Robotics & Control
Basic

Encoder Resolution

Smallest angle a rotary encoder can resolve.

Formula

θ=360N\theta = \frac{360}{N}

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Variables

θResolution (degrees)
NCounts per revolution

Example

N=1024: θ ≈ 0.35° per count

How it works

A rotary encoder turns angular motion into a fixed number of digital counts for each full 360° turn. If one revolution is divided into N equal count steps, then each count represents 360/N degrees, which is the smallest angle the encoder can distinguish in an idealized sense. So this formula tells you the angular step size per count.

When to use it

Use this when you need to estimate how precisely an encoder can measure position or motion, such as in motor shaft feedback, robot joints, or turntables. It helps you convert encoder counts into degrees and judge whether the encoder is fine enough for the task.

Worked example, step by step

Suppose a rotary encoder has N = 500 counts per revolution. Use the formula: θ = 360 / N Substitute the value: θ = 360 / 500 Calculate: θ = 0.72 Final answer: the encoder resolution is 0.72° per count

Common mistakes to avoid

  • Using the number of pulses from the output channel without checking whether quadrature decoding changes the effective count
  • Forgetting that N must be counts per full revolution, not counts per second or per degree
  • Mixing up resolution with accuracy; a small step size does not guarantee the encoder is perfectly accurate

Did You Know?

Quadrature encoders read two offset channels to quadruple resolution and detect direction.

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Reviewed & maintained by the FormulaWon editorial teamLast reviewed September 2026