Stepper Motor Step Angle Calculator
Calculate stepper motor step angle, steps per revolution, microstepping, and linear distance per step for CNC and robotics projects.
Stepper motors move in discrete steps rather than continuous rotation. Each electrical pulse from the driver moves the motor shaft by a precise angular increment called the step angle. This makes stepper motors ideal for CNC machines, 3D printers, robotics, and any application requiring precise positioning without encoders.
The fundamental formulas:
Step Angle (°) = 360° ÷ (Rotor Teeth × Phases × 2)
For a standard 2-phase hybrid motor that reduces to: Step Angle (°) = 360° ÷ (Rotor Teeth × 4), or simply 90° ÷ Rotor Teeth
Check it against the motor on your bench: a 50-tooth rotor gives 90 ÷ 50 = 1.8°, which is the number printed on nearly every NEMA 17 you will ever buy. The factor is four, not two. Halving it is the classic slip, and it gives you 3.6°, a step angle no common motor actually has.
A more practical formula when you already know the step count: Step Angle (°) = 360° ÷ Full Steps Per Revolution
Common step angles:
- 1.8°: most common, = 200 full steps/revolution (50 tooth rotor, 2-phase)
- 0.9°: high resolution, = 400 full steps/revolution (100 tooth rotor)
- 7.5°: older/smaller motors, 48 full steps/revolution
- 15°: toy and simple positioning motors, 24 steps/revolution
Microstepping: Modern stepper drivers (like the A4988, DRV8825, or TMC2208) divide each full step into smaller microsteps by controlling current levels in the windings:
| Microstepping | Effective Steps/Rev (1.8° motor) | Step Angle |
|---|---|---|
| Full step | 200 | 1.8° |
| Half step | 400 | 0.9° |
| 1/4 step | 800 | 0.45° |
| 1/8 step | 1,600 | 0.225° |
| 1/16 step | 3,200 | 0.1125° |
| 1/32 step | 6,400 | 0.05625° |
Important note on microstepping torque: Microstepping improves smoothness and reduces vibration but does NOT improve positioning accuracy in practice, and the torque penalty is much steeper than most people expect. The torque available to hold or correct a single microstep is:
Incremental torque = Holding torque × sin(90° ÷ Microsteps per full step)
| Microstepping | Torque per microstep |
|---|---|
| Full step | 100% |
| Half step | 70.7% |
| 1/4 step | 38.3% |
| 1/8 step | 19.5% |
| 1/16 step | 9.8% |
| 1/32 step | 4.9% |
At 1/16 the motor has under a tenth of its holding torque to resist a single microstep of error, which is why a machine set to 1/16 can report a beautiful 0.000625 mm resolution and still sit several microsteps away from where the controller thinks it is. Friction alone eats that. Use microstepping for quiet, smooth motion, not for accuracy you intend to rely on.
Linear distance per step (for CNC / 3D printers): If the motor drives a leadscrew or belt: mm per step = (Lead of screw OR belt pitch × pulley teeth) ÷ Steps per revolution
Example: 1.8° motor + 1/16 microstepping (3,200 steps/rev) + 2mm pitch leadscrew: mm/step = 2 ÷ 3,200 = 0.000625 mm per step (very precise!)
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
SuperGlobalCalculator is independently built and maintained. See how we build and verify our calculators.