Motor Sizing Basics: How to Calculate Torque, Inertia and Speed

Choosing a motor by guesswork usually ends one of two ways: it is too small and stalls or loses position, or it is far too large and wastes money and panel space. A proper motor sizing calculation takes less than an hour and avoids both. This guide walks through the method we use for stepper and servo motors, with a worked example.

Step 1: Define the motion

Write down what the axis must do:

• Distance or angle to move
• Time allowed for the move (and any dwell time)
• Mass of the load and the mechanism type (ball screw, belt, rack and pinion, rotary table, conveyor)
• Orientation: horizontal or vertical
• Required positioning accuracy

From the distance and time, work out the speed profile. A trapezoidal profile with acceleration, constant speed and deceleration phases is a good starting point; a common assumption is that acceleration and deceleration each take about a quarter to a third of the move time.

Step 2: Calculate the load torque

Load torque is the steady torque needed to move the load at constant speed, from friction, gravity and any process force. For a ball screw:

TL = (F × P) / (2π × η)

where F is the axial force (N), P is the screw lead (m) and η is the screw efficiency (about 0.9 for ball screws). For a horizontal axis, F = μ × m × g; for a vertical axis, add the full weight m × g.

Step 3: Calculate the load inertia

Inertia resists changes in speed, and is often the biggest factor in acceleration-heavy machines. Useful formulas:

• Solid cylinder or disc: J = (1/8) × m × D²
• Linear mass moved by a screw: J = m × (P / 2π)²
• Through a gear ratio i: reflected inertia = Jload / i²

Step 4: Calculate the acceleration torque

Ta = (JL + JM) × α, with α = ω / tacc and ω = 2π × N / 60, where JM is the motor rotor inertia and N is speed in rpm.

Step 5: Add a safety factor

Required torque = (TL + Ta) × safety factor. For open-loop steppers we use 1.5 to 2, because a stepper that runs out of torque loses steps. Servo systems are checked against both peak torque during acceleration and the RMS (effective) torque over the whole cycle, which must stay within the motor's continuous rating.

Worked example: horizontal ball screw table

• Table and workpiece mass: 20 kg; friction coefficient μ = 0.05
• Ball screw: 16 mm diameter, 500 mm long, 10 mm lead, η = 0.9
• Target speed: 1,000 rpm (10 m/min), reached in 0.1 s

Before adding motor rotor inertia, the required torque is about 0.017 + 0.080 = 0.097 N·m. With a safety factor of 2, we look for a motor that delivers at least about 0.2 N·m at 1,000 rpm (plus its own rotor inertia term), then recheck with the chosen motor's actual rotor inertia. Note that the acceleration torque is almost five times the friction torque: in fast-moving machines, inertia usually dominates.

Step 6: Check the inertia ratio

The ratio of load inertia to motor rotor inertia affects stability and settling. Each manufacturer publishes recommended limits; as a broad guide, standard steppers prefer a modest ratio (often around 10:1 or lower), while servos can handle higher ratios depending on the model and tuning. If the ratio is too high, add a gearhead or choose a motor with a larger rotor.

Step 7: Check speed and the torque curve

Confirm the required torque sits comfortably under the motor's speed-torque curve at the operating speed, with the driver and supply voltage you plan to use. For steppers this is where most sizing mistakes happen, since torque drops significantly at higher speeds.

Let us do the sizing for you

As an authorised Oriental Motor distributor and Mitsubishi Electric channel partner, AB Automation provides free selection calculations for stepper, servo and brushless motors. Not sure which motor type to use? Read our stepper vs servo vs brushless guide, then send us your mechanism details.