Calculating the Resolution of Analog to Digital Converter Step Size

The voltage resolution (Least Significant Bit, or LSB step size) of a 10-bit ADC with a 5.0V reference is exactly 4.88 mV, while a 12-bit ADC at 3.3V yields 0.805 mV per step. You calculate this using the formula LSB = V_ref / 2^n. For a standard Arduino Uno (10-bit, 5V), the math is 5.0 / 2^10 = 5.0 / 1024 = 0.00488V. For an ESP32 (12-bit, 3.3V), it is 3.3 / 2^12 = 3.3 / 4096 = 0.000805V. This raw number tells you the smallest voltage change the silicon can theoretically detect, but as we will see, real-world noise and reference stability dictate your actual usable resolution.

The Core Formula and Neighboring Reference Voltages

The fundamental assumption that fixes your ADC resolution answer is the Reference Voltage (V_ref) and the Bit Depth (n). The formula LSB = V_ref / 2^n assumes an ideal, noise-free environment. According to Analog Devices Tutorial MT-010, the theoretical resolution is only valid if your V_ref is perfectly stable. If you are using the microcontroller's internal VCC as your reference (common on basic Arduino setups), a 5% sag in your USB power supply directly injects a 5% error into every reading, rendering the last bit or two of resolution mathematically useless.

To illustrate how sensitive a 12-bit ADC is to reference voltage drift, here is a table showing the LSB step size shifting across a ±20% range around a nominal 3.3V baseline. This mimics what happens if you attempt to run a 3.3V sensor on a sagging battery or an unregulated linear regulator.

12-Bit ADC Step Size Shift (±20% V_ref Variance)

V_ref State	Actual V_ref	LSB Step Size	Impact on 1.0V Signal Reading
-20% (Brownout)	2.64V	0.644 mV	Reads 1552 (instead of 1242)
-10% (Sag)	2.97V	0.725 mV	Reads 1379
Base (Nominal)	3.30V	0.805 mV	Reads 1242
+10% (Overvoltage)	3.63V	0.886 mV	Reads 1128
+20% (Fault)	3.96V	0.966 mV	Reads 1035

How Resolution Shifts When Scaling to Mains (120V vs 230V vs 3-Phase)

While ADC resolution is strictly a low-voltage DC concept, makers frequently use ADCs to measure AC mains voltage via potential transformers (like the ZMPT101B) or voltage dividers. In these scenarios, the DC LSB step size maps to an AC RMS granularity. How the answer shifts depends entirely on your scaling ratio.

If you are using a 12-bit ADC (3.3V reference) to monitor mains voltage, your 0.805 mV DC step size translates differently depending on the target grid:

• 120V AC Systems (North America): You typically scale the voltage divider so that 170V peak (120V RMS) maps to the 3.3V ADC ceiling. With a 200V full-scale mapping, each 0.805 mV step represents ~0.048V AC. This is excellent granularity for detecting a 2V brownout on a household circuit.
• 230V AC Systems (EU/UK/AU): The peak voltage is ~325V, requiring a 400V full-scale mapping to avoid clipping. Here, your 0.805 mV step now represents ~0.097V AC. You lose half your granularity, but it remains sufficient for standard energy monitoring.
• 3-Phase Industrial (400V Line-to-Line): Measuring line-to-line requires mapping up to 600V peak. Your 12-bit step size now equates to ~0.146V AC per step. If you need to detect sub-0.1V imbalances across phases, a 12-bit internal ADC is no longer sufficient; you must step up to a 16-bit external ADC like the ADS1115.

Real-World Maker ADC Modules and the Noise Floor Limit

The theoretical conversion becomes entirely meaningless when the noise floor exceeds the LSB step size. This is measured as ENOB (Effective Number of Bits). According to Texas Instruments' Data Converter fundamentals, a 16-bit ADC on a noisy breadboard next to a switching buck converter might only yield 10 to 12 effective bits of clean data because the 2mV of EMI ripple swallows the bottom 6 bits of resolution.

Furthermore, internal microcontroller ADCs often suffer from non-linearity. As noted in the Espressif ESP32 Technical Reference, the ESP32's internal 12-bit SAR ADC is notoriously non-linear near the 0V and 3.3V rails, effectively dropping its usable resolution to 10 or 11 bits in those regions unless you apply software calibration curves.

Common Maker ADC Hardware Comparison

Module / IC	Advertised Bits	Real-World ENOB	Interface	Best Use Case
ATmega328P (Uno)	10-bit	~8.5 to 9 bits	Internal	Basic potentiometers, crude light sensing
ESP32 (Internal)	12-bit	~10 to 11 bits	Internal	Battery voltage monitoring, basic NTC thermistors
MCP3008	10-bit	~9.5 bits	SPI	Adding multiple analog channels to Raspberry Pi
ADS1115	16-bit	~14 to 15 bits	I2C	Precision load cells, shunt current sensing, mains monitoring
HX711	24-bit	~18 to 20 bits	Custom Serial	Strain gauges and digital scales (includes integrated PGA)