Rotary Encoder Resolution Vs. Accuracy

When a Smartech-cnc frame is equipped with an electro‑spindle, or when a lathe is fitted with a C‑axis, an encoder is provided. 

"Resolution" and "accuracy" are the two most misused words on an encoder datasheet. Buyers and machine builders routinely assume that an encoder with more lines per revolution is automatically "more accurate." It isn't - and confusing the two can either make you overpay for interpolation you don't need, or underspecify a rotary axis that quietly drifts out of tolerance.

Here explains the two concepts from first principles. We start with an everyday analogy, then walk through real incremental and angle encoders to show exactly how resolution and accuracy are defined, how they are measured, and - most importantly - why they are independent.

1. Start with a three-hand watch

The quickest way to grasp the difference is a mechanical watch with hour, minute and second hands. The resolution of the hour hand is one hour, of the minute hand one minute, and of the second hand one second. With quick eyes you can even read the gap between the second ticks - down to roughly 0.3 seconds. Every mechanical three-hand watch can do this; the "resolution" offered is essentially the same from one watch to the next.

Accuracy is something else entirely: it is how well the watch keeps true time. Every watch is different, and a single watch changes over its life - it runs fast or slow - typically by an amount between 1 and 30 seconds. A watch with a very fine second hand can still be hopelessly inaccurate, while a watch with a coarse dial can keep excellent time.

Resolution is how finely you can read a measurement. Accuracy is how correct the reading is. The two are independent.

Figure 1 -A three-hand mechanical watch: the smallest readable unit is its resolution; the deviation from true time is its accuracy.

Figure 2 -Resolution divides an angle into finer increments; accuracy is how close the reported angle is to the true angle.

2. The same two ideas inside a rotary encoder

A rotary encoder converts shaft angle into an electrical signal, and the same pair of concepts applies:

Resolution -the smallest angular change the encoder can detect and output. It is expressed by parameters such as lines per revolution (lines), pulses per revolution (PPR), the minimum measuring step (step) and bits.

Accuracy -how close the encoder's output is to the true angle of the shaft. It is expressed in angular units: arc minutes (′) and arc seconds (″).

3. Resolution in detail - lines, PPR, steps and bits

3.1 Lines and PPR: the square-wave case

The line is the optical grating line on the encoder's code disc. If the encoder outputs square-wave (TTL/HTL) signals directly, the line count is the PPR - the number of pulses the encoder emits per revolution.

Figure 3 -Simplified cross-section of an incremental optical rotary encoder: light passes through the scanning reticle and the rotating code disc onto a photocell array.

Incremental encoders output two square-wave channels, A and B, offset by a quarter of a pulse period (90°). By evaluating both the rising and falling edges of both channels, the control system counts four states per period - quadrature "4×" decoding. The resulting increment is the minimum measuring step. Strictly speaking, this minimum measuring step is the true resolution of the encoder.

Figure 4 -A and B channels differ by 1/4 period; counting all edges of both channels yields 4 counts per signal period (4× PPR).

3.2 Interpolation: turning analog phase into finer steps

When the encoder outputs sinusoidal (sin/cos, ≈ 1 Vpp) signals instead of square waves, the analog phase carries information finer than one grating line. Electronic interpolation - performed inside the encoder or in the evaluating electronics - subdivides each signal period into many steps, multiplying the effective PPR.

Figure 5 -1 Vpp sin/cos output and electronic interpolation: the phase of the analog signal is subdivided into many steps within one signal period.

Worked example 1 - HEIDENHAIN ROD 426 (square-wave output):

3600 lines, TTL square-wave output → 3600 PPR

signal period: 360° / 3600 = 0.1°

with A/B 4× evaluation → minimum measuring step 0.025°

accuracy given by HEIDENHAIN: 18 arc-seconds (0.005°)

resolution (0.025°) is coarser than accuracy (0.005°): resolution > accuracy.

Worked example 2 - HEIDENHAIN ROD 486 (sin/cos output):

3600 lines, ≈ 1 Vpp sin/cos output

25× electronic interpolation → 90,000 PPR (3600 × 25)

signal period after interpolation: 360° / 90,000 = 0.004°

with 4× evaluation → minimum measuring step 0.001°

accuracy of the raw encoder: still 18 arc-seconds (0.005°), excluding interpolation error

resolution (0.001°) is now finer than accuracy (0.005°): resolution < accuracy.

The two examples use the same physical scale - 3600 lines. Only the output type and the interpolation factor differ. In the first case the reported resolution is coarser than the accuracy; in the second it is finer. Nothing about the accuracy changed.

Figure 6 -A 58 mm synchro-flange incremental rotary encoder of the ROD 400 family (illustration): the same line count can be delivered with square-wave or sin/cos output.

3.3 Absolute encoders: resolution expressed in bits

Absolute encoders (and serial-output encoders such as EnDat, BiSS or SSI) express resolution in bits: the circle is divided into 2ᴿ segments. A 17-bit encoder gives 2¹⁷ = 131,072 positions per revolution. Note that "17-bit" already describes the subdivided step - the bit count already includes any internal interpolation.

Figure 7 -Absolute encoder code disc in Gray code: each radial sector is a unique position code, so resolution is expressed in bits (2ᴿ positions per revolution).

4. Accuracy in detail - arc minutes and arc seconds

4.1 Accuracy is only partially related to resolution

Accuracy is expressed in arc minutes (′) and arc seconds (″). It has some relation to resolution - but only partial. The HEIDENHAIN ROD 400 family illustrates this clearly:

below 5000 lines, the given grating accuracy is roughly 1/20 of the line (grating-period) width - here accuracy is related to line count;

from 6000 to 10,000 lines, accuracy is specified as 12 arc-seconds - independent of line count.

For angle encoders, accuracy is even less tied to resolution. HEIDENHAIN's RON angle encoders span the same line range (9000–36,000 lines), yet their system accuracy differs sharply by series:

Table 1 -HEIDENHAIN RON angle-encoder series: the same line counts, different accuracy grades.

All of these can carry the same number of lines. The accuracy is set by the manufacturing grade, not by resolution.

Figure 8 -A large hollow-shaft angle encoder (illustration): angle encoders for rotary tables and C axes are specified by system accuracy in arc-seconds, typically ±5″ down to ±0.4″.

4.2 The four groups of factors that set accuracy

In practice, encoder accuracy is the result of four groups of factors.

Figure 9 -The four groups of factors that determine encoder accuracy: optical, mechanical, electrical, and installation/use.

A · Optical

the code disc: master-grating precision, line count, grating (line-width) accuracy, line-width consistency, and edge sharpness;

the light source: beam parallelism and consistency, light attenuation;

the receivers: scanning angle and readout response;

after use: contamination and signal attenuation.

The master grating is the foundation. HEIDENHAIN's masters are widely regarded as the world reference - produced in clean rooms with strict temperature stabilization and vibration isolation. A commonly told story describes the facility as deeply buried and doubly suspended, isolated even from ocean infrasound and distant traffic vibration. Whatever the exact facility, the practical consequence is the same: many encoder manufacturers buy their masters from HEIDENHAIN rather than make their own. Because imaging time, temperature, physico-chemical changes and contamination all affect line width and edge quality, two encoders with the same line count can differ in accuracy from one manufacturer to the next.

B · Mechanical

shaft machining and mounting precision;

bearing precision and structural design;

code-disc mounting concentricity and optical-assembly alignment;

concentricity between the mounting datum and the shaft.

A single-bearing design cannot cancel its own bearing error, and the deviation grows with use; double-bearing or multi-support structures significantly reduce it.

C · Electrical

supply stability, which affects the light source and the receivers;

readout response and errors from the electronic processing circuit;

electrical noise - set by the encoder's immunity to interference;

electronic subdivision itself introduces error: per HEIDENHAIN, the interpolation error and the deviation of the sin/cos curves are on the order of 1% of the original line width.

D · Installation and use

concentricity of the coupling between the encoder and the measured shaft;

cable immunity and signal delay over long distances or at high frequency;

the response and internal processing of the receiving device;

dynamic response error at high speed;

wear and drift of mechanical parts over time.

5. Practical takeaways for machine builders

1. Never equate resolution with accuracy. Higher PPR or more bits improves the fineness of reading; it cannot fix systematic error. Budget accuracy deliberately - as a rule of thumb, let the encoder consume only a fraction (often one-third or less) of the total allowed axis error.

2. Choose the output to match the requirement. Axis/servo motors use high-resolution incremental encoders for smooth speed control, or absolute multi-turn encoders (EnDat/BiSS/SSI) so position is known at power-on without homing. Spindles (rigid tapping, spindle orientation) need fine resolution - often ≤0.001°, e.g. a 20-bit absolute encoder - more than extreme accuracy. Rotary tables and C axes need the highest accuracy; this is where true angle encoders (±5″ down to ±0.4″) belong. Handwheels and manual pulse generators need only modest resolution, e.g. ≈100 PPR × 4.

3. "Absolute" tells you how position is reported (single-turn or multi-turn, known at power-on) - not how accurate it is. An absolute encoder is not automatically more accurate than an incremental one.

4. Read the datasheet separately. Resolution appears as PPR, bits or lines; accuracy appears as arc-seconds. They are not interchangeable, and neither implies the other.

6. Conclusion

Resolution is how finely an encoder divides a revolution; accuracy is how correctly it measures the true angle. They are independent properties, and the best machines specify both - giving the accuracy budget at least as much attention as the line count. Understand which one your application actually needs, and you will neither overpay for interpolation you don't need, nor underspecify the accuracy your rotary axis cannot live without.

Encoder signal requirements differ for various CNC controllers. Please specify CNC system brand upon machine‑frame. in the order to Smartech-cnc.