To size a motor, you calculate the torque needed to overcome the load at the output shaft, add the torque needed to accelerate the moving mass to speed, add friction losses, then divide by the gear ratio and drivetrain efficiency to get the torque required at the motor itself — and finally multiply by a safety factor for duty cycle and heat. Skipping any one of those terms is why so many first prototypes either stall under load or ship with a motor three times larger and more expensive than necessary. The math is not difficult; the discipline is in listing every contribution honestly, and it is one of the most common mechanical engineering tasks in a new product.

What required torque is actually made of

Torque is force multiplied by the distance from the axis of rotation. In a real mechanism it comes from four sources that add together:

  • Static load torque. Whatever the motor must hold or move against — gravity on a lifted arm, a spring being compressed, material being cut, a lid being pushed shut. For a rotating arm, this is the weight of the load times the horizontal distance from the pivot, and it peaks when the arm is horizontal.
  • Friction torque. Bearings, seals, guide rails, gear meshes, and belts all consume torque before any useful work happens. In small, low-load mechanisms friction is often the dominant term, and it is the one designers most often ignore.
  • Acceleration torque. Getting mass moving takes torque proportional to the moment of inertia divided by the time you allow. A mechanism that must reach speed in a tenth of a second needs far more torque than the same mechanism given a full second.
  • Breakaway torque. Static friction exceeds running friction, and grease is stiff when cold. The torque needed to start moving is always higher than the torque needed to keep moving.

The calculation, step by step

  1. Define the duty precisely. What moves, how far, how fast, how often, in which orientation, at what temperature. Vague motion requirements produce vague motors. This belongs in your product requirements document before anyone picks a part number.
  2. Compute the load torque at the output. Use the worst-case geometry, not the nominal one — the arm fully extended, the container fully loaded, the seal at its tightest.
  3. Estimate friction. Add a realistic allowance for every bearing, seal, and sliding interface. When in doubt, measure it on a prototype with a torque wrench or a spring scale rather than guessing.
  4. Compute the acceleration term. Find the total inertia reflected to the output shaft, then divide the required change in speed by the allowed ramp time.
  5. Sum them. The peak requirement is usually load plus friction plus acceleration at the worst instant of the cycle; the continuous requirement is load plus friction during steady motion. You need both numbers, because motors are rated on both.
  6. Reflect through the drivetrain. Divide output torque by the gear ratio, then divide again by efficiency to get motor torque. Multiply required output speed by the ratio to get motor speed.
  7. Apply a safety factor and check the result against the motor's continuous rating at your supply voltage, not its stall torque.

Gearing changes the entire picture

A gearbox trades speed for torque. A 50:1 reduction multiplies output torque by 50 and divides speed by 50, minus efficiency losses — and it multiplies reflected inertia by the square of the ratio, which is why heavily geared systems feel sluggish to accelerate even when they have torque to spare.

Practical consequences worth knowing:

  • Spur gearboxes are efficient and backdrivable. Good when you want the mechanism to be moved by hand or to fail safe.
  • Worm gears are compact and often self-locking, which holds a load without power — excellent for lifting, poor for efficiency.
  • Planetary gearboxes handle high torque in a small diameter and are the usual answer in handheld products.
  • Belts and lead screws convert rotation to linear motion; a lead screw's pitch and its friction coefficient dominate the torque requirement, and a low-lead screw can be self-locking too.

Gearing also changes which motor family makes sense. The comparison in stepper versus servo versus DC motors matters here, because a stepper loses torque steeply with speed while a brushless motor with a controller behaves very differently.

Safety factor, duty cycle, and heat

A motor's stall torque is a specification, not an operating point — at stall it draws maximum current, produces no mechanical output, and converts everything into heat. Design for continuous operation at a modest fraction of stall.

  • Apply a safety factor of roughly 1.5 to 2 on the calculated requirement for well-characterized mechanisms, more when friction is uncertain or the load is variable.
  • Check the duty cycle. A motor that runs for two seconds every minute can be pushed far harder than one running continuously.
  • Check temperature. Motor torque constants and magnet strength degrade as the winding heats, and a motor sized at room temperature can fade inside a sealed enclosure.
  • Check the power source. Peak current at startup may sag the supply and reduce the torque you thought you had. This constraint feeds directly into battery pack design and vice versa.

From a number to a real component

Once you have a motor torque and speed target, plot your requirement on candidate motors' torque-speed curves and confirm your operating point sits in the efficient region, not near stall. Then check the physical realities: shaft diameter and mounting pattern, whether the assembly fits the enclosure, whether cogging or noise is acceptable, driver requirements, and long-term availability. Two-year lead times on a motor you designed around are a real risk worth checking early, the same way you would for any critical line item on the bill of materials.

Finally, measure. Build the mechanism, instrument it, and compare actual current draw and torque to your calculation. Prototyping the drivetrain is fast and cheap compared to discovering a stall in the field — rapid prototyping exists for exactly this kind of question, and for anything airborne the specialized tradeoffs in drone motors and propellers apply instead.

Need help sizing a motor and drivetrain for a mechanism you are designing? Tell us about the motion through our contact form and we will work through the torque budget with you.