Dynamic Range Calculator Formula

Understand the math behind the dynamic range calculator. Each variable explained with a worked example.

Use the Dynamic Range Calculator

Formulas Used

Dynamic Range

dynamic_range = max_signal_dbm - noise_floor_dbm

Equivalent ADC Bits

equivalent_bits = (max_signal_dbm - noise_floor_dbm - 1.76) / 6.02

Max Signal (mW)

max_linear = pow(10, max_signal_dbm / 10)

Variables

VariableDescriptionDefault
max_signal_dbmMaximum Signal Level(dBm)10
noise_floor_dbmNoise Floor(dBm)-80

How It Works

What is Dynamic Range?

Dynamic range is the ratio between the largest and smallest signals a system can handle, expressed in decibels.

Formula

DR (dB) = Max Signal Level - Noise Floor

Equivalent Bits = (DR - 1.76) / 6.02

The equivalent bits tell you the ADC resolution needed to digitize this range. Each bit adds about 6 dB of dynamic range.

Examples

  • CD audio (16-bit): 96 dB
  • Professional audio (24-bit): 144 dB theoretical
  • FM radio: ~70 dB
  • Human ear: ~120 dB

    • Worked Example

    Receiver with max signal +10 dBm and noise floor -80 dBm.

    max_signal_dbm = 10noise_floor_dbm = -80
    1. 01Dynamic range: 10 - (-80) = 90 dB
    2. 02Equivalent bits: (90 - 1.76) / 6.02 = 14.7 bits
    3. 03A 16-bit ADC would cover this range

    Ready to run the numbers?

    Open Dynamic Range Calculator