{"id":1266,"date":"2025-02-18T08:22:00","date_gmt":"2025-02-18T14:22:00","guid":{"rendered":"http:\/\/blog.misumiusa.com\/?p=1266"},"modified":"2025-02-18T15:49:51","modified_gmt":"2025-02-18T21:49:51","slug":"understanding-gear-tooth-profile-gear-module-formula","status":"publish","type":"post","link":"https:\/\/us.misumi-ec.com\/blog\/understanding-gear-tooth-profile-gear-module-formula\/","title":{"rendered":"Spur Gear Tooth Geometry: Understanding Gear Module and Pitch Diameter"},"content":{"rendered":"\n<p><em><strong>Updated on February 18th, 2025<\/strong><\/em><\/p>\n\n\n\n<p>The geometry of a simple <a href=\"http:\/\/us.misumi-ec.com\/vona2\/mech\/M1000000000\/M1006000000\/M1006010000\/\" target=\"_blank\" rel=\"noopener noreferrer\">spur gear tooth<\/a> is complex. Numerous dimensional parameters define the shape of the tooth profile, determine how the gears fit together, and identify locations where forces act at the gear teeth.<\/p>\n\n\n\n<h2>Gear Profile: Pitch Diameter and Module<\/h2>\n\n\n\n<p>Two of the most important parameters that are often confused with each other are:&nbsp;<\/p>\n\n\n\n<ul><li>The pitch diameter (or thread pitch diameter), typically denoted as (d)<\/li><li>The module (or modulus), typically denoted as (m)<\/li><\/ul>\n\n\n\n<h2>What is Pitch Diameter?\u00a0<\/h2>\n\n\n\n<p>The pitch diameter is the diameter of an invisible cylinder that would pass through approximately the \u201cmiddle\u201d of gear teeth, defining what\u2019s commonly referred to as the \u201cpitch circle.&#8221; This pitch circle is defined as the circle centered at the gear axis that goes through the pitch point at the spur gear teeth.<\/p>\n\n\n\n<p>This pitch point is located between the root of the spur gear tooth, which denotes the minor diameter, and the crest of the spur gear tooth, which denotes the major diameter of the spur gear tooth. This diameter is relatively easy to spot in typical <a href=\"https:\/\/www.agma.org\/\" target=\"_blank\" rel=\"noopener noreferrer\">American Gear Manufacturer\u2019s Association<\/a> (AGMA) standard gear sizes because it\u2019s quoted as a diameter somewhere in between the minor and major diameters of the gear.<\/p>\n\n\n\n<p>The pitch diameter also defines the approximate mating envelope of two gears, meaning that the teeth will mesh along the pitch diameter. In this way, it also defines an important concept called the line of action or pressure line. This line defines the direction of the force acting on each tooth. The pitch diameter also forms the basis on which the pressure angle of the tooth, the tooth thickness, and the helix angle of the gear are defined.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" src=\"https:\/\/blog.misumiusa.com\/wp-content\/uploads\/2025\/02\/1.png\" alt=\"graphic of gears meshing at the pitch circle misumi \" class=\"wp-image-14233\" width=\"593\" height=\"421\"\/><\/figure><\/div>\n\n\n\n<p>Unfortunately, pitch diameter cannot be measured directly on a physical gear. Typically, an adequate approximation of the pitch diameter measurements can be obtained by measuring with calipers across two <a href=\"https:\/\/us.misumi-ec.com\/vona2\/maker\/misumi\/mech\/M1800000000\/M1807000000\/?srsltid=AfmBOoq_Atty-b1b_ME4CxJuMtuNYZBlfizit0GzoGstp9ceOLLCFNA3\" title=\"\">dowel pins<\/a> placed in between the teeth of the gear at opposite locations on the gear.<\/p>\n\n\n\n<p>To arrive at an estimate of the pitch diameter, the diameter of one of the pins is subtracted from the measurement obtained by the calipers.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" src=\"https:\/\/blog.misumiusa.com\/wp-content\/uploads\/2025\/02\/2.png\" alt=\"\" class=\"wp-image-14234\" width=\"789\" height=\"561\"\/><\/figure><\/div>\n\n\n\n<p>This is part of the reason why the concept of the module (m) of the gear was introduced. Quite simply, it\u2019s the ratio of the pitch diameter (d) to the number of teeth (N) on the gear:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter is-resized\"><a href=\"http:\/\/blog.misumiusa.com\/wp-content\/uploads\/2015\/07\/gear-module-formula.png\"><img loading=\"lazy\" src=\"http:\/\/blog.misumiusa.com\/wp-content\/uploads\/2015\/07\/gear-module-formula.png\" alt=\"gear module formula\" class=\"wp-image-1270\" width=\"247\" height=\"204\" srcset=\"https:\/\/us.misumi-ec.com\/blog\/wp-content\/uploads\/2015\/07\/gear-module-formula.png 180w, https:\/\/us.misumi-ec.com\/blog\/wp-content\/uploads\/2015\/07\/gear-module-formula-150x124.png 150w\" sizes=\"(max-width: 247px) 100vw, 247px\" \/><\/a><\/figure><\/div>\n\n\n\n<h2>What is a Gear Module?<\/h2>\n\n\n\n<p>The module is typically quoted in standardized gear sizing charts with implied units of length, either (mm) for SI units or (in) for BG units. In a sense, it\u2019s a measure of the unit size of the gear on the basis of the number of teeth present on the gear.<\/p>\n\n\n\n<p>A useful analogy is that the module defines the \u201csize\u201d of each tooth as a portion of the pitch diameter \u201cpie.\u201d This means that each tooth possesses a \u201cmodule\u201d unit of the portion of the total pitch diameter. For example, a gear that possesses a module of 10 (quoted in SI units) quite literally means that each tooth \u201cuses\u201d 10 (mm) of the total pitch diameter.<\/p>\n\n\n\n<p>In this way, the module is an easy parameter to use to determine if two gears of differing pitch diameters will be able to mate together; two gears with different modules will not mate together because the unit size of the gear, as discussed above, must match in order for gears to mate together.<\/p>\n\n\n\n<p>Finally, given only the gear module, a number of other geometric gear parameters can be calculated, such as diametric pitch and circular pitch. Both gear pitch diameter and gear module are two related yet distinct parameters that are very useful to know for gear selection and sizing, as international gear standards and general design disciplines now rely heavily on the use of these parameters.<\/p>\n\n\n\n<h2>Pitch Diameter and Module: Why They Matter<\/h2>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" src=\"https:\/\/blog.misumiusa.com\/wp-content\/uploads\/2025\/02\/110300428430_20210319140906.jpg\" alt=\"MISUMI Spur Gears - Pressure Angle 20 Degrees, Module 1.0\" class=\"wp-image-14238\" width=\"223\" height=\"223\"\/><figcaption><a href=\"https:\/\/us.misumi-ec.com\/vona2\/detail\/110300428430\/\">MISUMI Spur Gears &#8211; Pressure Angle 20 Degrees, Module 1.0<\/a><\/figcaption><\/figure><\/div>\n\n\n\n<p>The pitch diameter and module are two fundamental yet distinct parameters that play a critical role in gear design and functionality. The pitch diameter defines an imaginary reference circle that governs how gears mesh, while the module provides a standardized way to determine gear size based on the number of teeth. <\/p>\n\n\n\n<p>Understanding these parameters ensures proper gear selection, compatibility, and efficient power transmission. While the pitch diameter cannot be directly measured, the module offers a practical approach for assessing gear compatibility. <\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><a href=\"https:\/\/us.misumi-ec.com\/vona2\/mech\/M1000000000\/M1006000000\/M1006010000\/\"><img loading=\"lazy\" src=\"https:\/\/blog.misumiusa.com\/wp-content\/uploads\/2025\/02\/Copy-of-Copy-of-Copy-of-Copy-of-Copy-of-Copy-of-Shop-Punch-Die-Components-1.png\" alt=\"\" class=\"wp-image-14237\" width=\"200\" height=\"63\"\/><\/a><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Here is everything you need to know about two of the most important spur gear tooth parameters: the pitch diameter and the module.<\/p>\n","protected":false},"author":46,"featured_media":14239,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"om_disable_all_campaigns":false},"categories":[1136],"tags":[191],"aioseo_notices":[],"gutentor_comment":2,"_links":{"self":[{"href":"https:\/\/us.misumi-ec.com\/blog\/wp-json\/wp\/v2\/posts\/1266"}],"collection":[{"href":"https:\/\/us.misumi-ec.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/us.misumi-ec.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/us.misumi-ec.com\/blog\/wp-json\/wp\/v2\/users\/46"}],"replies":[{"embeddable":true,"href":"https:\/\/us.misumi-ec.com\/blog\/wp-json\/wp\/v2\/comments?post=1266"}],"version-history":[{"count":5,"href":"https:\/\/us.misumi-ec.com\/blog\/wp-json\/wp\/v2\/posts\/1266\/revisions"}],"predecessor-version":[{"id":14241,"href":"https:\/\/us.misumi-ec.com\/blog\/wp-json\/wp\/v2\/posts\/1266\/revisions\/14241"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/us.misumi-ec.com\/blog\/wp-json\/wp\/v2\/media\/14239"}],"wp:attachment":[{"href":"https:\/\/us.misumi-ec.com\/blog\/wp-json\/wp\/v2\/media?parent=1266"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/us.misumi-ec.com\/blog\/wp-json\/wp\/v2\/categories?post=1266"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/us.misumi-ec.com\/blog\/wp-json\/wp\/v2\/tags?post=1266"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}