Free Stepper Motor Torque Calculator

Calculate dynamic acceleration torque, total required holding torque, load-to-rotor inertia ratio, and select the optimal NEMA frame size.

⚙️ Motion & Inertia Parameters

Application Type & Load Setup

Target Speed (RPM) Operating velocity

Accel Time (ms) 0 to target speed

Load Inertia J_L (g·cm²) Reflected load inertia

Friction Torque (N·m) Seal/guide friction

Open-Loop Safety Factor

📊 Recommended Sizing & Sizing Curve

Required Motor Holding Torque

0.38 N·m

53.8 oz-in / 38.0 N·cm

Recommended Motor

NEMA 17 (42mm)

40-48mm body length

Inertia Ratio (J_L / J_M)

2.1 : 1 (Ideal)

Under 5:1 for responsive moves

Angular Acceleration (α): 392.7 rad/s²

Acceleration Torque (T_acc): 0.071 N·m

Dynamic Running Torque: 0.111 N·m

Pulse Frequency (1/16 step): 16.0 kHz

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How to Size a Stepper Motor

Stepper motors do not deliver constant torque across their speed range. Unlike brushless DC or servo motors, a stepper motor's available torque drops sharply as rotational speed rises due to winding back-EMF and inductance. Sizing must account for dynamic acceleration torque, static friction, and an essential 100% (2.0×) safety margin to prevent lost steps.

The Stepper Sizing Equations

\alpha = \frac{2 \pi \cdot (RPM / 60)}{t_{accel}} \quad \text{(Angular Acceleration in rad/s²)}

T_{accel} = (J_{load} + J_{rotor}) \cdot \alpha \quad \text{(Acceleration Torque in N·m)}

T_{dynamic} = T_{accel} + T_{friction}

T_{holding\_req} = T_{dynamic} \cdot S.F. \cdot \frac{1}{\eta_{pullout}(RPM)}

Common NEMA Stepper Motor Ranges

NEMA Size	Faceplate	Holding Torque	Typical Applications
NEMA 14	35 × 35 mm	0.10 – 0.25 N·m	Direct drive 3D printer extruders (Orbiter, Sherpa)
NEMA 17	42 × 42 mm	0.25 – 0.65 N·m	Desktop 3D printers (Ender, Prusa, Voron), mini laser engravers
NEMA 23	57 × 57 mm	1.0 – 3.2 N·m	Desktop CNC routers (Shapeoko, PrintNC), heavy pick-and-place
NEMA 34	86 × 86 mm	4.0 – 12.0 N·m	Heavy industrial CNC mills, plasma tables, large automation

Frequently Asked Questions

Why do stepper motors lose torque at higher speeds?

As a stepper motor spins faster, its internal stator coils generate back-electromotive force (back-EMF) that opposes the driving voltage. Furthermore, the coil inductance (L) limits the rate at which current can build up during the brief step pulses (tau = L/R). Operating the stepper driver at higher bus voltages (such as 36V or 48V instead of 12V or 24V) helps overcome coil inductance, preserving high-speed torque.

What is the optimal inertia ratio for a stepper motor?

The ratio of load inertia (JL) to motor rotor inertia (JM) should ideally be 5:1 or lower for high-speed, dynamic positioning applications like 3D printers and pick-and-place machines. Ratios up to 10:1 are acceptable for steady-speed feeding or heavy leadscrews. Ratios above 10:1 cause severe resonance, overshoot, and sudden step skipping.

Why is a 2.0x safety factor recommended for open-loop steppers?

Open-loop stepper motors have zero position feedback. If instantaneous acceleration torque, bearing friction, or resonance exceeds the motor pull-out torque curve for even one microstep, the rotor slips and position synchronization is permanently lost. A 2.0x safety factor guarantees the motor operates safely beneath its pull-out curve under real-world temperature variations.