Quantization Error Calculator

Enter ADC/DAC resolution and full-scale range to compute LSB step size, max quantization error, RMS quantization noise, and ideal quantization SNR.

How to Use

  1. Set Bit depth (N) for your ADC/DAC.
  2. Set the Full-scale range (FSR) or Vref span your code covers.
  3. Choose coding (unipolar/bipolar) and quantizer type (midtread/midrise) if needed.
  4. Open Show Work to see the formulas in base units.
Quantization Readout
Step size and noise metrics derived from your settings.
LSB
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Max Error
—
Noise (RMS)
—
SNR (Ideal)
—
Quantization Severity: —
Code Steps
Shows step height (LSB) and a sample quantization error band.
Set N and FSR to render the step height and ±½ LSB band.
Inputs & Settings
Defaults assume uniform quantization. Change coding/type if your converter differs.
Typical: 8, 10, 12, 14, 16, 24 (audio)
For unipolar: FSR ≈ Vmax − Vmin (e.g., 0–3.3V → 3.3V). For bipolar: use total span (e.g., ±10V → 20V).
If provided, the tool can estimate code index and percent-of-range. Error band still uses ±½ LSB unless you select a different model.
Most unipolar ADCs are effectively midtread. Some models differ at the endpoints (clipping/saturation).
Show Work (step-by-step)
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Work is shown in base units (volts, dB) for clarity. “Ideal SNR” is the textbook quantization-only estimate.

Reference

For a uniform N-bit quantizer over full-scale range FSR:

  • LSB (step size): LSB = FSR / 2^N (common convention)
  • Max quantization error: e_max = ±0.5 × LSB
  • RMS quantization noise: e_rms = LSB / √12 (uniform error assumption)
  • Ideal quantization SNR (full-scale sine): SNR ≈ 6.02N + 1.76 dB
Notes: Real converters add thermal noise, INL/DNL, jitter, reference noise, and front-end limitations, so measured SNR is often lower.

FAQ

Is quantization error always ±½ LSB?

In the basic model for an ideal uniform quantizer with rounding, the instantaneous error is bounded by about ±½ LSB. Endpoint behavior (clipping) and quantizer type can change edge cases.

Why does the RMS noise use √12?

If the quantization error is modeled as a uniform random variable over a width of 1 LSB, its standard deviation is LSB/√12.

What is the difference between bits and ENOB?

Bits (N) is the converter’s code width. ENOB is an “effective bits” estimate based on measured noise/distortion; ENOB is usually lower than N.

Does ideal SNR apply to DC measurements?

The classic 6.02N + 1.76 dB assumes a full-scale sine wave and quantization noise dominance. For DC or low-frequency measurement systems, other noise sources often dominate.

Tool Info

Last updated:

Updates may include additional endpoint conventions, code index reporting, and export formats.