Stall torque is the maximum torque a motor produces when its shaft is held completely still under load. You calculate it with a simple formula: divide the supply voltage by the motor’s winding resistance to get the stall current, then multiply that current by the motor’s torque constant. If a gearbox sits between the motor and the output shaft, you multiply again by the gear ratio and the gearbox’s efficiency. The math is straightforward once you know where to find the right numbers.
The Core Formula
Stall torque for a DC motor comes down to three values:
Stall Torque = Torque Constant × Stall Current
Or written in symbols: T_s = K_t × I_s
The torque constant (K_t) tells you how much torque the motor produces per amp of current. It’s listed on the motor’s datasheet in units like N·m/A or oz·in/A. The stall current (I_s) is the maximum current that flows through the motor when it’s powered on but the shaft can’t rotate. Because there’s no back-EMF being generated by a spinning rotor, nothing limits the current except the winding resistance itself. That means:
Stall Current = Supply Voltage ÷ Winding Resistance
So putting it all together: T_s = K_t × (V ÷ R), where V is your supply voltage and R is the phase resistance of the windings.
A Worked Example
Say you have a small DC motor rated at 12 V with a winding resistance of 4 ohms and a torque constant of 0.05 N·m/A. First, find the stall current: 12 V ÷ 4 Ω = 3 A. Then multiply by the torque constant: 0.05 N·m/A × 3 A = 0.15 N·m of stall torque.
For a different example using imperial units: a motor with a torque constant of 1.309 oz·in/A and a maximum usable current of 0.327 A produces 0.327 × 1.309 = 0.428 oz·in of torque. The relationship is always the same linear multiplication, regardless of the unit system.
Adding a Gearbox to the Calculation
Most real-world applications put a gear reducer between the motor and the load. Gears trade speed for torque, so the output stall torque increases dramatically compared to the bare motor. The formula is:
Output Torque = Motor Stall Torque × Gear Ratio × Gearbox Efficiency
Efficiency matters because every gear stage loses some energy to friction and heat. A typical gearbox runs between 70% and 95% efficient depending on the type and number of stages. A motor producing 1 N·m through a 60:1 gear reduction at 95% efficiency delivers 1 × 60 × 0.95 = 57 N·m at the output shaft, while the speed drops from 3,600 RPM to just 60 RPM.
If your system has multiple gear stages, multiply through each one. A 0.876 ft·lb motor torque through a 50:1 reduction at 90% efficiency gives 0.876 × 50 × 0.90 = 39.4 ft·lb at the output. Forgetting to account for efficiency will make your calculated torque 5% to 30% higher than what the system actually delivers.
Where to Find the Numbers You Need
The torque constant and winding resistance are listed on the motor’s datasheet. Some manufacturers list stall torque and stall current directly, which saves you the calculation entirely. If you only have the stall torque and no-load speed, you can plot the motor’s linear torque-speed curve and read off any operating point, but for a pure stall torque calculation, you just need K_t and R.
If no datasheet is available, you can measure winding resistance with a multimeter across the motor terminals (rotate the shaft slowly while measuring to find the maximum reading, since brush position affects the reading on brushed motors). The torque constant is harder to measure directly, but it equals the back-EMF constant in consistent units. Spin the motor at a known speed, measure the voltage it generates, and divide voltage by speed in radians per second to get K_t.
Measuring Stall Torque Directly
Sometimes you want to verify a calculation with a physical measurement. The classic method uses a lever arm attached to the motor shaft. Power the motor, prevent the shaft from rotating using a known moment arm, and measure the force at a known distance from the center of rotation. The basic torque equation from physics applies:
Torque = Force × Distance × sin(θ)
Where θ is the angle between the force direction and the lever arm. When the force is perpendicular to the arm (the most common setup), sin(θ) = 1, and torque is simply force times distance.
A more formal approach is a Prony brake, which wraps a rope or band around the shaft. One end connects to a spring scale, the other to a hanging weight. The effective force on the shaft is the weight minus the scale reading, and you multiply that by the effective radius of the shaft plus the rope. This method generates significant heat from friction, so it’s best for quick measurements rather than sustained testing.
Modern setups use inline torque sensors or load cells, which give a direct digital readout and avoid the heat problem entirely.
Why Real Stall Torque Differs From Calculated
The formula T_s = K_t × (V ÷ R) assumes room-temperature conditions, but a stalled motor heats up fast. Copper winding resistance increases with temperature, which reduces the stall current and therefore the torque. At the same time, the permanent magnets inside the motor lose some of their magnetic strength as they warm up, which lowers the torque constant. Both effects push the actual stall torque below the calculated value.
For brushless DC motors, the torque constant and resistance values on datasheets are typically measured at 25°C (77°F). Running at stall for even a few seconds can push winding temperatures well above 100°C, where resistance may be 30% or more higher than the rated value. If your application holds the motor near stall for extended periods, use the hot resistance and derated torque constant to get a realistic number.
Voltage sag is another factor. Your power supply has its own internal resistance, and at the high currents drawn during stall, the voltage at the motor terminals drops below the nominal supply voltage. If you’re running a 12 V motor on a battery that sags to 10.5 V under heavy load, your actual stall torque drops proportionally.
Common Unit Conversions
Stall torque is expressed in different units depending on the industry and region. The most common conversions you’ll need:
- 1 N·m = 0.7376 ft·lb
- 1 ft·lb = 1.3558 N·m
- 1 N·m = 141.6 oz·in
- 1 oz·in = 0.007062 N·m
Small hobby motors are often rated in oz·in or mN·m, while industrial motors and automotive applications use N·m or ft·lb. Make sure your torque constant and current units are consistent before multiplying, or your answer will be off by orders of magnitude.