ADC Resolution Calculator Formula

Understand the math behind the adc resolution calculator. Each variable explained with a worked example.

Use the ADC Resolution Calculator

Formulas Used

Digital Output Code

digital_code = floor(input_voltage / step_v)

Step Size (1 LSB)

step_mv = step_v * 1000

Reconstructed Voltage

reconstructed_v = floor(input_voltage / step_v) * step_v

Quantization Error

quant_error_mv = abs(input_voltage - floor(input_voltage / step_v) * step_v) * 1000

Total Levels

total_levels = pow(2, adc_bits)

Variables

VariableDescriptionDefault
adc_bitsADC Resolution (bits)10
v_refReference Voltage(V)3.3
input_voltageInput Voltage(V)1.65
max_codeDerived value= pow(2, adc_bits) - 1calculated
step_vDerived value= v_ref / pow(2, adc_bits)calculated

How It Works

ADC Resolution and Digital Conversion

An ADC maps a continuous voltage range to discrete digital codes. The resolution determines the smallest detectable voltage change.

Formulas

Step Size = V_ref / 2^N

Digital Code = floor(V_input / Step Size)

Quantization Error = V_input - Code x Step Size

The maximum quantization error is +/- 0.5 LSB.

Worked Example

10-bit ADC with 3.3 V reference, input 1.65 V.

adc_bits = 10v_ref = 3.3input_voltage = 1.65
  1. 01Step size: 3.3 / 1024 = 3.223 mV
  2. 02Digital code: floor(1.65 / 0.003223) = 512
  3. 03Reconstructed: 512 x 0.003223 = 1.6504 V
  4. 04Error: |1.65 - 1.6504| = 0.4 mV

Ready to run the numbers?

Open ADC Resolution Calculator