Stepper Motor Step Angle
θ = 360 / (steps × microstep)
Quick answer
This calculator solves θ = 360° / (steps_per_rev × microstep_divisor) for Step Angle. With Full Steps/Rev 0.5, Microstep Divisor 1.1, the result is 654.5 °. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
A stepper motor moves in discrete angular increments. The base step angle depends on the motor construction: 200 steps/rev (1.8°/step) is the most common, with 400 steps/rev (0.9°/step) for higher precision applications. Microstepping divides each full step into smaller increments by controlling the current ratio between adjacent coil phases. Common microstep settings are 2 (half-step), 4, 8, 16, 32, 64, and 256. While microstepping increases positioning resolution, the actual angular accuracy at microstep positions is limited by motor construction tolerances.
Variables
- θ — Angular displacement per microstep (degrees)
- steps — Full steps per revolution (typically 200 or 400)
- microstep — Microstep divisor (1, 2, 4, 8, 16, 32, etc.)
Practical Notes
A 200-step motor at 16× microstepping: θ = 360/(200×16) = 0.1125°, giving 3200 microsteps/rev. Practical accuracy of microsteps degrades beyond about 16×-32× due to detent torque, load, and driver current precision. For a 3D printer with 200-step motor, 16× microstepping, and 8 mm lead screw with 2 mm pitch: linear resolution = 2/(200×16) = 0.000625 mm = 0.625 µm per microstep.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| theta | Step Angle | ° | ° |
| steps | Full Steps/Rev | — | — |
| microstep | Microstep Divisor | — | — |
Step by step
- 1. What you know: Full Steps/Rev 0.5, Microstep Divisor 1.1
- 2. The relation: θ = 360° / (steps_per_rev × microstep_divisor)
- 3. Substitute: steps = 0.5, microstep = 1.1
- 4. Result: Step Angle = 654.5 °
Worked examples
Minimum range
Given: Full Steps/Rev 0.025, Microstep Divisor 0.055
Result: Step Angle = 261800 °
Low range
Given: Full Steps/Rev 0.25, Microstep Divisor 0.55
Result: Step Angle = 2618 °
Typical
Given: Full Steps/Rev 0.5, Microstep Divisor 1.1
Result: Step Angle = 654.5 °
High range
Given: Full Steps/Rev 0.8, Microstep Divisor 1.76
Result: Step Angle = 255.7 °
Maximum range
Given: Full Steps/Rev 8, Microstep Divisor 17.6
Result: Step Angle = 2.557 °
Solving for each variable
Solve for Step Angle
Full Steps/Rev 0.025, Microstep Divisor 0.055 → 261800 °
Solve for Full Steps/Rev
Step Angle 1.5 °, Microstep Divisor 0.055 → 4364
Solve for Microstep Divisor
Step Angle 1.5 °, Full Steps/Rev 0.025 → 9600
How Step Angle changes with Full Steps/Rev
| Full Steps/Rev (input) | Step Angle (result) |
|---|---|
| 0.05 | 6545 ° |
| 0.125 | 2618 ° |
| 0.25 | 1309 ° |
| 0.375 | 872.7 ° |
| 0.5 | 654.5 ° |
| 0.75 | 436.4 ° |
| 1 | 327.3 ° |
| 2 | 163.6 ° |
| 3.5 | 93.51 ° |
| 5 | 65.45 ° |
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<p><a href="https://vbatpower.com/formulas/stepper-step-angle/">Stepper Motor Step Angle</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Stepper Motor Step Angle?
Use θ = 360° / (steps_per_rev × microstep_divisor). With Full Steps/Rev 0.5, Microstep Divisor 1.1, Step Angle works out to 654.5 °.
What is the formula for Stepper Motor Step Angle?
The formula is θ = 360° / (steps_per_rev × microstep_divisor). A stepper motor moves in discrete angular increments.
How do you find Full Steps/Rev when you know the other values?
Rearrange for Full Steps/Rev: with Step Angle 1.5 °, Microstep Divisor 0.055, Full Steps/Rev is 4364.
How do you find Microstep Divisor when you know the other values?
Rearrange for Microstep Divisor: with Step Angle 1.5 °, Full Steps/Rev 0.025, Microstep Divisor is 9600.
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