How to Calculate Motor Torque from Weight

Accurately calculate motor torque from weight, radius, and acceleration

Torque Sensitivity Analysis

Torque Requirements at Different Inclines

Table 1: Estimated torque requirements based on varying incline angles while keeping mass and acceleration constant.

Incline Angle	Total Force (N)	Torque per Motor (kg-cm)	Torque per Motor (Nm)

Understanding how to calculate motor torque from weight is a fundamental skill for engineers, hobbyists, and robotics designers. Whether you are building a combat robot, an electric skateboard, or an industrial winch, selecting the right motor ensures your system moves efficiently without overheating or stalling. This guide breaks down the physics, formulas, and practical steps to determine the exact torque specifications for your project.

What is Motor Torque?

Torque is the rotational equivalent of linear force. While force moves an object in a straight line, torque rotates an object around an axis. In the context of motors, torque is the "turning power" the motor shaft delivers to the wheels, pulleys, or gears.

Many beginners confuse torque with speed (RPM). A high-speed motor might not have enough torque to move a heavy load from a standstill. Conversely, a high-torque motor might move a heavy load easily but slowly. Calculating the required torque ensures your motor can overcome static friction, gravity, and inertia to get your load moving.

The Motor Torque Formula and Mathematical Explanation

To calculate the required torque, we must first determine the total linear force needed to move the object. The core formula for torque ($T$) is:

T = F × r

Where:

• T = Torque (Newton-meters or kg-cm)
• F = Total Force required (Newtons)
• r = Radius of the wheel or pulley (meters)

Step-by-Step Derivation of Total Force (F)

The total force ($F_{total}$) is the sum of forces resisting motion. For a vehicle or robot on an incline, these are:

1. Gravity Force ($F_g$): The component of weight pulling the object down the slope.
   Formula: $F_g = m \times g \times \sin(\theta)$
2. Acceleration Force ($F_a$): The force needed to speed up the object.
   Formula: $F_a = m \times a$
3. Friction/Efficiency Loss: Mechanical systems are never 100% efficient. We divide the total force by an efficiency factor ($\eta$).

Variables Table

Table 2: Key variables used in torque calculations.

Variable	Meaning	Standard Unit	Typical Range
m	Mass of the load	kg	1kg – 1000kg+
g	Gravitational Acceleration	m/s²	9.81 m/s² (Earth)
a	Desired Acceleration	m/s²	0.1 – 5.0 m/s²
θ (theta)	Incline Angle	Degrees (°)	0° (flat) – 90° (vertical)
η (eta)	Efficiency	Percentage (%)	50% – 85%

Practical Examples (Real-World Use Cases)

Example 1: Mobile Robot on a Ramp

Imagine you are building a delivery robot. You need to know how to calculate motor torque from weight to ensure it can climb a wheelchair ramp.

• Mass: 20 kg
• Wheel Radius: 0.1 meters (10 cm)
• Incline: 10 degrees
• Desired Acceleration: 0.5 m/s²
• Motors: 2 drive motors

Calculation:

1. Gravity Force: $20 \times 9.81 \times \sin(10^\circ) \approx 34.07 \text{ N}$
2. Accel Force: $20 \times 0.5 = 10 \text{ N}$
3. Total Force: $44.07 \text{ N}$
4. Apply Efficiency (assume 65%): $44.07 / 0.65 \approx 67.8 \text{ N}$
5. Total Torque: $67.8 \text{ N} \times 0.1 \text{ m} = 6.78 \text{ Nm}$
6. Per Motor: $6.78 / 2 = 3.39 \text{ Nm}$

Result: You need two motors rated for at least 3.4 Nm of continuous torque.

Example 2: Vertical Winch Lift

You are designing a hoist to lift a crate vertically.

• Mass: 50 kg
• Pulley Radius: 0.05 meters (5 cm)
• Incline: 90 degrees (Vertical)
• Acceleration: 1 m/s²

Calculation:

1. Gravity Force: $50 \times 9.81 \times 1 = 490.5 \text{ N}$
2. Accel Force: $50 \times 1 = 50 \text{ N}$
3. Total Force: $540.5 \text{ N}$
4. Apply Efficiency (assume 80% for gears): $540.5 / 0.80 = 675.6 \text{ N}$
5. Torque: $675.6 \text{ N} \times 0.05 \text{ m} = 33.78 \text{ Nm}$

Result: A single motor with ~34 Nm torque is required.

How to Use This Motor Torque Calculator

1. Enter Total Mass: Input the full weight of your vehicle, robot, or load in kilograms. Include the weight of the motors and batteries themselves.
2. Measure Wheel Radius: Measure from the center of the axle to the ground. Enter this in centimeters.
3. Set Acceleration: Determine how quickly you need to reach top speed. For slow, steady movements, use a low value (0.1–0.5 m/s²). For snappy robotics, use higher values.
4. Define Incline: If the motor moves on flat ground, enter 0. If lifting vertically, enter 90.
5. Adjust Efficiency: No system is perfect. Gearboxes and friction reduce power. A safe default is 65%.
6. Select Motor Count: Choose how many motors will share the load.

Key Factors That Affect Motor Torque Results

When learning how to calculate motor torque from weight, consider these critical factors that influence your final hardware choice:

1. Wheel Diameter

Larger wheels require more torque to produce the same linear force ($T = F \times r$). If your motor lacks torque, using smaller wheels acts like a "gear down," increasing force at the expense of top speed.

2. Friction and Efficiency

Internal friction in gearboxes, bearings, and tire-to-ground contact consumes power. Ignoring efficiency is the #1 reason for motor failure. Always apply a safety margin (efficiency factor) of 50-70% for hobby projects.

3. Acceleration Requirements

Holding a load requires less torque than accelerating it. High acceleration demands significantly more current and torque (Newton's Second Law: $F=ma$). If your application requires rapid starts and stops, size your motor for "Peak Torque" rather than "Continuous Torque."

4. Incline and Gravity

On flat ground, you only fight friction and inertia. On an incline, you fight gravity. Even a small 10° slope significantly increases the torque demand compared to flat ground.

5. Voltage and Current Limits

Motors produce torque proportional to current ($K_t$ constant). Ensure your battery and motor driver can supply the current required to generate the calculated torque.

6. Gear Reduction

If the calculated torque is too high for a direct-drive motor, use a gearbox. A 10:1 gearbox increases torque by roughly 10x (minus efficiency losses) while reducing speed by 10x.

Frequently Asked Questions (FAQ)

1. Does weight affect motor speed?

Indirectly. Heavier weights require more torque. If the motor cannot supply enough torque, it will run slower than its rated speed or stall completely. However, if torque is sufficient, weight does not dictate the theoretical top speed.

2. What is the difference between stall torque and rated torque?

Stall Torque is the maximum torque a motor can produce when the shaft is held still (0 RPM). Rated (Continuous) Torque is the torque it can produce indefinitely without overheating. Always design for Rated Torque, not Stall Torque.

3. How do I convert kg-cm to Nm?

1 kg-cm is approximately equal to 0.098 Nm. Roughly, you can divide kg-cm by 10 to get Nm.

4. Why is my calculated torque so high?

Check your wheel radius and acceleration. Large wheels act as long levers, requiring massive torque. High acceleration values also spike the force requirement.

5. Can I use this for a tank-tread robot?

Yes. For tank treads, use the radius of the drive sprocket (the wheel attached to the motor) as the "Wheel Radius."

6. What if I have 4 wheels but only 2 motors?

Select "2 Motors" in the calculator. The passive wheels support weight but do not contribute torque. The two active motors must move the entire mass.

7. How does voltage affect torque?

Voltage determines the motor's top speed. Current determines torque. However, higher voltage allows the motor to push enough current through the windings to reach higher torque at speed.

8. Should I use a safety factor?

Yes. We recommend calculating your needs and then multiplying by 1.5 or 2.0 to ensure reliability and longevity.

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