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Motor

Encoder Resolution Calculator

Calculate encoder counts per revolution, angular resolution, and maximum frequency for quadrature and single-channel encoders.

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Formula

CPR = PPR × 4 (quadrature), θ = 360°/CPR

PPR— Pulses per revolution (pulses)
CPR— Counts per revolution (×4 for quadrature) (counts)

How It Works

A rotary encoder converts shaft angular position into a digital signal. Incremental encoders output a pulse train (A/B quadrature channels plus an optional Z index pulse) with a fixed number of pulses per revolution (PPR). Quadrature decoding multiplies effective resolution by 4 (one count per edge on both channels), giving counts per revolution (CPR) = 4 × PPR. Position resolution in degrees is 360° / CPR. Absolute encoders output a unique digital word for each shaft position, so no homing is required after power-up.

Worked Example

A 500 PPR quadrature encoder is used with a 20:1 gearbox. The output shaft must be positioned to within 0.1°. Step 1 — Counts per revolution at encoder shaft: CPR = 4 × PPR = 4 × 500 = 2000 counts/rev Step 2 — Angular resolution at encoder shaft: θ_enc = 360° / 2000 = 0.18°/count Step 3 — Angular resolution at gearbox output shaft: θ_out = θ_enc / gear_ratio = 0.18° / 20 = 0.009°/count Step 4 — Required resolution check: 0.009° < 0.1° requirement → the encoder is adequate with 11× margin Step 5 — Maximum pulse frequency at 3000 RPM motor speed: f_max = PPR × RPM / 60 = 500 × 3000 / 60 = 25 000 Hz = 25 kHz Result: A 500 PPR encoder with 4× quadrature decoding satisfies the 0.1° output shaft resolution requirement. Ensure the microcontroller quadrature decoder can handle 25 kHz input pulses at maximum motor speed.

Practical Tips

  • ✓Place the encoder on the load side of a gearbox when absolute position accuracy matters — motor-side placement cannot detect gearbox backlash or compliance errors
  • ✓Use differential line driver outputs (RS-422) rather than single-ended TTL for encoder cables longer than 0.5 m to reject common-mode noise in motor environments
  • ✓Index pulse (Z channel) homing at power-up is essential for incremental encoders — without it, any power interruption loses position reference

Common Mistakes

  • ✗Confusing PPR (pulses per revolution) with CPR (counts per revolution) — a 500 PPR encoder with 4× decoding gives 2000 CPR, not 500
  • ✗Forgetting to account for gearbox backlash — a gearbox with 0.5° output backlash eliminates the benefit of high-resolution encoder placement on the motor shaft
  • ✗Exceeding the maximum encoder input frequency of the microcontroller decoder at high speeds, causing missed counts and position error accumulation

Frequently Asked Questions

Incremental encoders output a relative pulse count from a reference position; they lose position on power-down unless battery-backed or re-homed. Absolute encoders output a unique digital code for each shaft angle, retaining position through power cycles. Absolute encoders cost more but eliminate homing routines.
A quadrature encoder has two output channels (A and B) offset by 90°. By detecting all four edges (rising and falling on both A and B) and comparing the phase relationship between channels, a decoder determines both direction of rotation and increments a counter. This gives 4× the resolution of counting only one channel's rising edges.
Stepper motors in open-loop operation typically provide 200 full steps or 3200 microstepping positions per revolution. An encoder with CPR ≥ 3200 is needed to verify each microstep. In practice, 1000–2000 CPR is adequate for closed-loop stepper control because position is corrected each control cycle regardless of individual step accuracy.

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