How do you compute linear displacement from a rotary encoder with circumference C and counts per revolution CPR?

How do you compute linear displacement from a rotary encoder with circumference C and counts per revolution CPR?

• A. Displacement = (counts / CPR) × circumference; adjust for gearing if present.
• B. Displacement = (CPR / counts) × circumference.
• C. Displacement = counts × circumference × CPR.
• D. Displacement = circumference / (counts ÷ CPR).

Answer: (A)

Rotary encoder counts tell you how much of a turn has happened. Since one full turn equals the circumference length, the linear displacement is the fraction of a revolution (counts divided by CPR) times the circumference. If there’s gearing between the encoder and the moving part, you must also scale by the gearing ratio to reflect how encoder revolutions translate to wheel or pulley revolutions. Put together, the distance traveled is (counts / CPR) × circumference, optionally multiplied by the gearing ratio if present. This is why the stated formula is the correct approach.

Rotary encoder counts tell you how much of a turn has happened. Since one full turn equals the circumference length, the linear displacement is the fraction of a revolution (counts divided by CPR) times the circumference. If there’s gearing between the encoder and the moving part, you must also scale by the gearing ratio to reflect how encoder revolutions translate to wheel or pulley revolutions. Put together, the distance traveled is (counts / CPR) × circumference, optionally multiplied by the gearing ratio if present. This is why the stated formula is the correct approach.