Sensors & ADC Formulas

Sensor and ADC formulas connect resolution, reference voltage, and sampling to real-world measurement accuracy. These calculators help you choose converters and scale signals into their full range. They are essential for data acquisition and instrumentation.

Sensors & ADC Formula Calculators

Worked result for every Sensors & ADC formula

Formula Expression Worked result
ADC Resolution (LSB) LSB = Vref / 2^N Reference Voltage 0.33 V, Resolution (bits) 0.8 bits → LSB Voltage = 0.1895 V
ADC Theoretical SNR SNR = 6.02 × N + 1.76 dB Resolution (bits) 0.8 bits → SNR (dB) = 6.576 dB
Steinhart-Hart Temperature 1/T = A + B×ln(R) + C×(ln(R))³ Coefficient A 0.025, Coefficient B 0.055, Coefficient C 0.118, Thermistor Resistance 100 Ω → 1/T = -273.1
Wheatstone Bridge Vout = Vin × (R3/(R3+R4) − R2/(R1+R2)) Supply Voltage 0.33 V, R1 100 Ω, R2 0.22 kΩ, R3 0.47 kΩ, R4 47 Ω → Vout = 73.13 mV
Linear Sensor Transfer Function Vout = S × value + offset Sensitivity (V/unit) 0.001 V/unit, Measured Value 0.025, Offset 0.726 V → Sensor Output = 0.726 V
Oversampling SNR Improvement SNR_eff = SNR + 10 × log10(N) Original SNR 0.66 dB, Oversampling Ratio 0.025 → Effective SNR = -15.36 dB
RTD Callendar-Van Dusen R(T) = R0 × (1 + A×T + B×T²) R0 (at 0°C) 1 Ω, Coefficient A 0.025, Coefficient B 0.055, Temperature 2.5 °C → R(T) = 1.406 Ω
Strain Gauge Resistance Change ΔR = R × GF × ε Nominal Resistance 1 Ω, Gauge Factor 0.025, Strain (µε) 0.055 → Resistance Change = 1.38 × 10⁻⁶ mΩ
Hall Effect Voltage Vh = Rh × I × B / t Hall Coefficient 0.025 m³/C, Bias Current 100 µA, Magnetic Field 0.055 T, Plate Thickness 0.1 mm → Hall Voltage = 1.375 mV
NTC Thermistor Divider Vout = Vcc × Rntc / (Rntc + Rfixed) Supply Voltage 0.726 V, NTC Resistance 100 Ω, Fixed Resistor 0.22 kΩ → Output Voltage = 0.2269 V
Capacitive Sensor Change C = ε0 × A / d Permittivity (pF/m) 1 pF/m, Sensor Area 10 mm², Gap Distance 0.1 mm → Capacitance = 0.1 pF
Photodiode Current Iph = S × E × A Responsivity 0.025 A/W, Irradiance 0.055 W/m², Active Area 0.1 mm² → Photocurrent = 137.5 pA
Thermocouple Seebeck Voltage V = S × ΔT Seebeck Coefficient 0.025, Temperature Difference 2.5 °C → Thermocouple Voltage = 62.5 mV
Current Shunt Measurement I = Vshunt / Rshunt Shunt Voltage 10 mV, Shunt Resistance 0.1 mΩ → Measured Current = 100 A
Ultrasonic Distance Measurement d = v × t / 2 Round-Trip Time 100 ns → Distance = 0.01715 mm
Optical Encoder Speed n = (count / PPR) × 60 / t Pulse Count 0.055, Pulses Per Rev 0.118, Measurement Time 100 µs → Speed (RPM) = 279700
ADC SNR Limited by Clock Jitter SNR = −20 · log10(2π · f · tj) Input Frequency 100 kHz, RMS Jitter 1 ps → SNR = 124 dB
ADC Quantization Noise Voltage e = (FS / 2ᴺ) / √12 Full-Scale Range 0.33 V, Resolution (bits) 0.025 → RMS Quantization Noise = 93.63 mV
Voltage Reference Drift Error error(ppm) = TC · ΔT Temp Coefficient 0.5 ppm/°C, Temperature Span 2.5 °C → Error = 1.25

Variables used across Sensors & ADC formulas

  • LSB — Least significant bit voltage (V)
  • Vref — ADC reference voltage (V)
  • N — ADC resolution in bits
  • SNR — Maximum signal-to-noise ratio (dB)
  • T — Temperature in Kelvin (converted to °C in output)
  • A — Steinhart-Hart coefficient A (from calibration or datasheet)
  • B — Steinhart-Hart coefficient B (from calibration or datasheet)
  • C — Steinhart-Hart coefficient C (from calibration or datasheet)
  • R — Thermistor resistance at the temperature being measured (Ω)
  • Vout — Bridge output voltage (V)
  • Vin — Bridge excitation voltage (V)
  • R1 — Resistor in the first divider arm (Ω)
  • R2 — Resistor in the first divider arm (Ω)
  • R3 — Resistor in the second divider arm (Ω)
  • R4 — Resistor in the second divider arm (Ω)
  • S — Sensitivity or scale factor (V per unit of measurement)
  • measured_value — Physical quantity being measured
  • offset — Output voltage at zero input (V)
  • SNR_eff — Effective SNR after oversampling and decimation (dB)
  • R(T) — RTD resistance at temperature T (Ω)
  • R0 — Resistance at 0°C (Ω)
  • ΔR — Resistance change (Ω)
  • GF — Gauge factor (dimensionless)
  • ε — Mechanical strain in microstrain (µε)
  • Vh — Hall voltage (V)
  • Rh — Hall coefficient (m³/C)
  • I — Bias current through the Hall element (A)
  • t — Thickness of the Hall element (m)
  • Vcc — Supply voltage (V)
  • Rntc — NTC thermistor resistance at current temperature (Ω)
  • Rfixed — Fixed series resistor (Ω)
  • dC — Total electrode capacitance (F)
  • ε0 — Permittivity of the gap medium (F/m), typically 8.854 pF/m for air
  • d — Distance between finger and electrode (m)
  • Iph — Photocurrent generated by the photodiode (A)
  • E — Irradiance (optical power density) at the detector surface (W/m²)
  • V — Output voltage (µV level, entered in base unit V)
  • ΔT — Temperature difference between hot and cold junctions (°C)
  • V_shunt — Voltage drop across the shunt (V)
  • R_shunt — Shunt resistance (Ω)
  • n — Rotational speed (RPM)
  • count — Number of encoder pulses counted in the measurement period
  • PPR — Encoder pulses per revolution
  • f — Analog input frequency (Hz)
  • tj — RMS aperture/clock jitter (s)
  • e — RMS quantization noise voltage (V)
  • FS — Full-scale input range (V)
  • error — Total drift error (ppm)
  • TC — Temperature coefficient (ppm/°C)

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