Encoder Resolution Calculator
Enter PPR and the decoding mode (×1, ×2 or ×4 quadrature) to get counts per revolution, degrees and arcminutes per count, counts per degree and mm or inches per count on a lead screw or wheel. Also converts absolute encoder bits to positions and finds the PPR or bits needed for a target resolution.
With ×4 quadrature, counts per revolution = 4 × PPR, degrees per count = 360 ÷ CPR and mm per count = lead ÷ CPR: a 1,000 PPR encoder gives 4,000 counts, 0.09° per count and 1.25 µm per count on a 5 mm lead screw.
Use the Encoder Resolution Calculator
Encoder Configuration
Results update as you type.
Lines / cycles per channel per turn, from the datasheet.
Type CPR to work back to PPR (CPR ÷ decoding factor).
2N positions per revolution (e.g. 12, 16, 17, 20, 23 bits).
1 = encoder on the output shaft; 10 = motor encoder behind a 10:1 gearbox.
Linear motion — optional
Leave blank for rotary only.
Speed and target — optional
Rotary Angular Resolution
Linear Position Resolution
Signal Frequency & Speed Limit
Resolution Needed
All Units
| Metric | ×1 | Selected |
|---|
Common incremental encoders (×4 quadrature)
| PPR | Counts / rev | ° / count | arcmin / count | µm / count, 5 mm lead |
|---|---|---|---|---|
| 100 | 400 | 0.9 | 54 | 12.5 |
| 200 | 800 | 0.45 | 27 | 6.25 |
| 250 | 1,000 | 0.36 | 21.6 | 5 |
| 360 | 1,440 | 0.25 | 15 | 3.4722 |
| 500 | 2,000 | 0.18 | 10.8 | 2.5 |
| 512 | 2,048 | 0.17578 | 10.547 | 2.4414 |
| 600 | 2,400 | 0.15 | 9 | 2.0833 |
| 1,000 | 4,000 | 0.09 | 5.4 | 1.25 |
| 1,024 | 4,096 | 0.08789 | 5.273 | 1.2207 |
| 2,000 | 8,000 | 0.045 | 2.7 | 0.625 |
| 2,048 | 8,192 | 0.04395 | 2.637 | 0.6104 |
| 2,500 | 10,000 | 0.036 | 2.16 | 0.5 |
| 4,096 | 16,384 | 0.02197 | 1.318 | 0.3052 |
| 5,000 | 20,000 | 0.018 | 1.08 | 0.25 |
| 10,000 | 40,000 | 0.009 | 0.54 | 0.125 |
Absolute encoder bits to positions
| Bits | Positions / rev | ° / position | arcsec / position |
|---|---|---|---|
| 10 | 1,024 | 0.3515625 | 1,265.625 |
| 12 | 4,096 | 0.08789063 | 316.4063 |
| 13 | 8,192 | 0.04394531 | 158.2031 |
| 14 | 16,384 | 0.02197266 | 79.1016 |
| 16 | 65,536 | 0.00549316 | 19.7754 |
| 17 | 131,072 | 0.00274658 | 9.8877 |
| 18 | 262,144 | 0.00137329 | 4.9438 |
| 20 | 1,048,576 | 0.00034332 | 1.236 |
| 22 | 4,194,304 | 0.00008583 | 0.309 |
| 23 | 8,388,608 | 0.00004292 | 0.1545 |
| 24 | 16,777,216 | 0.00002146 | 0.0772 |
| 26 | 67,108,864 | 0.00000536 | 0.0193 |
Formulas
- CPR = PPR × decoding factor (1, 2 or 4). Absolute: positions = 2bits, no edge multiplication.
- Angular resolution = 360° ÷ (CPR × gear ratio); 1° = 60′ = 3,600″.
- Linear resolution = travel per output rev ÷ (CPR × gear ratio); travel = lead (pitch × starts), pulley teeth × belt pitch, or π × wheel diameter.
- Channel frequency = PPR × RPM ÷ 60; count rate = CPR × RPM ÷ 60; max RPM = max count rate × 60 ÷ CPR.
- Resolution is not accuracy: encoder error, runout, backlash and thermal growth add to the real position error.
Quick answer
Counts per revolution (CPR) = PPR × the decoding factor: ×1 counts one edge of channel A, ×2 both edges of A, ×4 every edge of A and B (full quadrature). So a 1,000 PPR encoder gives 4,000 CPR. Angular resolution = 360° ÷ CPR = 0.09° (5.4 arcmin) per count. Linear resolution = travel per revolution ÷ CPR: on a 5 mm lead screw that is 0.00125 mm (1.25 µm) per count; on a wheel, travel per revolution = π × diameter. An absolute encoder with N bits has 2^N positions: 17 bits = 131,072 positions = 9.89 arcsec.
Examples
| Encoder | Counts / rev | Degrees / count | On a 5 mm lead screw |
|---|---|---|---|
| 500 PPR, ×4 | 2,000 | 0.18° (10.8′) | 2.5 µm / count |
| 1,000 PPR, ×4 | 4,000 | 0.09° (5.4′) | 1.25 µm / count |
| 1,024 PPR, ×4 | 4,096 | 0.08789° (5.27′) | 1.2207 µm / count |
| 2,500 PPR, ×4 | 10,000 | 0.036° (2.16′) | 0.5 µm / count |
| 17-bit absolute | 131,072 | 0.002747° (9.89″) | 0.0381 µm / position |
Enter your PPR or bit depth and the screw lead or wheel diameter.
Summary
Convert incremental encoder pulses per revolution (PPR) into counts per revolution for ×1, ×2 or ×4 quadrature decoding, or an absolute encoder's single-turn bit depth into positions per revolution. The calculator gives angular resolution in degrees, arcminutes, arcseconds and milliradians, counts per degree, linear resolution in mm, µm or inches per count for a lead screw, belt pulley or measuring wheel (with an optional gear ratio), the encoder signal frequency at a given shaft speed, the maximum speed for a counter input, and the minimum PPR or bits needed to reach a target resolution.
How it works
- Choose Incremental (PPR) or Absolute (bits).
- Incremental: enter the PPR from the datasheet (or type the counts per revolution and it works out the PPR) and pick ×1, ×2 or ×4 decoding.
- Optional: choose lead screw/pulley travel or wheel diameter, enter the value in mm or inches and the gear ratio between the encoder and that shaft.
- Optional: enter a shaft speed to get the encoder signal frequency, or your counter's maximum count rate to get the top speed.
- Optional: enter a target resolution to get the minimum PPR or bits needed.
- Results update as you type.
Use cases
- Converting a datasheet PPR to the counts per revolution a PLC high-speed counter or motion controller reports.
- Finding mm or µm per count for a CNC axis lead screw or a belt-driven linear stage.
- Working out distance per count for a measuring wheel or a robot wheel encoder.
- Choosing an encoder PPR or absolute bit depth that meets a required positioning resolution.
- Checking that a counter input is fast enough for the encoder at maximum shaft speed.