{"id":3495,"date":"2026-10-08T15:48:17","date_gmt":"2026-10-08T07:48:17","guid":{"rendered":"http:\/\/www.amaroneonline.com\/blog\/?p=3495"},"modified":"2026-10-08T15:48:17","modified_gmt":"2026-10-08T07:48:17","slug":"how-to-calculate-the-electrical-time-constant-of-a-permanent-magnet-dc-motor-47c3-175e4f","status":"publish","type":"post","link":"http:\/\/www.amaroneonline.com\/blog\/2026\/10\/08\/how-to-calculate-the-electrical-time-constant-of-a-permanent-magnet-dc-motor-47c3-175e4f\/","title":{"rendered":"How to calculate the electrical time constant of a Permanent Magnet DC Motor?"},"content":{"rendered":"

Hey everyone, it\u2019s Jake here, and if you\u2019ve ever worked with PMDC motors (that\u2019s Permanent Magnet DC motors, for anyone new to the space), you\u2019ve probably run into the term \u201celectrical time constant\u201d before. Maybe you saw it on a spec sheet, or a design engineer asked you to calculate it for a custom project, and you were like\u2026 \u201cWait, what even is that again, and why does it matter so much?\u201d Trust me, I\u2019ve been there. Back when I first started out in the motor supply game, I\u2019d skip over that number all the time\u2014until a client came to me with a prototype that kept burning out drives, and it turned out I\u2019d misjudged the time constant by a mile. Lesson learned. Now, I\u2019m gonna break this down like I explain it to my interns, no overly complicated jargon, just real stuff that actually works when you\u2019re working with our PMDC motors. Permanent Magnet DC Moto<\/a><\/p>\n

<\/p>\n

First, let\u2019s get the basics out of the way. The electrical time constant (we usually just call it \u03c4_e, pronounced \u201ctau e\u201d around the shop) is basically the speed at which the current in the motor\u2019s windings reacts to changes in voltage. Think of it like this: when you flip a switch to power up a motor, the windings (which are just coils of copper wire) don\u2019t just jump to full current instantly. It takes a tiny bit of time for current to build up, and \u03c4_e is how long that takes. If you\u2019re using a motor in a fast-paced application\u2014like a robotic arm that needs to snap into position, or a power window motor that has to roll up in half a second\u2014this number is non-negotiable. Get it wrong, and your control system might lag, or even blow your motor\u2019s driver. That\u2019s why every engineer worth their salt cares about this, and as a PMDC motor supplier, it\u2019s one of the first questions I get when a client is spec\u2019ing a new unit.<\/p>\n

Now, let\u2019s get to the actual math. I know, I know\u2014math sounds scary, but stick with me. It\u2019s super straightforward, and I\u2019ll tie it back to our motors so it\u2019s not just a random formula. The electrical time constant for a PMDC motor is calculated using two key values: the armature inductance (let\u2019s call that L, measured in henries, or H for short) and the armature resistance (R, measured in ohms, \u03a9). The formula is just \u03c4_e = L \/ R. That\u2019s it. Two numbers, divide \u2019em, and you\u2019ve got your time constant. Wait, that\u2019s way simpler than I thought, right? But hold up\u2014you can\u2019t just grab any L or R, you need the right ones for the armature, which is the part of the motor that spins and carries current. No mixing up stator values or anything, that\u2019s a common rookie mistake.<\/p>\n

Let me break down what L and R actually are for our PMDC motors, because that\u2019s where a lot of people go wrong with the calculation. Armature resistance R is the total electrical resistance of the copper windings in the armature, right? This changes a tiny bit with temperature\u2014copper gets more resistant when it\u2019s hot, so we usually use the rated 25\u00b0C value from the motor\u2019s spec sheet for \u03c4_e calculations, unless you\u2019re working in extreme temp conditions, then you have to adjust it. For our standard PMDC motors, we test each unit\u2019s R during manufacturing, so you can always find that number on the spec sheet we send out when you request a quote. No guessing there.<\/p>\n

Then there\u2019s armature inductance L. That\u2019s the property of the windings that resists changes in current\u2014so that\u2019s what makes the current take time to build up, which is exactly what \u03c4_e is measuring. Inductance for PMDC motors depends on how many turns of wire are in the armature, the size of the wire, and the gap between the armature and the permanent magnets (which are fixed in the stator of a PMDC motor, unlike brushed DC motors that might have field windings). Again, for our motors, we test L with an inductance meter, so it\u2019s also on the spec sheet\u2014no need to calculate L from scratch, which is a huge relief. If you\u2019re using an off-the-shelf motor, that\u2019s easy, but if you\u2019re spec\u2019ing a custom one, we can run the L and R tests before we finalize the design, so you don\u2019t have to wait around.<\/p>\n

Wait, let\u2019s test this with an actual example from our shop, because that makes it real. Let\u2019s say we have a standard 12V PMDC motor we supply for small automation tasks. Its spec sheet says armature resistance R is 0.5 \u03a9, and armature inductance L is 0.002 H. Plugging into the formula: \u03c4_e = 0.002 \/ 0.5 = 0.004 seconds, or 4 milliseconds. That means it takes 4 milliseconds for the current to reach ~63% of its maximum value when we apply rated voltage. If you\u2019ve got a motor that needs to respond in less than 10 ms, this one\u2019s perfect. If you need something faster, we can tweak the winding design to lower L or R, which would bring \u03c4_e down. For a comparison, a larger PMDC motor for conveyor systems might have R = 0.2 \u03a9, L = 0.01 H, so \u03c4_e = 0.01 \/ 0.2 = 0.05 seconds, or 50 ms\u2014slower, but that makes sense for a heavy load that doesn\u2019t need to snap around fast.<\/p>\n

But hold up\u2014there\u2019s a common mistake here: mixing up electrical time constant with mechanical time constant. That\u2019s another number, \u03c4_m, which is about how fast the motor\u2019s shaft speed reacts, not current. New engineers especially mix these up, so let\u2019s clarify that right now. \u03c4_e is all about current rise time, \u03c4_m is about speed. For our 12V example, \u03c4_m would be a lot bigger\u2014like, maybe 0.2 seconds or something, because it includes the motor\u2019s inertia and torque. You don\u2019t calculate \u03c4_m with L and R, it uses Kt (torque constant) and J (inertia), so don\u2019t plug those numbers into the \u03c4_e formula. I can\u2019t tell you how many times I\u2019ve gotten an email from a client asking \u201cwait, why is your time constant different from what I calculated?\u201d and it\u2019s because they mixed up e and m. Don\u2019t do that, it\u2019ll save you hours of headaches.<\/p>\n

Another thing: why does this actually matter for your application? Let\u2019s go back to that client I mentioned earlier, the one with the burning drives. They were using a small PMDC motor for a pick-and-place robot, and they calculated \u03c4_e as 0.002 seconds, but they used the wrong R value\u2014they used the terminal resistance instead of the armature resistance, which is about 10% higher because of the brushes. Wait, right! Brushed PMDC motors have brushes that make contact with the commutator, so there\u2019s a small contact resistance in addition to the winding resistance. That\u2019s not included in the armature R from the windings, so if you just measure the resistance between the two motor terminals with a multimeter, that\u2019s the total terminal resistance, which is a tiny bit higher than the actual armature R we use for \u03c4_e. That client used the multimeter reading, which was 0.55 \u03a9 instead of our tested armature R of 0.5 \u03a9, so they calculated \u03c4_e as 0.002 \/ 0.55 = ~0.0036 seconds, which was almost the same, but when they ran the robot at full speed, the current spiked because they didn\u2019t account for the fact that \u03c4_e tells you how much current is flowing at a given time. If your drive is tuned for a \u03c4_e that\u2019s lower than the real one, it\u2019ll send too much current too fast, frying the drive or even the motor windings. That\u2019s why using the tested values from the motor\u2019s spec sheet is non-negotiable\u2014we list both terminal resistance and armature resistance on all our spec sheets, so you can pick the right one for \u03c4_e.<\/p>\n

Also, if you\u2019re designing a control system for your motor, the electrical time constant is a key factor in choosing the PWM (pulse-width modulation) frequency. PWM is what most motor drives use to control speed, right? They switch the voltage on and off really fast. If your PWM frequency is too close to 1\/\u03c4_e, you\u2019ll get current ripple that causes extra heat and wears out the motor faster. For our 12V motor with \u03c4_e = 4 ms, 1\/\u03c4_e is 250 Hz, so you\u2019d want to run your PWM at least 5 times that, like 1-2 kHz, to keep the ripple low. We always include a recommendation for PWM frequency on our custom motor quotes, based on the \u03c4_e we calculate for that specific unit, so you don\u2019t have to guess. That\u2019s the kind of value add we bring as a supplier\u2014we don\u2019t just sell motors, we give you the data you need to make your system work.<\/p>\n

Wait, what if you don\u2019t have the spec sheet? Maybe you have an old motor, or a prototype you\u2019re testing, and you need to calculate \u03c4_e without the L and R values. Is there a way to measure it, not just calculate it? Yeah, that\u2019s a good question, and I get asked that a lot. The direct way is to hook up the motor to a power supply that can measure current, apply a step voltage (like jump from 0 to rated voltage instantly), and record the current over time. The current rise will follow an exponential curve: I(t) = I_max * (1 – e^(-t\/\u03c4_e)). So if you wait for t = \u03c4_e, the current will be at ~63% of I_max, like I mentioned earlier. You can plot that current curve, find the time at which it hits 63% of max current, and that\u2019s your \u03c4_e. That\u2019s super easy to do with an oscilloscope and a current probe\u2014no fancy tools needed, just something that can track current over time. We do this test on every motor before it leaves our facility, so we\u2019ve got that data for every unit we ship.<\/p>\n

Another trick: if you know the motor\u2019s no-load current and stalled current, can you get a rough estimate? Maybe, but it\u2019s not as accurate. Stalled current is I_stall = V \/ R, so if you measure I_stall at rated voltage, you can get R = V \/ I_stall. Then L is a bit trickier\u2014you\u2019d need to calculate it from the motor\u2019s back EMF constant, but that\u2019s more involved and can throw off your \u03c4_e if your back EMF constant is off. For most applications, using the tested L and R from the spec sheet is way more reliable than a rough estimate.<\/p>\n

Now, let\u2019s talk about when \u03c4_e is a big deal, and when it\u2019s less so. Like I said earlier, if you\u2019re dealing with a high-speed, high-precision application\u2014robotics, CNC, medical devices, things that need to move fast and accurately\u2014\u03c4_e is critical. If your motor\u2019s \u03c4_e is too high, the current doesn\u2019t build up fast enough, so the motor can\u2019t produce torque when you need it, leading to slow response times or missed positions. On the flip side, if you have a low-speed application, like a door opener or a fan that just needs to turn at a steady speed, \u03c4_e matters way less. Those applications usually run at constant voltage, so the current stabilizes before you need to change anything. That\u2019s why when a client comes to us for a fan motor, we don\u2019t spend a ton of time tweaking \u03c4_e, but for a robotic arm motor, that\u2019s one of the first specs we discuss.<\/p>\n

As a PMDC motor supplier, we pride ourselves on being transparent with this stuff. We don\u2019t hide spec values, we explain what they mean, and we adjust designs to meet your \u03c4_e needs if your application requires it. A lot of big suppliers just send you a spec sheet and say \u201cgood luck,\u201d but we\u2019re here to help. If you\u2019re working on a new project and you need to calculate \u03c4_e, or you\u2019re not sure if the motor you\u2019re using has the right \u03c4_e for your system, just reach out. We can run the tests, adjust the winding design, or even give you a free consultation to make sure everything lines up. I\u2019ve been doing this for 12 years, so I\u2019ve seen every mistake in the book, and I\u2019d rather help you avoid them than have you come back with a broken motor or drive.<\/p>\n

Wait, let\u2019s recap to make sure we didn\u2019t miss anything. The electrical time constant for a PMDC motor is \u03c4_e = L \/ R, where L is armature inductance (henries) and R is armature resistance (ohms). Use the tested values from the motor\u2019s spec sheet, not terminal resistance, to get an accurate number. Don\u2019t mix it up with the mechanical time constant. It\u2019s critical for high-speed, high-precision applications, and it dictates the PWM frequency for your drive. If you need help calculating it, or you\u2019re looking for a PMDC motor that meets your specific \u03c4_e requirements, we\u2019re here to make it easy.<\/p>\n

At the end of the day, this stuff isn\u2019t rocket science, but it\u2019s the difference between a motor that works perfectly in your system and one that causes you headaches for weeks. I\u2019ve spent too many nights troubleshooting drives that blew up because someone messed up \u03c4_e, so trust me when I say getting this right pays off. If you\u2019re working on a new project, or you need to replace an old motor, or you just have questions about time constants or any other motor spec, don\u2019t hesitate to get in touch. We\u2019ll walk you through every step, no jargon, no runaround, just real answers and the right motor for your needs.<\/p>\n

<\/p>\n

And that\u2019s it for today\u2014next time you see \u03c4_e on a spec sheet, you\u2019ll know exactly what it means and how to use it. Hit us up anytime, we\u2019re here to help.<\/p>\n

DC Motor<\/a> References<\/p>\n

    \n
  1. Electrical Machines, Drives, and Power Systems, T. Wildi<\/li>\n
  2. Permanent Magnet DC Motor Design and Application Guide, Electric Power Research Institute<\/li>\n
  3. PMDC Motor Performance Specifications: A Practical Overview, Motion Control Magazine<\/li>\n
  4. Industrial Motor Control, S. Herman<\/li>\n<\/ol>\n
    \n

    Zibo Auric Mechanical and Electrical Technology Co., Ltd.<\/a>
    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.
    Address: B419, High-tech Entrepreneurship Park, High-tech Zone, Zibo City
    E-mail: cui@auricmotor.com
    WebSite:     https:\/\/www.auricmotor.com\/<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

    Hey everyone, it\u2019s Jake here, and if you\u2019ve ever worked with PMDC motors (that\u2019s Permanent Magnet … How to calculate the electrical time constant of a Permanent Magnet DC Motor?<\/span>Read more<\/a><\/p>\n","protected":false},"author":954,"featured_media":3495,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[3458],"class_list":["post-3495","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-industry","tag-permanent-magnet-dc-moto-4c44-183430"],"_links":{"self":[{"href":"http:\/\/www.amaroneonline.com\/blog\/wp-json\/wp\/v2\/posts\/3495","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.amaroneonline.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.amaroneonline.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.amaroneonline.com\/blog\/wp-json\/wp\/v2\/users\/954"}],"replies":[{"embeddable":true,"href":"http:\/\/www.amaroneonline.com\/blog\/wp-json\/wp\/v2\/comments?post=3495"}],"version-history":[{"count":0,"href":"http:\/\/www.amaroneonline.com\/blog\/wp-json\/wp\/v2\/posts\/3495\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/www.amaroneonline.com\/blog\/wp-json\/wp\/v2\/posts\/3495"}],"wp:attachment":[{"href":"http:\/\/www.amaroneonline.com\/blog\/wp-json\/wp\/v2\/media?parent=3495"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.amaroneonline.com\/blog\/wp-json\/wp\/v2\/categories?post=3495"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.amaroneonline.com\/blog\/wp-json\/wp\/v2\/tags?post=3495"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}