In this guide
Almost every student robot has the same two failure modes: a motor that stalls the moment the robot meets a slope, or a motor so oversized it drains the battery and eats the budget. Both come from the same mistake — picking a motor by feel instead of calculating the torque it needs. Torque is not a mysterious specification. It is a force applied at a distance from a shaft, and you can work it out on paper in ten minutes with a luggage scale and a tape measure.
This guide shows you how: the four torque terms that matter, a step-by-step sizing workflow, three worked examples with real numbers — a mobile robot, a robot-arm joint and a lead-screw lift — how gearboxes change the answer, and how to read a motor datasheet without being misled by its biggest number.
Quick answer
Add up static, dynamic, friction and loss torque, then multiply by a safety factor of 1.5 to 2. Torque equals force times radius, so a small wheel or a gearbox is often worth more than a bigger motor. Never size a motor on its stall torque — the usable continuous torque is roughly half of it.
Torque in one minute
Torque is rotational force: how hard something twists a shaft. The formula is simple:
T = F × r
where T is torque, F is the force in newtons, and r is the perpendicular distance from the shaft in metres. Push with 10 N at the end of a 0.2 m lever and you apply 2 N·m of torque. Double the lever, double the torque; halve it, halve the torque. That one relationship explains why wheel radius, arm length and screw lead dominate motor sizing.
Torque is quoted in two units you will meet constantly. N·m (newton-metres) is the SI unit and the one datasheets for larger motors use. kg·cm (kilogram-centimetres) is the unit hobby servos and small gear motors use. Convert with 1 kg·cm = 0.0981 N·m, or roughly 1 N·m = 10.2 kg·cm. Mixing the two up is the single most common arithmetic mistake in student motor sizing — always convert before you compare.
Two torque figures appear on every motor datasheet, and confusing them is the second most common mistake. Stall torque is the maximum the motor can produce with the shaft held still — impressive, and useless as a working figure, because a stalled motor is not moving and is heating up fast. Rated (continuous) torque is what the motor can deliver indefinitely without overheating. As a rule of thumb, rated torque is roughly half the stall torque; if a datasheet lists only stall torque, halve it before you size anything.
The four torque terms
A real mechanism needs more than the textbook T = F × r. Four terms add up to the torque your motor must deliver:
1. Static torque — holding the load still. Gravity acting on a load held at a distance from a pivot. For a robot arm held horizontal, T = m × g × r, where m is the mass beyond the joint, g is 9.81 m/s², and r is the distance to the centre of mass. This is usually the largest term for arms and lifts, and it is at its worst when the arm is horizontal.
2. Dynamic torque — accelerating the load. Changing speed needs torque: T = J × α, where J is the moment of inertia and α is the angular acceleration. For a wheeled robot this appears as the force needed to accelerate the mass: F = m × a, converted to torque through the wheel radius. Fast starts and stops make this term large; gentle acceleration makes it small.
3. Friction torque — what the mechanism itself eats. Rolling resistance of wheels, friction in bearings and gearboxes, drag in a lead screw. It is hard to calculate exactly, so students usually estimate it as a fraction of the load or measure it directly (see the FAQ).
4. Loss torque — gearbox and transmission efficiency. No gearbox is free. A spur-gear stage typically passes on 70–90% of the torque; each added stage costs more. The torque at the output is T_out = T_motor × gear ratio × efficiency, so a gearbox that multiplies torque by 30 with 70% efficiency delivers 21 times the motor torque, not 30.
Add them up, then apply a safety factor:
T_required = (T_static + T_dynamic + T_friction + T_loss) × safety factor
Use 1.5 to 2 for student builds. The safety factor covers everything you estimated badly — friction, an underestimated load, a slope you forgot, a battery that sags under load. A factor below 1.5 leaves no margin; above 2 usually means you are buying motor you do not need.
The sizing workflow
Follow these steps in order for any mechanism, and you will rarely size a motor wrong.
Step 1 — Define the motion. What moves, how far, how fast, and how quickly must it get there? Write down the mass, the radius or lever arm, the target speed and the target acceleration. If you cannot state these numbers, you are not ready to pick a motor.
Step 2 — Calculate the static torque. Worst case first: arm fully extended horizontally, lift at maximum load, robot on the steepest slope it must climb. Use T = F × r with the force the mechanism must resist.
Step 3 — Add the dynamic torque. From the acceleration you need: F = m × a for linear motion, T = J × α for rotation. If you do not know the inertia, the linear version through the wheel radius or lever arm is usually enough for a first calculation.
Step 4 — Add friction and losses. Estimate rolling resistance as roughly 2% of the weight for small rubber wheels on a smooth floor, and divide by gearbox efficiency (0.7–0.9 per stage). When in doubt, measure rather than guess — a spring scale pulling the mechanism tells you the real friction force.
Step 5 — Apply the safety factor and check speed. Multiply by 1.5–2, convert to the datasheet's units, and pick a motor whose rated torque clears the result. Then check speed: the motor must also reach the RPM your mechanism needs after the gearbox, and deliver enough power — P = T × ω, with ω in radians per second.
Worked example 1: a mobile robot
A 5 kg line-following robot with two drive wheels of 6.5 cm radius must accelerate at 0.8 m/s² and reach 1 m/s. Rolling resistance is about 2% of its weight on a smooth floor.
- Acceleration force: F = m × a = 5 × 0.8 = 4.0 N
- Rolling resistance: F = 0.02 × 5 × 9.81 = 0.98 N
- Total force: 4.98 N, shared by two motors: 2.49 N each
- Torque per motor: T = 2.49 × 0.065 = 0.162 N·m = 1.65 kg·cm
- With a 1.5 safety factor: 0.243 N·m ≈ 2.5 kg·cm rated torque
Speed check: at 1 m/s the wheels turn at 1 / 0.065 = 15.4 rad/s, about 147 RPM. Through a 1:30 gearbox the motor spins at roughly 4,400 RPM — comfortably inside the range of a small DC gear motor. Mechanical power per motor is 0.243 × 15.4 ≈ 3.7 W, so a small 6–12 V gear motor with a rated torque above 2.5 kg·cm does the job, and a 10 kg·cm motor would be wasted weight and current.
Worked example 2: a robot-arm joint
A robot-arm shoulder joint carries a 0.5 kg link whose centre of mass sits 0.2 m from the joint, plus a 0.3 kg payload at the gripper, 0.4 m out. Worst case is the arm horizontal.
- Link torque: 0.5 × 9.81 × 0.2 = 0.98 N·m
- Payload torque: 0.3 × 9.81 × 0.4 = 1.18 N·m
- Static torque: 2.16 N·m
- With a 1.5 safety factor: 3.24 N·m = 33 kg·cm
That is a large hobby servo — a standard 20 kg·cm servo stalls here. The lesson is not "buy a bigger servo" but "the arm's own weight is half the load": a lighter link, a shorter arm, a counterweight, or a gearbox on the joint all cut the number far more cheaply than a bigger motor. Size the joint from the full load, not the payload alone.
Worked example 3: a lead-screw lift
A small lift must raise 2 kg vertically on a T8 lead screw with an 8 mm lead. Trapezoidal screws are inefficient — about 30% is a fair working figure — because much of the torque goes into sliding friction.
T = F × lead / (2π × η) = (2 × 9.81) × 0.008 / (2π × 0.3) = 0.083 N·m = 0.85 kg·cm
A small NEMA 17 stepper delivers several times that, so torque is not the problem here — speed is. At 300 RPM the lift moves 8 mm per revolution, which is 40 mm/s: a 200 mm lift takes five seconds. Lead screws trade speed for force, which is exactly why they are used for lifts and Z-axes, and exactly why they are a poor choice for anything that must move fast.
Gearboxes: trading speed for torque
Small motors spin fast and push weakly; mechanisms usually need the opposite. A gearbox trades one for the other:
T_output = T_motor × gear ratio × efficiency
A motor rated at 0.1 N·m through a 1:30 gearbox at 70% efficiency delivers 0.1 × 30 × 0.7 = 2.1 N·m at the output — twenty-one times the torque — but the output spins thirty times slower. That is why the mobile robot above needs a geared motor: the bare motor spins at thousands of RPM with a fraction of a N·m, and the gearbox converts it into the slow, strong rotation the wheels need.
Three gearbox facts students forget: efficiency falls with every added stage, so one 1:30 stage beats three 1:3 stages; backlash (the small free play when direction reverses) grows with the ratio and ruins precision positioning unless the design allows for it; and the gearbox itself has a torque limit — a big motor through a plastic gearbox strips gears instead of moving loads.
Reading a motor datasheet
A datasheet tells you everything the worked examples need, if you know where to look.
- Stall torque and stall current: the maximum at zero speed, and the current drawn getting there. Size your motor driver and battery for the stall current, not the running current — a stalled wheel can pull several times the normal current.
- Rated torque and rated speed: the continuous working point. Your calculated requirement belongs here, with margin.
- No-load speed: the speed with no torque applied. Your mechanism's top speed after the gearbox must sit well below this, because speed falls as torque rises.
- Torque–speed curve: for a DC motor it is roughly a straight line from no-load speed at zero torque to stall torque at zero speed. The middle of that line is where the motor is efficient; the ends are where it is hot or useless.
- Current vs torque: current rises roughly linearly with torque, which is why a motor that stalls repeatedly can brown out your electronics or melt a driver that was sized for running current alone.
If a listing gives you only stall torque and no-load speed, treat the rated torque as roughly half the stall figure, and treat any listing with no datasheet at all as a gamble, not a specification.
A Python sizing helper
This small script repeats the mobile-robot calculation for any numbers you feed it, so you can test "what if the robot is heavier?" or "what if the wheels are bigger?" in seconds instead of redoing the arithmetic by hand.
def motor_torque(mass_kg, accel, wheel_radius_m, mu=0.02,
n_motors=2, safety=1.5, g=9.81):
"""Required rated torque per motor (N-m and kg-cm)."""
f_accel = mass_kg * accel
f_roll = mu * mass_kg * g
f_total = f_accel + f_roll
torque_nm = (f_total / n_motors) * wheel_radius_m * safety
return torque_nm, torque_nm / 0.0980665
for mass in (3, 5, 8):
nm, kgcm = motor_torque(mass, 0.8, 0.065)
print(f"{mass} kg robot -> {nm:.3f} N-m ({kgcm:.2f} kg-cm) per motor")
Running it prints 0.146, 0.243 and 0.389 N·m for the 3, 5 and 8 kg robots — the torque scales with the mass, exactly as the formula says. Change the wheel radius or the acceleration and watch which input moves the answer most; that is the input worth measuring carefully.
Common mistakes
- Sizing on stall torque. A motor rated 10 kg·cm stall delivers about 5 kg·cm continuously. Size on the rated figure, or halve the stall figure first.
- Forgetting the mechanism's own weight. The arm link, the gripper, the lead-screw nut and the gearbox all count. In the arm example above, the link itself was nearly half the torque.
- Ignoring gearbox efficiency. A 1:30 gearbox at 70% efficiency is a 21× multiplier, not 30×. The missing 30% becomes heat and a slower response.
- No safety factor — or an absurd one. 1.5–2 covers real-world friction and estimation error. A factor of 4 buys a motor that is heavy, thirsty and expensive for a problem that never existed.
- Mixing up radius and diameter. Torque uses the radius. Using the wheel diameter instead doubles the answer and sends you shopping for a motor twice as strong as you need.
- Sizing for flat floors and forgetting slopes. A ramp multiplies the force by the sine of the angle; even a gentle slope adds a term the flat-floor calculation never had. If the robot must climb, calculate for the slope.
- Buying the biggest motor "to be safe". Bigger means heavier, more current, a bigger driver and a bigger battery — and a bigger motor behind a weak driver or a small battery still stalls.
FAQ
What safety factor should I use?
1.5 to 2 for a student build. Use 1.5 when you measured the friction and weighed the parts; use 2 when you estimated them. Competition robots that take impacts go higher, but that is a different problem from a lab demo.
My motor stalls even though the torque looks enough. Why?
The usual suspects, in order: you sized on stall torque instead of rated torque; the battery voltage sags under load; the motor driver current-limits below the stall current; or the friction in your mechanism is higher than you estimated. Measure the actual current and voltage while it stalls — the numbers will point at the culprit.
Do I always need a gearbox?
Almost always for small motors. A bare DC motor spins at thousands of RPM with very little torque, and no wheeled robot or arm joint wants that. The exceptions are direct-drive gimbal motors and large servos with the gearing built in.
Servo or DC gear motor — which one?
A servo gives you position control out of the box and is the right choice for joints and steering. A DC gear motor gives continuous rotation and is the right choice for wheels and conveyors. If you need both position control and continuous rotation, that is a separate decision — our servo-versus-stepper guide covers the trade-offs.
How do I measure the torque my mechanism actually needs?
Hook a spring scale to the mechanism at a known distance from the pivot and pull until it moves. Force in newtons times distance in metres is the torque. Do it in the worst-case position — arm horizontal, lift fully loaded — and you have a measured number to check your calculation against.
Can I just buy the biggest motor available?
You can, but you will pay for it in weight, current draw, driver size and battery life — and a big motor with an undersized driver or battery performs worse than a right-sized motor with a matched driver. Size the motor, then size the driver and battery to match it.
Limitations
These are first-order estimates, not a substitute for measurement: friction coefficients and gearbox efficiencies are typical values, and your mechanism's real numbers will differ. Always verify with the spring-scale test above and with the datasheet of the exact motor you buy — two motors with the same stall torque can have very different rated torque, speed and current draw. The examples assume steady, rigid mechanisms; flexible links, belt stretch and backlash add behaviour this guide does not model. And if your project involves mains power, high currents above 10 A or lithium battery packs, get the design checked by a faculty member before powering it up.
Need help building it?
If you want this project built for you — the motor sized, the mechanism designed and the prototype assembled — message Projectech on WhatsApp with your project idea, your branch and your deadline. The reply is a quotation stating the scope, the price and the delivery timeline, before any work starts.