin: 10; padding-left: 1em; padding: 1em;\"><strong>Summary<\/strong><\/h2>\n<p><img decoding=\"async\" class=\"alignnone size-medium wp-image-11180\" src=\"https:\/\/cik-ele.com\/wp-content\/uploads\/2026\/05\/c7887a92414f854a9067849a51b9bb02-11-540x304.jpg\" alt=\"What Is Moment of Inertia? Calculation Formulas and Selection Criteria for Motor Design\" width=\"540\" height=\"304\" \/><\/p>\n<p>Moment of inertia is a physical quantity that indicates how easily a rotating body can be set in motion or brought to a stop; it is a key factor in motor design calculations, directly affecting the determination of required torque and the assurance of control stability. By following the correct procedure\u2014from understanding the basic formula T = J\u03b1 to applying calculation formulas for different shapes, and further verifying the inertia ratio and utilizing Geared motors\u2014it is possible to perform appropriate motor selection.<\/p>\n<p>In operations involving changes in rotational speed, the acceleration torque and deceleration torque increase in proportion to the magnitude of the moment of inertia. If you have any questions regarding motor design or selection that takes moment of inertia into account, please feel free to contact C.I. Takiron Corporation.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<div>\n<p>&nbsp;<\/p>\n<p><span style=\"text-decoration: underline;\">Product Information &amp; Inquiries<\/span><\/p>\n<p>For more details on C.I. Takiron\u2019s micro motor products, please visit the website below.<\/p>\n<ul>\n<li><strong> Product Site:<\/strong><a href=\"https:\/\/cik-ele.com\/en\/\"> https:\/\/cik-ele.com\/en\/<\/a><\/li>\n<li><strong> Coreless Motors:<\/strong><a href=\"https:\/\/cik-ele.com\/en\/products\/list\/coreless-motors-en\/\"> https:\/\/cik-ele.com\/en\/products\/list\/coreless_motor\/<\/a><\/li>\n<li><strong> Brushless Motors:<\/strong><a href=\"https:\/\/cik-ele.com\/en\/products\/list\/brushless_motors-en\/\"> https:\/\/cik-ele.com\/en\/products\/list\/brushless_motor\/<\/a><\/li>\n<li><strong> Geared Motors:<\/strong><a href=\"https:\/\/cik-ele.com\/en\/products\/list\/gearheads-en\/\"> https:\/\/cik-ele.com\/en\/products\/list\/gearhead\/<\/a><\/li>\n<li><strong> Encoders:<\/strong><a href=\"https:\/\/cik-ele.com\/en\/products\/list\/encoders-en\/\"> https:\/\/cik-ele.com\/en\/products\/list\/encoder\/<\/a><\/li>\n<\/ul>\n<p>If you are having trouble selecting a small motor for your product development, please feel free to contact us via the inquiry form. Our technical staff will discuss your application and requirements with you and propose the optimal solution.<\/p>\n<ul>\n<li><strong> Inquiries:<\/strong><a href=\"https:\/\/cik-ele.com\/en\/contact\/\"> https:\/\/cik-ele.com\/en\/contact\/<\/a><\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Moment of inertia is a physical quantity that indicates how easily a rotating object can be set in motion or brought to a stop, and it is an essential factor in motor design calculations. During motor selection, it is necessary to correctly calculate the load\u2019s moment of inertia and estimate the required torque and acceleration\/deceleration performance. If the moment of inertia is estimated incorrectly, depending on the motor type and operating conditions, this can lead to overshoot or undershoot during startup and stopping, control instability, or even operational failure. In this article, we will explain step-by-step everything from the basic definition of moment of inertia and its relationship to torque, to calculation formulas for typical motor configurations, and key points&#8230;<\/p>\n","protected":false},"author":8,"featured_media":11142,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_themeisle_gutenberg_block_has_review":false,"footnotes":""},"categories":[172],"tags":[253,446,447,531,608,618,784,785,786,787],"class_list":["post-11101","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-column","tag-coreless-motor","tag-torque","tag-rotational-motion","tag-motor","tag-geared-motor","tag-reduction-ratio","tag-moment-of-inertia","tag-angular-acceleration","tag-load-moment-of-inertia","tag-inertia-ratio"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.9 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>What Is Moment of Inertia? Calculation Formulas and Selection Criteria for Motor Design\uff5cC.I. TAKIRON Corporation. Micro motor product site.<\/title>\n<meta name=\"description\" content=\"\u00a0Motor shafts, which play a vital role in diverse fields such as industrial equipment, medical equipment, and automotive parts, are critical components that accurately transmit the rotational motion of a motor. To maximize motor performance, appropriate shape design tailored to the application, careful material selection, and high-precision machining techniques are essential.\u00a0In this article, we provide a detailed explanation of information that engineers can utilize in their daily work, covering everything from the basic roles and structure of motor shafts to representative types such as straight and stepped shapes, material properties of S45C and SCM, and major manufacturing processes such as turning and grinding.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"http:\/\/cxubw72.secure.ne.jp\/en\/column\/moment-of-inertia\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"What Is Moment of Inertia? Calculation Formulas and Selection Criteria for Motor Design\uff5cC.I. 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