ADC Quantization Error Calculator
Calculate the LSB size, maximum quantization error (±½ LSB), and RMS quantization error (LSB/√12) for an N-bit ADC with a given full-scale voltage range.
How to Use
- Enter the ADC resolution in bits (typically 8–24).
- Enter the full-scale voltage range (V<sub>ref</sub> for single-ended, 2·V<sub>ref</sub> for bipolar).
- The tool returns LSB size (smallest detectable change), peak quantization error (±½ LSB), and RMS error for uniform distribution assumption.
Show Work
Formulas
History of Quantization Error Analysis
The statistical treatment of quantization error traces to Bernard Widrow\'s 1956 MIT thesis, which proved that for \"busy\" signals (spanning many LSBs) the error between true input and quantized output behaves as white noise uniformly distributed over ±½ LSB. This gave engineers the tools to analyze ADCs as linear systems with an additive noise source — a crucial simplification that lets all the signal-processing techniques for analog noise carry over to digital.
Dithering — intentionally adding small random noise before quantization — was developed for digital audio by Stanley Lipshitz and John Vanderkooy at the University of Waterloo in the 1980s. They showed that triangular-PDF dither of 2 LSB peak-to-peak fully decouples quantization error from the signal, converting pattern noise into true white noise that can be averaged or filtered out. Every commercial digital audio recording today uses some form of dithering at mastering.
Modern high-resolution ADCs push the quantization error floor below thermal and Johnson noise. A 24-bit ADC with ±2 V range has LSB = 238 nV — already below the thermal noise of a 10 kΩ resistor at room temperature (~400 nV in a 10 kHz bandwidth). At 32-bit resolution, quantization error is below cosmic-ray-induced noise; further bit count is meaningless without cryogenic components.
About This Calculator
Enter resolution (bits) and full-scale voltage. The tool computes LSB size, peak quantization error, RMS quantization error, and total code count. Useful for calibration verification (what\'s the minimum detectable input change?), noise-budget planning, and cross-checking ADC datasheet specs.
This calculator computes ideal quantization error only — real ADCs add INL (integral nonlinearity), DNL (differential nonlinearity, missed codes), offset, gain, and temperature drift errors that combine into total unadjusted error (TUE). For full accuracy analysis, use the datasheet\'s TUE spec alongside this calculator\'s quantization baseline. Everything runs client-side.
Frequently Asked Questions
What is quantization error?
The difference between the true analog input and the discrete value the ADC outputs. Each ADC code represents a range of input voltages (one LSB wide); the code is the nearest "step" to the true input. Error is at most ±½ LSB when using optimal rounding (mid-tread quantization).
Mid-tread vs. mid-rise quantization?
Mid-tread: code 0 corresponds to input 0 (zero is a valid output code). Peak error is ±½ LSB. Standard for most signed and unsigned ADCs. Mid-rise: no code exactly represents zero — transitions happen at ±½ LSB, ±1½ LSB, etc. Used in some telecom codecs. Both have identical RMS error.
Why is RMS error LSB/√12?
Assuming quantization error is uniformly distributed over ±½ LSB (valid for busy input signals), the variance is LSB²/12 (from the integral of x² over [−½, +½]). RMS = √variance = LSB/√12 ≈ 0.289 LSB. This gives the familiar 6.02·N + 1.76 dB SNR formula.
Does dithering reduce quantization error?
Not the peak error — dithering adds small random noise to the input before quantization. It doesn\'t reduce the error of a single sample, but it randomizes the error pattern, which lets averaging recover sub-LSB information. Critical for low-level signals that would otherwise produce repetitive (correlated) quantization pattern noise.
Is quantization error the same as noise?
Approximately, for busy signals. The difference: noise is random and uncorrelated with the signal; quantization error is deterministic (given the signal, error is fully predictable). For many signals, quantization error looks and behaves statistically like white noise — which is why the same math applies to both.
Common Use Cases
MCU ADC Accuracy Check
Arduino Uno 10-bit ADC, 5 V range: LSB = 4.88 mV. Peak quantization error ±2.44 mV. If your sensor signal is 10 mV, quantization alone limits accuracy to ~20%.
ESP32 Sensor Interface
12-bit ADC, 3.3 V range: LSB = 806 µV, peak error ±403 µV, RMS ~233 µV. Fine for battery monitor; marginal for thermocouples.
Audio 16-bit
±2 V range, 16 bits: LSB = 61 µV, peak error ±31 µV, RMS 18 µV. Below human hearing floor → no audible quantization noise.
Precision Σ-Δ
24-bit, 5 V range: LSB = 298 nV, peak error ±149 nV. Approaching fundamental thermal-noise limits; real ADC performance dominated by front-end amp noise.
Oscilloscope 8-bit
8-bit flash ADC, 2 V range: LSB = 7.8 mV, peak error ±3.9 mV. Adequate for waveform shape display; insufficient for precision measurement.
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