Encoder Resolution Calculator
Calculate encoder counts per revolution, angular resolution, and maximum frequency for quadrature and single-channel encoders.
Formula
How It Works
This calculator determines encoder resolution and positioning accuracy from pulses per revolution, quadrature decoding, and gear ratio parameters. Motion control engineers, CNC developers, and robotics programmers use it to verify that encoder selection meets positioning requirements. Inadequate encoder resolution causes positioning errors; excessive resolution wastes cost and increases data processing overhead.
Per encoder fundamentals (Sick Stegmann application guide) and IEC 61800-7-1 (Adjustable speed electrical power drive systems — Generic interface and use of profiles), incremental encoders output PPR pulses per revolution on each of two quadrature channels (A and B) offset by 90°. Encoder resolution and accuracy specifications for motor control applications follow NEMA MG-1-2021 (Motors and Generators) Part 30 (Application Considerations for Constant Speed Motors Used on a Sinusoidal Bus with Harmonic Content and General Purpose Drives) and IEC 60034-1 (Rotating electrical machines — Rating and performance). Quadrature decoding counts all four edges (rising/falling on both channels), yielding CPR = 4 × PPR counts per revolution. A 1000 PPR encoder provides 4000 CPR or 0.09° resolution at the encoder shaft.
When mounted through a gearbox, effective resolution improves by the gear ratio: θ_output = θ_encoder / GR. A 1000 PPR encoder through a 50:1 gearbox achieves 0.09°/50 = 0.0018° (6.5 arc-seconds) output resolution. However, gearbox backlash (typically 3-30 arc-minutes for spur gears, 1-5 arc-minutes for planetary per AGMA standards) may exceed encoder resolution, making motor-side mounting ineffective for absolute positioning—load-side encoder placement eliminates backlash uncertainty but requires higher resolution or loses the gear ratio multiplication benefit.
Worked Example
Select an encoder for a rotary indexing table requiring ±0.05° positioning accuracy. System uses a 100:1 harmonic drive (1 arc-min backlash) with 3000 RPM motor speed.
Step 1 — Determine required encoder resolution at output: Required resolution: ±0.05° → need at least 0.025° per count for margin Counts per revolution minimum: 360° / 0.025° = 14,400 CPR at output
Step 2 — Calculate encoder requirement at motor shaft: With 100:1 ratio, motor-side encoder sees 100× higher resolution Effective output CPR = Motor_CPR × GR = Motor_CPR × 100 Required motor CPR: 14,400 / 100 = 144 CPR minimum With 4× quadrature: PPR = 144 / 4 = 36 PPR minimum Select standard 100 PPR encoder (400 CPR) for margin
Step 3 — Verify effective output resolution: Output CPR = 400 × 100 = 40,000 counts/rev Output resolution = 360° / 40,000 = 0.009° per count This exceeds 0.025° requirement by 2.8× margin—adequate
Step 4 — Check backlash impact: Harmonic drive backlash: 1 arc-min = 0.0167° Encoder resolution: 0.009° Backlash is 1.9× encoder resolution—motor-side mounting is effective (For standard gearbox with 10 arc-min backlash, load-side encoder required)
Step 5 — Verify maximum pulse frequency: Motor speed: 3000 RPM = 50 rev/s Pulse frequency: 100 PPR × 50 = 5000 Hz (quadrature: 20 kHz) Verify MCU decoder handles 20 kHz—most 32-bit MCUs support 1+ MHz
Result: A 100 PPR (400 CPR) encoder on the motor shaft achieves 0.009° output resolution through the 100:1 harmonic drive—meeting the ±0.05° requirement with 5.6× margin. The 1 arc-min drive backlash is acceptable for this application.
Practical Tips
- ✓Per Sick Stegmann guidelines, place encoder on load side of gearbox when absolute position accuracy matters—motor-side placement cannot detect or correct for gearbox backlash, compliance, or thermal expansion
- ✓For cable lengths >0.5m in electrically noisy motor environments, use differential (RS-422/485) encoder outputs per EMC guidelines—single-ended TTL signals suffer 5-20% count errors from motor EMI
- ✓Per motion control practice, verify encoder index pulse (Z channel) alignment during commissioning—reference homing requires consistent index-to-mechanical-position relationship across power cycles
Common Mistakes
- ✗Confusing PPR with CPR: Per encoder specifications, PPR is single-channel pulses while CPR = 4×PPR with quadrature decoding—using PPR in calculations underestimates resolution by 4×, causing insufficient positioning accuracy
- ✗Ignoring gearbox backlash: Per AGMA standards, spur gearbox backlash is typically 3-30 arc-minutes; encoder resolution finer than backlash provides no positioning benefit for motor-side mounted encoders
- ✗Exceeding MCU decoder frequency limits: Per STM32 specifications, hardware quadrature decoders support 1-10 MHz; at 10,000 RPM with 10,000 PPR encoder, frequency reaches 1.67 MHz—verify MCU capability before selecting high-resolution encoders
Frequently Asked Questions
Shop Components
As an Amazon Associate we earn from qualifying purchases.
Related Calculators
Motor
DC Motor
Calculate DC motor speed, torque, power, and efficiency from electrical parameters
Motor
Servo Motor
Calculate servo motor torque, speed, efficiency, and back-EMF from electrical and load parameters.
Motor
Gear Ratio
Calculate gear ratio, output speed, torque multiplication, and power transmission efficiency for gear trains.
Motor
Stepper Motor
Calculate stepper motor speed, step frequency, and travel per revolution