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Encoder Resolution & Speed Calculator

Work out effective counts per revolution, angular resolution, and the minimum and maximum measurable speed for an incremental quadrature encoder and control loop.

Encoder lines/rev (PPR)500Quadrature decodingx4Gear ratio (motor:output)1.0 : 1Control loop sample period1.0 msMax counter input frequency1.0 MHz

Gear ratio scales counts to the output shaft. Max counter input frequency is the fastest quadrature edge rate your timer/counter peripheral can reliably capture.

Effective counts / rev (output)

2,000

counts = PPR × quad × gear ratio

Angular resolution

0.1800°

θ = 360° / counts

Minimum detectable speed

0.030 RPM

RPM_min = 60 / (counts × t_sample)

Max measurable speed

30,000 RPM

RPM_max = 60 × f_max / counts

counts_per_rev = PPR × quad_factor × gear_ratio

angular_resolution = 360° / counts_per_rev

RPM_min = 60 / (counts_per_rev × sample_period_s)

RPM_max = 60 × max_counter_freq / counts_per_rev

RPM_min is the slowest speed that still moves at least one count within a sample period — below it, the loop sees zero velocity even though the shaft is turning. RPM_maxis where the quadrature edge rate saturates the counter, not a limit of the motor itself.

References

Standard incremental quadrature encoder relationships (x1/x2/x4 decoding, counter-limited bandwidth)