Linear Sensor Transfer Function

Vout = S × value + offset

Quick answer

This calculator solves Vout = S × (measured_value) + offset for Sensor Output. With Sensitivity (V/unit) 1 V/unit, Measured Value 0.5, Offset 26.4 V, the result is 26.9 V. It solves in 4 directions, so you can enter the values you have and get the one you need.

Calculator

Sensor Output (V)
—

Formula

Vout = S × (measured_value) + offset

Description

Many sensors produce an output voltage that is linearly proportional to the measured physical quantity plus a constant offset. The sensitivity S (also called scale factor or gain) defines how much the output changes per unit change in the measured quantity, while the offset represents the output at zero input. Calibration involves determining both S and offset from measurements at two or more known reference points. This linear model applies to accelerometers, pressure sensors, current sensors, temperature sensors (LM35, TMP36), and many other transducers within their specified operating range.

Variables

  • Vout — Sensor output voltage (V)
  • S — Sensitivity or scale factor (V per unit of measurement)
  • measured_value — Physical quantity being measured
  • offset — Output voltage at zero input (V)

Practical Notes

The TMP36 temperature sensor, for example, has S = 10 mV/°C and offset = 500 mV (0.5V at 0°C). An ADXL345 accelerometer has S = 3.9 mg/LSB. For ratiometric sensors (output proportional to supply voltage), sensitivity is specified as a fraction of Vcc. Two-point calibration determines S and offset; more calibration points can reveal and correct nonlinearity.

Symbols and units

Symbol Meaning Default unit Accepted units
Vout Sensor Output V pV, nV, µV, mV, V, kV
S Sensitivity (V/unit) V/unit V/unit
meas Measured Value — —
offset Offset V pV, nV, µV, mV, V, kV

Step by step

  1. 1. What you know: Sensitivity (V/unit) 1 V/unit, Measured Value 0.5, Offset 26.4 V
  2. 2. The relation: Vout = S × (measured_value) + offset
  3. 3. Substitute: S = 1 V/unit, meas = 0.5, offset = 26.4 V
  4. 4. Result: Sensor Output = 26.9 V

Worked examples

Minimum range

Given: Sensitivity (V/unit) 0.001 V/unit, Measured Value 0.025, Offset 0.726 V

Result: Sensor Output = 0.726 V

Low range

Given: Sensitivity (V/unit) 0.01 V/unit, Measured Value 0.25, Offset 7.26 V

Result: Sensor Output = 7.263 V

Typical

Given: Sensitivity (V/unit) 1 V/unit, Measured Value 0.5, Offset 26.4 V

Result: Sensor Output = 26.9 V

High range

Given: Sensitivity (V/unit) 10 V/unit, Measured Value 0.8, Offset 0.506 kV

Result: Sensor Output = 0.514 kV

Maximum range

Given: Sensitivity (V/unit) 100 V/unit, Measured Value 8, Offset 5.06 kV

Result: Sensor Output = 5.86 kV

Solving for each variable

Solve for Sensor Output

Sensitivity (V/unit) 0.001 V/unit, Measured Value 0.025, Offset 0.726 V → 0.726 V

Solve for Sensitivity (V/unit)

Sensor Output 0.33 V, Measured Value 0.025, Offset 0.726 V → -15.84 V/unit

Solve for Measured Value

Sensor Output 0.33 V, Sensitivity (V/unit) 0.001 V/unit, Offset 0.726 V → -396

Solve for Offset

Sensor Output 0.33 V, Sensitivity (V/unit) 0.001 V/unit, Measured Value 0.025 → 0.33 V

How Sensor Output changes with Sensitivity (V/unit)

Sensitivity (V/unit) (input) Sensor Output (result)
0.1 V/unit 26.45 V
0.25 V/unit 26.53 V
0.5 V/unit 26.65 V
0.75 V/unit 26.78 V
1 V/unit 26.9 V
1.5 V/unit 27.15 V
2 V/unit 27.4 V
4 V/unit 28.4 V
7 V/unit 29.9 V
10 V/unit 31.4 V

The same result in other units

Unit Value
mV 26900
V 26.9
kV 0.0269

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Frequently asked questions

How do you calculate Linear Sensor Transfer Function?

Use Vout = S × (measured_value) + offset. With Sensitivity (V/unit) 1 V/unit, Measured Value 0.5, Offset 26.4 V, Sensor Output works out to 26.9 V.

How do you calculate pressure sensor sensitivity and offset calculation?

Rearrange for Sensor Output: with Sensitivity (V/unit) 0.01 V/unit, Measured Value 0.25, Offset 7.26 V, Sensor Output is 7.263 V.

How do you calculate linear operating range of a sensor calculate?

Rearrange for Sensor Output: with Sensitivity (V/unit) 1 V/unit, Measured Value 0.5, Offset 26.4 V, Sensor Output is 26.9 V.

What is the formula for Linear Sensor Transfer Function?

The formula is Vout = S × (measured_value) + offset. Many sensors produce an output voltage that is linearly proportional to the measured physical quantity plus a constant offset.

How do you find Sensitivity (V/unit) when you know the other values?

Rearrange for Sensitivity (V/unit): with Sensor Output 0.33 V, Measured Value 0.025, Offset 0.726 V, Sensitivity (V/unit) is -15.84 V/unit.

How do you find Measured Value when you know the other values?

Rearrange for Measured Value: with Sensor Output 0.33 V, Sensitivity (V/unit) 0.001 V/unit, Offset 0.726 V, Measured Value is -396.

Related Concepts

All Sensors & ADC formulas →
ADC Resolution (LSB) ADC Theoretical SNR Steinhart-Hart Temperature Wheatstone Bridge Linear Sensor Transfer Function Oversampling SNR Improvement RTD Callendar-Van Dusen Strain Gauge Resistance Change

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