Electronics & General Electrical
ADC Resolution & LSB Calculator
Work out the number of codes, the LSB voltage and the dynamic range of an ADC from its resolution in bits and its full-scale range.
About this calculator
An analogue-to-digital converter divides its input range into a fixed number of equal steps and reports which step the input fell into. A converter with N bits of resolution has 2^N of those steps, so an 8-bit converter has 256, a 12-bit converter has 4096 and a 16-bit converter has 65 536.
The size of one step is the LSB — the weight of the least significant bit, and the smallest input change the converter can represent. It is the full-scale range divided by the number of steps: LSB = FSR / 2^N. For the very common case of a 12-bit converter running from a 3.3 V reference, that is 3.3 / 4096, or about 0.806 mV.
Two details cause most of the confusion in this calculation, and this tool makes both explicit rather than assuming them. The first is that the full-scale range is not always the reference voltage: a bipolar converter spanning −Vref to +Vref has to divide 2·Vref into its codes, so its LSB is twice what dividing Vref alone would give. The second is the difference between 2^N and 2^N − 1. A 12-bit converter has 4096 codes and its highest code is 4095, because counting starts at zero. Both numbers are shown side by side.
Resolution is not accuracy. Every number here describes an ideal converter in which the only imperfection is the finite step size. A real device adds differential and integral non-linearity, offset and gain error, noise and, at speed, aperture jitter — which is why a real 16-bit converter never delivers 16 honest bits. What this calculator gives you is the ceiling, not the measurement.
Design notes & common mistakes
- Resolution is not accuracy. It is the ceiling a converter's step size sets, and every real error term — non-linearity, noise, reference drift, amplifier offset — moves the achievable figure below it.
- A bipolar ±Vref input has twice the full-scale range of a unipolar 0-to-Vref one, and therefore twice the LSB at the same resolution. Reading a datasheet's Vref and dividing by 2^N without checking the range type is a reliable way to be wrong by a factor of two.
- There are 2^N codes and the top one is 2^N − 1. A 12-bit converter counts 0 to 4095, so its highest code represents one LSB below full scale rather than full scale itself.
- Adding bits gets expensive quickly: each one halves the step and adds about 6 dB of dynamic range, but the analogue design needed to keep noise below that smaller step gets harder faster than the converter gets dearer.
Assumptions
- The converter is ideal: its only imperfection is the finite step size, and every step is exactly the same width.
- The full-scale range is exactly the reference voltage for a unipolar input, or twice it for a bipolar one, with no headroom lost at either end.
- The reference voltage is stable and accurate — its own error scales every code equally and appears as a gain error.
- LSB is defined as FSR divided by 2^N, the step between adjacent codes.
When to use this calculator
Appropriate for
- Finding the smallest input change a converter of a given resolution can represent
- Choosing a resolution from a required measurement step size
- Checking how a bipolar rather than unipolar input range changes the LSB
- Comparing the ceiling that different bit depths set on a measurement
- Teaching or learning what resolution means in a data-acquisition chain
Not suitable for
- Predicting the accuracy a real converter will achieve, which needs its datasheet non-linearity, noise and effective-number-of-bits figures rather than this ideal ceiling
- Budgeting overall measurement uncertainty, which is a full study spanning sensor, conditioning, reference and converter
- Assessing performance at speed, where jitter and bandwidth dominate and this static model says nothing
Engineering use
Intended use. Educational calculation of the resolution, step size and dynamic range of an ideal analogue-to-digital converter.
Applicable for
- Converting between resolution in bits, number of codes and LSB voltage
- Handling unipolar and bipolar input ranges correctly
- Expressing one LSB as a share of full scale, in percent or ppm
- Establishing the theoretical ceiling a given bit depth sets
Does not account for
- Differential and integral non-linearity, which make real steps unequal
- Offset and gain error in the converter
- Reference voltage error and drift, which scale every code
- Input noise and the amplifier stages ahead of the converter
- Aperture jitter and bandwidth limits at speed
- Codes reserved or lost to headroom at the ends of the range
Verification required
- Confirm from the datasheet whether the input range is unipolar or bipolar, and whether the full range is usable
- Confirm the reference voltage actually present, not the nominal value
- Confirm the device's effective number of bits before treating this resolution as achievable accuracy
What this calculator does not cover
- Gives resolution, not accuracy. A real converter adds differential and integral non-linearity, offset and gain error, and noise, so a 16-bit device does not deliver 16 honest bits — its effective number of bits is always lower.
- Does not model reference error or drift, which multiplies every reading and is often the dominant error in a precision measurement chain.
- Does not account for input-amplifier offset, gain error or noise ahead of the converter, which are outside the converter's own specification but inside the measurement.
- Does not consider sampling rate, aperture jitter or bandwidth, all of which degrade effective resolution as signal frequency rises.
- Assumes the full range is usable; many real converters lose a little headroom at one or both ends, and some deliberately reserve codes.
- As with every calculator on this site: results are preliminary and educational, are not verified for any specific installation, and must be reviewed against the applicable code edition and stamped by a licensed Professional Engineer before real-world use.
Frequently asked questions
What is the LSB of a 12-bit ADC with a 3.3 V reference?
About 0.806 mV. A 12-bit converter has 2¹² = 4096 codes, so one step is 3.3 V ÷ 4096 = 0.0008057 V. That is the smallest input change the converter can represent — anything finer is invisible to it however clean the rest of the circuit is.
How do I calculate ADC resolution?
Take the full-scale range and divide it by the number of codes: LSB = FSR / 2^N, where N is the resolution in bits. The number of codes doubles with every bit, so each extra bit halves the step size and adds about 6 dB of dynamic range.
Is the full-scale range the same as the reference voltage?
Only for a unipolar input running from 0 to Vref. A bipolar converter spans −Vref to +Vref, so its full-scale range is 2·Vref and its LSB is twice as large at the same resolution. Dividing the reference by 2^N without checking the range type is a common factor-of-two error, which is why the range type is an explicit choice here.
Does a 16-bit ADC really give 16 bits of accuracy?
No. Resolution is a ceiling, not a measurement. Differential and integral non-linearity, offset and gain error, input noise, reference drift and — at speed — aperture jitter all push the achievable figure below the nominal resolution. That achievable figure is the effective number of bits, and it is always lower than N.
Why does a 12-bit ADC have 4096 codes but a maximum of 4095?
Because counting starts at zero. There are 2¹² = 4096 distinct codes, numbered 0 through 4095. The top code therefore represents one LSB below full scale rather than full scale itself, which is why an input at exactly the reference voltage has no code of its own.
References
- Standard data-acquisition relations: the number of codes 2^N, the step size FSR/2^N, and dynamic range 20·log₁₀(2^N). These follow directly from the definition of uniform quantisation.
- Walt Kester (ed.), The Data Conversion Handbook, Analog Devices.
- Bela G. Liptak (ed.), Instrument Engineers' Handbook, Volume 1: Process Measurement and Analysis.
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