Stepper Motor Calculator
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Motor Engineering

Stepper Motor Calculator

Compute step angle, holding torque, detent torque, torque-speed curves, microstepping resolution, and resonance frequency. Real-time visualization for motor selection and drive design.

Motor Specifications
Holding Torque Th 0.50 N·m
Detent Torque Ratio 10 %
Rotor Inertia Jr 0.150 kg·cm²
Rated Current I 2.00 A
Microstepping
Max Speed 600 rpm
Load Conditions
Load Inertia JL 0.300 kg·cm²
Load Torque TL 0.10 N·m
1.800°
Full Step Angle
0.1125°
Microstep Angle
0.050 N·m
Detent Torque
Resonance Freq [Hz]
Max Pulse Rate [pps]
Torque Safety Factor
Torque-Speed Curve

Torque-Speed Relationship

Pull-out torque drops at high speed due to the winding's electrical time constant:

$$T(f) = \frac{T_0}{\sqrt{1 + (2\pi f L / R)^2}}$$

Step angle: $\theta_{step} = \dfrac{360°}{N_{teeth} \times N_{phases} \times 2}$

Resonance: $f_{res} = \dfrac{1}{2\pi}\sqrt{\dfrac{T_h \cdot N_s}{2\pi (J_r + J_L)}}$

CAE Note: For robot joint drives, keep the load-to-rotor inertia ratio JL/Jr below 10:1. High inertia mismatch amplifies torque ripple, which feeds into FEM vibration models as a forcing function.
Microstepping Resolution Comparison

Microstepping Current Profile

Phase currents follow a sinusoidal profile to subdivide each full step:

$$I_A(k) = I_0 \cos\!\left(\frac{2\pi k}{4M}\right), \quad I_B(k) = I_0 \sin\!\left(\frac{2\pi k}{4M}\right)$$

Torque correction factor: $\eta \approx \sin(\pi/(2M)) / (\pi/(2M))$ — approaches 1 as $M \to 1$

Microstepping Resolution Table
DivisionStep Angle [°]Steps/RevTorque CorrectionResolution [μm/step]*
* Ball screw pitch 5 mm, reduction ratio 1:1