Analog Sensor Linear Scaling Calculator
Convert analog sensor voltage or current into engineering units, invert engineering targets back to voltage or current, and review slope, intercept, span percentage, reverse-acting ranges, overrange behavior and electrical uncertainty propagation.
This calculator is for ideal two-point linear scaling. It does not perform nonlinear calibration, least-squares regression, ADC bit-depth analysis, sensor-specific physical conversion or signal-conditioning circuit design.
Engineering tool
Analog Sensor Linear Scaling Calculator
Scale analog sensor voltage or current into engineering units and invert engineering targets back to signal values using a generic two-point linear model.
Calculation mode
Parameter panel
Result console
- Engineering Value
- 75%
- Electrical Percentage
- 75%
- Range Status
- Within Range
- Slope
- 10%/V
- Intercept
- 0%
- Direction
- Direct Acting
Analog Sensor Linear Scaling Formula Audit
| Generic Linear Model | Two electrical endpoints and two engineering endpoints define one ideal transfer line. |
|---|---|
| Forward Formula | X = X1 + (E-E1)(X2-X1)/(E2-E1). |
| Inverse Formula | E = E1 + (X-X1)(E2-E1)/(X2-X1). |
| Slope Definition | m = (X2-X1)/(E2-E1), preserving sign. |
| Intercept Definition | b = X1 - mE1. |
| Electrical Span | E2-E1 may be positive or negative; only span magnitude uses abs(). |
| Engineering Span | X2-X1 may be positive or negative; reverse-acting sensors are supported. |
| Percentage of Span | P = (value-point1)/(point2-point1) × 100%, without clamping. |
| Direct Acting | Displayed when slope is positive. |
| Reverse Acting | Displayed when slope is negative. |
| 4-20 mA Formula | X = XLOW + (I-4mA)(XHIGH-XLOW)/16mA. |
| Live-Zero Boundary | 4 mA is 0% of span; 0 mA is not silently treated as 0%. |
| Voltage Presets | Presets only populate endpoints; the generic engine still performs the calculation. |
| Out-of-Range Policy | Values outside endpoint min/max are flagged as below or above range. |
| Extrapolation Policy | Out-of-range values are mathematically extrapolated and never silently clamped. |
| Tolerance Propagation | Electrical uncertainty is recalculated at E-ΔE and E+ΔE. |
| Displayed Equation Units | Displayed slope uses %/V; E in the equation is displayed in V. |
| Internal Unit Convention | Voltage is converted to V and current to A for internal calculations. |
| Rounding Policy | Unrounded values are used internally; rounding is display-only. |
| SEN-005 Boundary | Pressure-specific transmitter workflows remain in the Pressure Sensor Scaling Calculator. |
| SEN-006 Boundary | Measured calibration datasets, residuals and regression remain in the Sensor Calibration Calculator. |
| SEN-007 Boundary | ADC codes, ENOB and LSB resolution remain in the Sensor ADC Resolution Calculator. |
Formula reference
Analog Sensor Linear Scaling Formulas
Analog sensor scaling uses one signed two-point linear model. Electrical and engineering endpoints do not need to start at zero, and reverse-acting sensors are supported.
X = X1 + (E - E1)(X2 - X1)/(E2 - E1)E = E1 + (X - X1)(E2 - E1)/(X2 - X1)m = (X2 - X1)/(E2 - E1)b = X1 - mE1P = (value - point1)/(point2 - point1) × 100%4-20 mA: X = XLOW + (I - 4mA)(XHIGH - XLOW)/16mA|ΔX| = |m| × ΔEVariable definitions
- E
- electrical signal, in the displayed voltage or current unit
- X
- engineering value in the user-defined unit
- E1, E2
- electrical endpoints
- X1, X2
- engineering endpoints
- m
- signed slope
- b
- intercept
- P
- percentage of span
Analog Sensor Linear Scaling Formula Audit
| Generic Linear Model | Electrical endpoints E1/E2 and engineering endpoints X1/X2 define the ideal line. |
|---|---|
| Forward Formula | X = X1 + (E-E1)(X2-X1)/(E2-E1). |
| Inverse Formula | E = E1 + (X-X1)(E2-E1)/(X2-X1). |
| Slope | m = (X2-X1)/(E2-E1), preserving sign. |
| Intercept | b = X1 - mE1. |
| Electrical Span | E2-E1 may be positive or negative. |
| Engineering Span | X2-X1 may be positive or negative. |
| Percentage of Span | P = (value-point1)/(point2-point1) × 100%, with no clamp. |
| Direct Acting | Slope greater than zero. |
| Reverse Acting | Slope less than zero. |
| 4-20 mA | X = XLOW + (I-4mA)(XHIGH-XLOW)/16mA. |
| Live Zero | 4 mA is the lower endpoint; 0 mA is not interpreted as 0%. |
| Voltage Presets | 0-5 V, 0-10 V, 1-5 V and 0.5-4.5 V only populate endpoints. |
| Out-of-Range | Classification uses endpoint min/max, not assumed point order. |
| Extrapolation | Out-of-range values are displayed and warned, not clamped. |
| Tolerance | E-ΔE and E+ΔE are recalculated through the same line. |
| Displayed Equation Units | Slope and E must use the same displayed electrical unit. |
| Internal Units | Voltage uses V and current uses A internally. |
| Rounding | Calculations use unrounded values; formatting is display-only. |
| SEN-005 Boundary | Pressure process assumptions stay in Pressure Sensor Scaling. |
| SEN-006 Boundary | Measured calibration and regression stay in Sensor Calibration. |
| SEN-007 Boundary | ADC codes and ENOB stay in Sensor ADC Resolution. |
Worked Examples
0-5 V midpoint
Known: 0-5 V maps to 0-100 units, input 2.5 V
Engineering value is 50 units.
0-10 V scaling
Known: 0-10 V maps to 0-100%, input 7.5 V
Engineering value is 75%.
1-5 V non-zero range
Known: 1-5 V maps to -50 to 150 °C, input 3 V
Engineering value is 50 °C.
0.5-4.5 V generic sensor
Known: 0.5-4.5 V maps to 0-100 bar, input 2.5 V
Engineering value is 50 bar.
4-20 mA midpoint
Known: 4-20 mA maps to 0-100 bar, input 12 mA
Engineering value is 50 bar.
4 mA endpoint
Known: 4-20 mA maps to 0-100 bar, input 4 mA
Engineering value is 0 bar.
20 mA endpoint
Known: 4-20 mA maps to 0-100 bar, input 20 mA
Engineering value is 100 bar.
0 mA extrapolation
Known: Same 4-20 mA mapping, input 0 mA
Mathematical value is -25 bar with below-range warning.
22 mA extrapolation
Known: Same 4-20 mA mapping, input 22 mA
Mathematical value is 112.5 bar with above-range warning.
Range crossing zero
Known: 4-20 mA maps to -100 to 100 °C, input 12 mA
Engineering value is 0 °C.
Inverse 4-20 mA
Known: Target 50 bar on 0-100 bar span
Required current is 12 mA.
Upper inverse endpoint
Known: Target 100 bar
Required current is 20 mA.
Reverse electrical range
Known: 10 V to 0 V maps to 0-100%, input 7.5 V
Engineering value is 25%.
Reverse engineering range
Known: 0-10 V maps to 100-0%, input 2.5 V
Engineering value is 75%.
Both ranges reversed
Known: 10-0 V maps to 100-0%, input 7.5 V
Engineering value is 75%.
Slope
Known: 0-10 V maps to 0-100 units
m=10 units/V.
Intercept
Known: 1-5 V maps to -50 to 150 °C
m=50 °C/V and b=-100 °C.
Percentage midpoint
Known: 2.5 V in 0-5 V
Span percentage is 50%.
Percentage overrange
Known: 6 V in 0-5 V
Span percentage is 120%.
Percentage underrange
Known: -1 V in 0-5 V
Span percentage is -20%.
Round trip
Known: Forward E to X, then inverse X to E
Original electrical value is recovered within floating precision.
Signal uncertainty
Known: 0-10 V maps to 0-100 units, 5 V ±0.1 V
Nominal 50 units with ±1 unit from electrical uncertainty.
Reverse tolerance
Known: 0-10 V maps to 100-0 units, 5 V ±0.1 V
Minimum and maximum are ordered correctly.
mV/V consistency
Known: 2500 mV and 2.5 V
Same internal voltage.
mA/A consistency
Known: 12 mA and 0.012 A
Same internal current.
Invalid zero span
Known: E1=E2 or X1=X2
Rejected because the transfer line is undefined for this V1 policy.
Engineering Notes
| Analog Sensor | Many analog sensors and transmitters can be approximated by a two-point linear transfer function. |
|---|---|
| Linear Scaling | Two electrical endpoints and two engineering endpoints define the ideal mapping. |
| Transfer Function | The transfer function is X=mE+b when displayed with a stated electrical unit. |
| Slope | Slope carries direction; do not take an absolute value inside the signed equation. |
| Offset | Non-zero electrical endpoints such as 1-5 V or 4-20 mA are common. |
| Intercept | Intercept depends on the electrical unit used in the equation. |
| Span | Span magnitude is useful for display, but signed span controls the math. |
| Zero | The electrical lower endpoint and engineering lower endpoint do not have to be zero. |
| Live Zero | 4 mA is a live-zero endpoint, and the nominal 4-20 mA span is 16 mA. |
| 0-10 V | 0-10 V outputs are common in industrial control and data acquisition. |
| 0-5 V | 0-5 V outputs are common in embedded systems. |
| 1-5 V | 1-5 V behaves like a voltage live-zero range. |
| 0.5-4.5 V | 0.5-4.5 V is common but not pressure-specific in this generic calculator. |
| Direct Acting | Direct acting means higher electrical signal maps to higher engineering value. |
| Reverse Acting | Reverse acting means higher electrical signal maps to lower engineering value. |
| Interpolation | Inside the endpoint range, the result is interpolation. |
| Extrapolation | Outside the endpoint range, the result is extrapolated and should be reviewed carefully. |
| Tolerance | Electrical uncertainty propagation is not total sensor accuracy. |
Common Mistakes
- Treating a 4-20 mA span as 20 mA instead of 16 mA.
- Thinking 12 mA is not 50% of a 4-20 mA span.
- Assuming 4 mA equals 4%.
- Assuming 0 mA equals 0% in a 4-20 mA loop.
- Assuming every sensor starts at 0 V.
- Assuming every engineering range starts at zero.
- Using abs() on a reverse-acting slope.
- Silently clamping overrange values to 100%.
- Mixing mA and A in the same equation.
- Mixing mV and V in the same equation.
- Displaying a slope in units/mA while the equation uses amps.
- Using an intercept based on the wrong electrical unit.
- Confusing ideal interpolation with measured calibration.
- Treating electrical uncertainty as total sensor accuracy.
- Reusing display-rounded values in later calculations.
Related Calculators
Pressure Sensor Scaling Calculator
AvailableUse pressure-specific voltage, current-loop and 4-20 mA workflows.
Open CalculatorSensor Calibration Calculator
AvailableFit two-point and multi-point calibration data with residual analysis.
Open CalculatorSensor ADC Resolution Calculator
AvailableAnalyze ADC codes, LSB size and engineering resolution after analog scaling.
Open CalculatorAccelerometer Voltage & g Calculator
AvailableUse a sensor-specific voltage-to-g transfer function.
Open CalculatorPhotodiode Sensor & TIA Calculator
AvailableConvert optical power and photodiode current through a TIA signal chain.
Open CalculatorVoltage Divider Calculator
AvailableReview a common signal-conditioning circuit that can feed analog inputs.
Open CalculatorSupport reference
FAQ
How do I scale an analog sensor signal?
Define two electrical endpoints and two engineering endpoints, then use linear interpolation: X = X1 + (E-E1)(X2-X1)/(E2-E1).
How do I convert sensor voltage to engineering units?
Enter the sensor voltage endpoints, engineering endpoints and measured voltage. The calculator preserves non-zero offsets such as 1-5 V or 0.5-4.5 V.
How do I convert engineering units back to voltage?
Use the inverse formula E = E1 + (X-X1)(E2-E1)/(X2-X1), provided the engineering span is non-zero.
How do I scale a 4-20 mA signal?
Use X = XLOW + (I-4 mA)(XHIGH-XLOW)/16 mA. A 4-20 mA loop has a 16 mA span.
What engineering value does 12 mA represent in a 4-20 mA loop?
12 mA is halfway between 4 mA and 20 mA, so it represents 50% of the configured engineering span.
Why is 4 mA called a live zero?
4 mA represents the lower engineering endpoint while leaving current below the normal span for diagnostics, fault indication or underrange behavior depending on the system.
How do I scale a 0-10 V sensor?
Use 0 V and 10 V as the electrical endpoints, then enter the engineering range such as 0-100%, 0-1000 rpm or -50 to 150 degrees.
How do I scale a 0-5 V sensor?
Use 0 V and 5 V as the electrical endpoints. The engineering endpoints do not have to start at zero.
How do I scale a 1-5 V sensor?
Use 1 V and 5 V as endpoints. The lower endpoint maps to 0% span or to whatever engineering value you assign to point 1.
How do I scale a 0.5-4.5 V sensor?
Use 0.5 V and 4.5 V as endpoints. This calculator treats it generically and does not assume the sensor measures pressure.
How do I calculate the slope of a sensor transfer function?
Slope is (X2-X1)/(E2-E1). The sign is preserved so reverse-acting sensors work correctly.
How do I calculate the sensor scaling intercept?
After solving the slope, use b = X1 - mE1. The displayed equation must use the same electrical unit as the displayed slope.
How do I scale a reverse-acting sensor?
Enter the endpoints in their real order. Do not take absolute values inside the transfer equation.
What happens when the input is outside the sensor range?
The calculator extrapolates mathematically and marks the value below or above range. It does not silently clamp to the endpoint.
Should analog sensor values be clamped to 0-100%?
No for engineering review. Values below 0% or above 100% are useful for identifying underrange, overrange or wiring issues.
How does electrical signal error affect engineering value?
For an ideal linear mapping, the engineering error magnitude is |m| times the electrical uncertainty. This is not total sensor accuracy.
What is the difference between scaling and calibration?
Scaling uses ideal endpoints. Calibration uses measured data to fit or correct the transfer function and belongs in the Sensor Calibration Calculator.
What is the difference between this calculator and the Sensor ADC Resolution Calculator?
This calculator maps analog signal to engineering value. The ADC calculator analyzes codes, LSB size, ENOB and quantization resolution.