Most errors in gear motor torque calculations come from using the right formula with the wrong number in it. A gear motor involves at least four different torque figures, and they are all quoted in the same units on the same datasheet. Sorting out which one belongs in the calculation takes less time than correcting the design afterwards.

The Torque Figures, and Which One You Need

The motor torque is what the motor produces at its own shaft, before the gearbox. The output torque is what reaches the load, and it is larger by the ratio and smaller by the gearbox losses. The stall torque, sometimes called the starting torque, is the maximum the motor can produce at zero speed; it is a peak figure and not a working figure. The rated or continuous torque is what the motor can hold indefinitely without overheating. The load torque is what the machine actually demands, and it is the only one of the five that comes from the application rather than the catalogue.

The calculation is a chain from the load backwards to the motor, not from the motor forwards. Work out the load torque at the required output speed, divide by the ratio and the gearbox efficiency to get the motor torque, and then confirm the motor can produce that torque at the speed it will be running at.

From Motor Torque to Output Torque

Output torque is the motor torque multiplied by the ratio and by the gearbox efficiency. The efficiency matters more than people expect because it is not a single number across gearbox families: a spur or planetary gearhead typically returns ninety percent or more, while a worm gearhead at a high self-locking ratio can return well under half. Two 50:1 gearboxes of different types given the same motor will not deliver the same output torque.

The relationship also sets the limit that no ratio can escape. Power at the output is power at the input less the losses, so at a given output speed the torque available is set by the motor’s power, and the ratio only decides where the motor sits on its own speed-torque line. Choosing a higher ratio to obtain more torque works only as long as the motor still has the speed to drive that ratio at the output speed the machine needs.

Getting the Motor Torque From the Data You Have

Three routes are open, and they should agree.

If the datasheet carries a speed-torque curve, read the torque at the speed the motor will run at. The line falls in a straight line from the no-load speed down to the stall torque, so the torque at any speed is the stall torque multiplied by one minus the speed divided by the no-load speed. This is exact when the stall torque and the no-load speed are both true shaft figures.

If the datasheet carries the voltage constant rather than the torque curve, the torque constant follows from it. In SI units the two constants are the same number, so a torque constant in mN·m per amp equals 9.549 times the voltage constant in volts per thousand rpm. The same factor converts in the other direction, which matters because most micro motor datasheets publish the speed constant and leave the torque constant to be derived.

If the motor is already running, the torque is visible as current. Multiply the torque constant by the current above the no-load current, not by the total current. The no-load current produces no output torque; it covers bearing friction, windage and iron loss. Using the total current overstates the torque by the no-load figure, which on a small motor can be a fifth of the reading.

A Worked Example

Take a 24V motor with a voltage constant of 4.8 V per thousand rpm, a resistance of 24 Ω and a no-load current of 0.1 A. The torque constant is 9.549 times 4.8, or about 45.8 mN·m per amp. The no-load speed is the supply less the no-load drop, divided by the constant, which gives 4.5 thousand rpm, and the stall current is 24 V over 24 Ω, or 1.0 A.

The stall torque is the torque constant multiplied by the current above no-load, which is 45.8 multiplied by 0.9, or about 41 mN·m. The shaft output torque at 3000 rpm is then 41 multiplied by one minus 3000 over 4500, giving about 13.7 mN·m.

Through a 50:1 planetary gearhead at 75 percent efficiency, that is 13.7 mN·m multiplied by 50 and by 0.75, or roughly 514 mN·m at the output, which is a little over 0.5 N·m, at an output speed of 60 rpm. As a cross-check, the same torque corresponds to a current of 13.7 divided by 45.8 plus 0.1, or about 0.40 A, which is what the electrical model predicts at 3000 rpm. When the two routes disagree by more than a few percent, the no-load current or the resistance is the figure to re-examine.

The Units Your Customer Uses

Unit confusion causes as many errors as the choice of torque figure. One newton metre is 10.2 kgf·cm, 8.85 lbf·in or 142 oz·in. Going the other way, one kgf·cm is 98 mN·m and one oz·in is 7.06 mN·m. A torque constant quoted in oz·in per amp converts to mN·m per amp by multiplying by 7.06, and a voltage constant in V per thousand rpm converts to a torque constant in mN·m per amp by multiplying by 9.549, or to oz·in per amp by multiplying by 1.35. Units are not a detail to be fixed at the end of a project: a factor of 7 or 10 in a torque figure looks entirely plausible on a drawing and will not be obvious until the machine is built.

Verifying the Calculation by Measurement

Two measurements close the loop. The first gives the torque constant of a motor whose datasheet is incomplete: couple the shaft to a known-speed drive such as a drill or a lathe, spin it, and measure the open-circuit voltage between the leads. The voltage per unit of speed is the voltage constant, and the torque constant follows. The second gives the torque directly: fit a lever arm of known length to the output shaft, apply a force at the end with a spring balance or a hanging weight, and note the reading at which the shaft starts to turn. Torque is the force multiplied by the arm length, and while it measures holding torque rather than running torque, it is enough to confirm an order of magnitude and to catch a unit error.

Before committing a design, send us the required output speed, the load torque including acceleration and any worst case, the duty cycle, the supply voltage and its tolerance, and the required holding behaviour with the power removed. With those five, the engineering team can check the motor and ratio combination against the motor’s own line rather than against a nominal figure.