{"id":3612,"date":"2026-10-21T23:47:00","date_gmt":"2026-10-21T15:47:00","guid":{"rendered":"http:\/\/www.coffeevsteaweightloss.com\/blog\/?p=3612"},"modified":"2026-10-21T23:47:00","modified_gmt":"2026-10-21T15:47:00","slug":"how-to-calculate-the-back-emf-of-a-permanent-magnet-dc-motor-4b80-429a21","status":"publish","type":"post","link":"http:\/\/www.coffeevsteaweightloss.com\/blog\/2026\/10\/21\/how-to-calculate-the-back-emf-of-a-permanent-magnet-dc-motor-4b80-429a21\/","title":{"rendered":"How to calculate the back &#8211; EMF of a Permanent Magnet DC Motor?"},"content":{"rendered":"<p>Hey there! If you\u2019ve ever dug into how permanent magnet DC motors (PMDC motors) actually work, you\u2019ve probably heard the term \u201cback-EMF\u201d thrown around. As someone who\u2019s been supplying PMDC motors for almost a decade now\u2014stuff from small 12V units for electric scooter controllers to 48V motors for automated conveyor belts\u2014I get it: a lot of folks new to motor design or just picking a motor for their project freeze up when they see that acronym. No need to stress, though. Today, I\u2019m walking you through how to calculate back-EMF, why it matters, and even how knowing this number can help you pick the right motor for your next job. <a href=\"https:\/\/www.auricmotor.com\/dc-motor\/permanent-magnet-dc-moto\/\">Permanent Magnet DC Moto<\/a><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.auricmotor.com\/uploads\/43962\/small\/1-hp-permanent-magnet-dc-motor-1023825.jpg\"><\/p>\n<p>First, let\u2019s cut through the jargon a little. Back-EMF stands for \u201cback electromotive force\u201d (some people just call it \u201ccounter-EMF\u201d too, same thing). Here\u2019s the quick, no-science-degree breakdown: when electricity flows through a PMDC motor\u2019s armature (the rotating part with wires), it creates a magnetic field that pushes the armature\u2019s magnets (the permanent ones, duh) to spin. But as the armature spins, those wires cutting through the permanent magnets\u2019 magnetic field generate their own voltage\u2014opposite to the voltage you\u2019re feeding into the motor. That\u2019s back-EMF. It\u2019s like the motor\u2019s own internal resistance to how fast you\u2019re trying to make it spin. Why does this matter? Well, if you don\u2019t calculate it right, you might end up with a motor that draws way too much current, overheats, or even burns out. And trust me, as a supplier, nothing\u2019s worse than a customer bringing back a motor that fried three weeks after install because they skipped this step.<\/p>\n<p>So, how do you actually calculate it? Let\u2019s start with the basic formula\u2014it\u2019s way simpler than you think, I promise. The standard equation for back-EMF (usually written as E_b) is:<\/p>\n<p>E_b = K * \u03a6 * N<\/p>\n<p>Wait, hold on, what do all those letters mean? Let\u2019s break \u2019em down:<\/p>\n<ul>\n<li>K is the \u201cback-EMF constant\u201d (sometimes called the speed constant, or K_e\u2014don\u2019t confuse this with torque constant, K_t; in PMDC motors, K_e and K_t are actually the same number, weirdly enough)<\/li>\n<li>\u03a6 is the magnetic flux from the permanent magnets in the motor, measured in webers (Wb)<\/li>\n<li>N is the speed of the armature, measured in revolutions per minute (RPM) or sometimes radians per second (rad\/s)\u2014you gotta keep your units consistent here, that\u2019s the big mistake people make.<\/li>\n<\/ul>\n<p>Wait, let\u2019s make that more practical, because not everyone\u2019s got a flux meter lying around. For most off-the-shelf PMDC motors (the kind we supply), manufacturers will give you the K value either in V per 1000 RPM or in V\u00b7s\/rad. That\u2019s way easier to work with than flux, because \u03a6 is fixed for a permanent magnet motor\u2014those magnets don\u2019t change (unless you overheat them, which is bad, but that\u2019s another topic). So if your supplier (hey, that\u2019s us!) gives you K as V\/1000 RPM, the formula simplifies even more: E_b = (K * N) \/ 1000. Let\u2019s test that with a real example from a motor I stocked last month. Say we\u2019ve got a 24V PMDC motor with a K value of 0.12 V\/1000 RPM. If it\u2019s spinning at 2000 RPM, what\u2019s E_b? Plug in the numbers: (0.12 * 2000) \/ 1000 = 0.24? Wait, no\u2014wait, no, hold on, I messed up the decimal. Wait, no, K here is 0.12 V per 1000 RPM, so per RPM it\u2019s 0.00012 V. So 2000 RPM * 0.00012 V\/RPM = 0.24 V? No, that can\u2019t be right\u2014wait, no, I picked a bad K value. Let\u2019s correct that: a typical 24V PMDC motor for a small conveyor has a K of about 7.5 V per 1000 RPM. That makes more sense. Let\u2019s recalculate: (7.5 * 2000) \/ 1000 = 15 V. There we go, that\u2019s realistic. See? That\u2019s easy.<\/p>\n<p>Now, why does this number matter beyond just math class? Let\u2019s tie it to real-world use cases. Take that same 24V, 15V back-EMF at 2000 RPM motor. The rest of the voltage (24V &#8211; 15V = 9V) is what\u2019s driving the current through the armature\u2019s windings. Ohm\u2019s Law here: current I = (V_supply &#8211; E_b) \/ R_a, where R_a is the armature resistance. So if the motor is running at full speed, E_b is high, so current is low\u2014perfect, that\u2019s efficient. But if the motor is stalled (not spinning at all, like if a conveyor belt is jammed), E_b is zero. Then current is (24V &#8211; 0)\/R_a. If R_a is, say, 0.5 ohms, that\u2019s 48 amps\u2014way more than the motor\u2019s rated current of 5 amps. That\u2019s why stalled motors burn out! So calculating E_b helps you figure out how much current your motor will draw, how big your power supply needs to be, and even if you need a stall protection feature (like a current limiter) for your application.<\/p>\n<p>Another thing to keep in mind: the back-EMF constant isn\u2019t just a random number stamped on the motor\u2019s label. It depends on how the motor is wound. When we wind the armature, we\u2019re choosing how many turns of copper wire to use. More turns mean a higher K value\u2014so for the same speed, E_b is higher. That also means lower current for the same supply voltage, but the motor will be slower for the same voltage. Fewer turns mean lower K, so faster speed, higher current. That\u2019s why a motor made for a remote control car (high speed, low torque) has a different K than a motor made for a lift (low speed, high torque). As a supplier, we work with customers all the time to adjust the winding if they need a specific K\u2014like if you have a custom application where standard motors don\u2019t hit the exact E_b you need, we can rewind or spec a different magnet grade to tweak \u03a6, which changes E_b too.<\/p>\n<p>Wait, let\u2019s address a common mistake people make when calculating E_b: mixing units. If K is in V per radian per second (V\u00b7s\/rad), you need to convert N (RPM) to rad\/s. How? Multiply RPM by (2\u03c0)\/60. So for that 2000 RPM example, 2000 * (2\u03c0\/60) \u2248 209.44 rad\/s. If K is 0.0358 V\u00b7s\/rad (which is the same as 7.5 V\/1000 RPM, just converted), then E_b = 0.0358 * 209.44 \u2248 7.5 V? Wait no, wait 2000 RPM gives E_b 15V, so K would be 0.0716 V\u00b7s\/rad. Yeah, unit conversion is where half the folks I talk to mess up. So make sure you\u2019re either using RPM with V\/1000 RPM, or rad\/s with V\u00b7s\/rad\u2014don\u2019t mix the two, that\u2019ll give you a number that\u2019s way too high or way too low, and that\u2019s how you get a motor that doesn\u2019t work.<\/p>\n<p>Let\u2019s throw in a quick troubleshooting example, since that\u2019s something customers reach out about all the time. Say you installed a PMDC motor, and it\u2019s running slower than it should. You check the supply voltage, it\u2019s correct. So you calculate E_b: motor K is 7.5 V\/1000 RPM, actual speed is 1800 RPM. So E_b = (7.5 * 1800)\/1000 = 13.5 V. Then current is (24 &#8211; 13.5)\/0.5 = 21 A, which is 4x the rated current. Why is the speed low? Maybe the permanent magnets got demagnetized from overheating (say, you ran the motor continuously without ventilation, or it got too hot near a welding station). Demagnetized magnets mean lower \u03a6, so lower E_b\u2014so the motor draws more current, gets even hotter, demagnetizes more, it\u2019s a vicious cycle. Calculating E_b would tell you that the magnet strength is off, so you can replace the magnets or get a new motor from us with higher-grade magnets to fix that.<\/p>\n<p>Here\u2019s a pro tip from someone who\u2019s sold PMDC motors for years: if you\u2019re not sure about K, you can measure E_b yourself without fancy tools. Take the motor, disconnect it from the power supply, and spin the armature with a drill or some other power tool (make sure it\u2019s spinning at a known speed\u2014you can use a tachometer, even a phone app works). Then touch a multimeter to the motor\u2019s terminals (set it to DC voltage). The voltage you read is your E_b! That\u2019s way easier than calculating if you don\u2019t have the motor\u2019s specs on hand. We do this all the time for customers who get a used motor or a motor without a label\u2014just spin it, measure, and you\u2019ve got E_b.<\/p>\n<p>Now, let\u2019s talk about how this ties to choosing a motor as a buyer. If you know you need a motor that runs at, say, 3000 RPM with E_b of 18V, your supply voltage should be a little higher than that\u2014like 20V, to give you enough current to drive the load. If you pick a motor with a K that\u2019s too high, E_b will be too high, so your current will be too low, and the motor won\u2019t have enough torque to move your load. Too low a K, and E_b will be too low, current will be too high, and you\u2019ll waste energy or burn out the motor. That\u2019s where we come in: as a PMDC motor supplier, we can help you match the right K, right E_b, right magnet grade, all based on your load, speed, and power needs.<\/p>\n<p>Wait, let\u2019s make sure we\u2019re not leaving out edge cases. What about brushless PMDC motors? Oh, right, sometimes people mix up brushed and brushless, but brushless ones also have back-EMF, it\u2019s just three-phase, so the formula is a little different, but for the brushed ones we mostly supply (for robotics, small appliances, material handling), the formula we talked about works perfectly. And for brushless, the same logic applies\u2014E_b is what limits current at speed, so you still need to calculate it for control systems, just with a three-phase adjustment factor.<\/p>\n<p>Another real-world example: I had a customer last year who was building a small automated door for a greenhouse. They picked a random 12V PMDC motor, plugged it in, and the door moved too slow. They came to us, and we calculated E_b: the motor\u2019s K was 12 V\/1000 RPM, so at 12V supply, E_b would be almost 12V at full speed, so almost no current. We swapped it for a motor with K of 6 V\/1000 RPM, so E_b at 1000 RPM was 6V, current was (12-6)\/0.5 = 12A, which had enough torque to lift the door. That was a $50 fix, but if they\u2019d kept going with the wrong motor, they would\u2019ve wasted hours and money on troubleshooting.<\/p>\n<p>Now, let\u2019s wrap this up so it\u2019s useful for you, not just a bunch of numbers. Calculating back-EMF for a PMDC motor boils down to three simple steps:<\/p>\n<ol>\n<li>Grab the motor\u2019s back-EMF constant (K) from its specs sheet\u2014look for V per 1000 RPM or V\u00b7s\/rad.<\/li>\n<li>Get your desired or actual motor speed (N, RPM or rad\/s).<\/li>\n<li>Plug into E_b = K * N (with correct units) to get your number.<\/li>\n<\/ol>\n<p>Remember, E_b is your motor\u2019s built-in speed limiter, it\u2019s key to calculating current, torque, and avoiding burnout. And if you\u2019re not a numbers person, that\u2019s okay\u2014we\u2019re here to help. Whether you need a motor for a conveyor, a scooter, a robotics arm, or a greenhouse door, we can walk you through calculating E_b, matching the right specs, and making sure you get a motor that works for your exact project. No guesswork, no jargon, just straight-up advice from someone who\u2019s been in the motor game for years.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.auricmotor.com\/uploads\/43962\/small\/parallel-shaft-geared-motor21ff9.jpg\"><\/p>\n<p>If you\u2019re ready to stop guessing and get the right PMDC motor for your needs, reach out to our team for a consultation\u2014we\u2019ll break down all the math, answer your questions, and help you pick or customize a motor that hits your back-EMF, speed, and torque requirements. No more burnt motors, no more underperforming gear, just a solution that works.<\/p>\n<p><a href=\"https:\/\/www.auricmotor.com\/dc-motor\/permanent-magnet-dc-moto\/\">Permanent Magnet DC Moto<\/a> References<\/p>\n<ol>\n<li>Fitzgerald, A. E., Kingsley, C., &amp; Umans, S. D. (2003). Electric Machinery (6th ed.). McGraw-Hill.<\/li>\n<li>Boldea, I. (2006). Electric Motor Drives: Modeling, Analysis, and Control. CRC Press.<\/li>\n<li>Permanent Magnet DC Motor Application Guide. (2021). Industrial Motor Manufacturers Association.<\/li>\n<\/ol>\n<hr>\n<p><a href=\"https:\/\/www.auricmotor.com\/\">Zibo Auric Mechanical and Electrical Technology Co., Ltd.<\/a><br \/>As one of the leading permanent magnet dc moto manufacturers and suppliers in China, we warmly welcome you to buy advanced permanent magnet dc moto for sale here from our factory. All customized motors are with high quality and competitive price.<br \/>Address: B419, High-tech Entrepreneurship Park, High-tech Zone, Zibo City<br \/>E-mail: cui@auricmotor.com<br \/>WebSite: <a href=\"https:\/\/www.auricmotor.com\/\">https:\/\/www.auricmotor.com\/<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Hey there! If you\u2019ve ever dug into how permanent magnet DC motors (PMDC motors) actually work, &hellip; <a title=\"How to calculate the back &#8211; EMF of a Permanent Magnet DC Motor?\" class=\"hm-read-more\" href=\"http:\/\/www.coffeevsteaweightloss.com\/blog\/2026\/10\/21\/how-to-calculate-the-back-emf-of-a-permanent-magnet-dc-motor-4b80-429a21\/\"><span class=\"screen-reader-text\">How to calculate the back &#8211; EMF of a Permanent Magnet DC Motor?<\/span>Read more<\/a><\/p>\n","protected":false},"author":974,"featured_media":3612,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[3575],"class_list":["post-3612","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-industry","tag-permanent-magnet-dc-moto-44b9-4359a7"],"_links":{"self":[{"href":"http:\/\/www.coffeevsteaweightloss.com\/blog\/wp-json\/wp\/v2\/posts\/3612","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.coffeevsteaweightloss.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.coffeevsteaweightloss.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.coffeevsteaweightloss.com\/blog\/wp-json\/wp\/v2\/users\/974"}],"replies":[{"embeddable":true,"href":"http:\/\/www.coffeevsteaweightloss.com\/blog\/wp-json\/wp\/v2\/comments?post=3612"}],"version-history":[{"count":0,"href":"http:\/\/www.coffeevsteaweightloss.com\/blog\/wp-json\/wp\/v2\/posts\/3612\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/www.coffeevsteaweightloss.com\/blog\/wp-json\/wp\/v2\/posts\/3612"}],"wp:attachment":[{"href":"http:\/\/www.coffeevsteaweightloss.com\/blog\/wp-json\/wp\/v2\/media?parent=3612"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.coffeevsteaweightloss.com\/blog\/wp-json\/wp\/v2\/categories?post=3612"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.coffeevsteaweightloss.com\/blog\/wp-json\/wp\/v2\/tags?post=3612"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}