How do you calculate ADC resolution (LSB)?

LSB = Vref / (2^N − 1), where Vref is the reference voltage and N is the number of bits. A 12-bit ADC with 3.3 V reference: LSB = 3.3 / 4095 ≈ 0.806 mV.

How is the digital output code calculated?

D_out = round(V_in / LSB). The result is a whole number between 0 and 2^N − 1, then expressed in binary and hex.

What is quantization error?

Quantization error is the difference between the true analog input and the nearest digital level. For an ideal ADC the maximum error is ±0.5 LSB.

What is the SNR of an ideal ADC?

SNR = 6.02 × N + 1.76 dB for an ideal N-bit ADC sampling a full-scale sine wave. A 12-bit ADC has ~74 dB SNR. Each extra bit adds ~6.02 dB.

Effective Number of Bits: ENOB = (SINAD − 1.76) / 6.02. It tells you how many 'ideal' bits the ADC actually achieves after accounting for noise and distortion. A 12-bit ADC typically has 10–11 ENOB.

What is the Nyquist sampling theorem?

To accurately digitise a signal, the sampling rate must be at least twice the highest frequency component: f_sample ≥ 2 × f_max. Below this, aliasing occurs and the signal cannot be reconstructed.

How does reference voltage affect resolution?

A lower Vref gives a smaller LSB (finer resolution) but reduces the input range. A higher Vref gives a wider range but coarser resolution. Choose Vref to match your signal's amplitude.

What is the difference between 8-bit, 10-bit, and 12-bit ADCs?

8-bit: 256 levels, ~48 dB SNR. 10-bit: 1024 levels, ~62 dB. 12-bit: 4096 levels, ~74 dB. Each extra bit doubles the number of levels and adds ~6 dB of dynamic range.

What is dynamic range of an ADC?

Dynamic range = 20 × log10(2^N − 1) ≈ 6.02 × N dB. It's the ratio between the largest signal the ADC can represent and the smallest step. A 16-bit ADC has ~96 dB dynamic range.

ADC Calculator – Resolution, LSB Step Size, SNR, ENOB & Quantization Error

Input Parameters Active Config

ADC Resolution (N bits)

bits

Reference Voltage (Vref)

Input Voltage (Vin)

Digital Output (Decimal)

(0 - 1023)

Digital Output (Binary)

(10-bit)

Formulas

Resolution (Step Size) = V_ref2^N − 1

Digital Output (Decimal) = V_inV_ref × (2^N − 1)

Input Voltage = Digital Output2^N − 1 × V_ref

Calculation Results

Resolution (Step Size)

4.8876 mV

(Voltage per LSB)

Max Digital Output

1023

(2¹⁰ − 1)

Digital Output (Decimal)

512

(Approx.)

Digital Output (Binary)

1000000000

(10-bit)

Quantization Error

±2.4438 mV

(±0.5 LSB)

Input Voltage (Calculated)

2.5024 V

(From Digital Output)

ADC Transfer Characteristic click chart to trace input voltages

Ideal Transfer Quantized Output

Vin: 2.50 V | Dout: 512

Summary

✓

ADC Type

Ideal Conversion

▤

Total Levels

1,024 codes

⚡

Voltage Range

0V to 5V

∿

LSB Size

4.8876 mV

✓

Accuracy

±0.5 LSB

💡

Note An analog-to-digital converter (ADC) converts a continuous, infinite analog voltage input into an approximate discrete digital value. The Resolution (Step Size) determines the precision of the conversion and is defined as the voltage difference per Least Significant Bit (LSB). The quantization error represents the gap between the measured analog input and quantized digital equivalent.

ADC Calculator — Complete Guide to Resolution, LSB, SNR & Quantization

This ADC calculator computes every key parameter of an analog-to-digital converter — LSB step size, digital output code (decimal, binary, hex), quantization error, SNR, ENOB, and dynamic range — for any bit width from 4 to 32 bits and any reference voltage. A live transfer characteristic curve updates in real time as you adjust parameters, making it easy to visualise how resolution, range, and error trade off in your design.

Key ADC Formulas

Parameter	Formula	Unit
LSB step size	LSB = V_ref / (2^N − 1)	V (or mV)
Quantization levels	2^N	—
Digital output code	D_out = round(V_in / LSB)	integer
Quantization error	±0.5 × LSB (max)	V
SNR (ideal)	6.02 × N + 1.76	dB
ENOB	(SINAD − 1.76) / 6.02	bits
Dynamic range	20 × log₁₀(2^N − 1)	dB

ADC Bit Resolution Comparison

Bits (N)	Levels	LSB @ 3.3 V	LSB @ 5 V	Ideal SNR	Typical Use
8	256	12.94 mV	19.61 mV	49.9 dB	Audio, basic sensors
10	1 024	3.23 mV	4.89 mV	62.0 dB	Arduino, general MCU
12	4 096	0.806 mV	1.22 mV	74.0 dB	STM32, ESP32, precision
14	16 384	0.201 mV	0.305 mV	86.1 dB	Instrumentation
16	65 536	50.4 µV	76.3 µV	98.1 dB	Audio DAQ, medical
24	16.7M	0.197 µV	0.298 µV	146.2 dB	Precision measurement

Worked Examples

🔢 Example 1 — Arduino 10-bit ADC, 5 V Ref, Input = 2.5 V

GivenN = 10 bits, V_ref = 5.0 V, V_in = 2.5 V

Step 1LSB = 5.0 / (1024 − 1) = 5.0 / 1023 = 4.888 mV

Step 2D_out = round(2.5 / 0.004888) = round(511.5) = 512

Step 3Binary: 10 0000 0000 | Hex: 0x200

Step 4Q error = 2.5 − (512 × 0.004888) = 2.5 − 2.5027 = −2.7 mV (within ±0.5 LSB)

ResultD_out = 512 (0x200) | LSB = 4.888 mV | SNR = 62.0 dB

⚡ Example 2 — STM32 12-bit ADC, 3.3 V Ref, Input = 1.65 V

GivenN = 12 bits, V_ref = 3.3 V, V_in = 1.65 V

Step 1LSB = 3.3 / 4095 = 0.8059 mV

Step 2D_out = round(1.65 / 0.0008059) = round(2047.5) = 2048

Step 3Binary: 1000 0000 0000 | Hex: 0x800

Step 4SNR = 6.02 × 12 + 1.76 = 74.0 dB | Dynamic range = 72.2 dB

ResultD_out = 2048 (0x800) | LSB = 0.806 mV | Exactly mid-scale as expected

Common ADC Types & Architectures

Type	Speed	Resolution	Typical Use
Flash	Very fast (> 1 GSPS)	4–8 bits	Oscilloscopes, radar
SAR	Medium (10 kSPS–10 MSPS)	8–18 bits	MCU built-in, DAQ
Delta-Sigma (ΔΣ)	Slow (10–10k SPS)	16–32 bits	Precision measurement, audio
Pipeline	Fast (10–500 MSPS)	10–16 bits	Communications, video
Dual-Slope	Very slow	12–22 bits	DMM, integrating meters

Practical Design Considerations

Noise budget: Real ADCs have noise that limits ENOB below the ideal N bits. A 12-bit SAR ADC typically achieves 10–11 ENOB.
Reference voltage quality: Vref noise adds directly to quantization error. Use a dedicated voltage reference IC for precision applications.
Input impedance & settling: The ADC's sample-and-hold capacitor must charge fully within the acquisition time.
Anti-aliasing filter: Place a low-pass filter before the ADC input with cutoff at f_sample/2 to prevent aliasing.
Oversampling: Sampling at M× the Nyquist rate and decimating gains ~3 dB (0.5 bits) per 4× oversampling.

Frequently Asked Questions

What does 12-bit resolution mean?

It means the ADC can distinguish 4096 (2¹²) voltage levels. With 3.3 V Vref, each step is ~0.8 mV — enough for most sensor and control applications.

How do I improve ADC accuracy?

Use a clean Vref, minimize noise on the analog input, add an anti-aliasing filter, oversample and average, and calibrate offset and gain errors.

What is the Nyquist frequency?

Half the sampling rate: f_Nyquist = f_sample / 2. Signals above this frequency alias into the baseband. Always filter before sampling.

Related Calculators

Attenuation Calculator — dB, FSPL, cable loss, link budget
Antenna Gain Calculator — gain in dBi from aperture and efficiency
Bitwise Calculator — binary operations for digital output codes
Ohm's Law Calculator — V = I × R

ADC CALCULATOR