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ADC Resolution Calculator

Work out an ADC's LSB (the voltage one code step stands for), its number of quantisation levels, or the bit count needed for a wanted resolution — using LSB = Vrange / 2^N.

Formula

  • LSB = Vrange / 2^N
  • Levels = 2^N
  • N ≥ log2(Vrange / LSB)

Vrange is the full-scale input span the converter covers — 5 V for a unipolar 0–5 V ADC, 10 V for a ±5 V converter — and N is the resolution in bits. An N-bit converter divides that span into 2^N equal quantisation levels, so the voltage one code step stands for (1 LSB) is the range divided by the number of levels.

That is the ideal code-step size: the arithmetic step for an N-bit converter over the given full-scale range, before any offset, gain or noise error. Each extra bit doubles the number of levels and halves the step, so more bits means a finer measurement — and asking for a wanted step size works back to the smallest bit count that meets it.

About this calculation

An analogue-to-digital converter with N bits divides its input range into 2^N codes, so the smallest voltage change it can register is one least significant bit, LSB = Vrange / 2^N. Enter the range, the bit count or a target resolution and the calculator returns whichever one you left out, along with the number of codes and the percentage of full scale that one step represents.

Assumptions and limits

  • The converter is ideal and uniform: no missing codes, no noise, and no gain, offset, integral or differential non-linearity, all of which a real part has.
  • The range is the full-scale span you enter. A bipolar ±5 V converter spans 10 V, so its LSB is twice the size of a 0–5 V converter with the same bit count.
  • Resolution is not accuracy. Bits set how finely the converter can divide the range; accuracy says how close those codes are to the truth, and noise and reference drift usually dominate.

A worked example

A 12-bit converter with a 5 V range has 2¹² = 4096 codes, so one LSB is 5 / 4096 ≈ 1.22 mV — and any signal smaller than that will be lost in the quantisation step.

See also Nyquist Sampling and Voltage Divider.