Lower range value
Density assigned to the lower signal endpoint.
Unit Converters
Density Sensor Scale Calculator
Translate a current, voltage, frequency, or other linear sensor signal into engineering density while preserving both signal and density endpoints and clearly flagging extrapolation.
Linear transmitter calibration
Map a live sensor signal to density without hiding extrapolation
Use two documented signal and density endpoints to calculate a linear transfer function, live density, span fraction, sensitivity, and out-of-range status.
Mapped density—
Signal span fraction—
Density sensitivity—
Signal span—
Density span—
Range status—
Map a live sensor signal to density without hiding extrapolation ledgerUnrounded values drive calculations and decisions
| Calibration point | Signal | Density | Interpretation |
|---|
How to use
Map a live sensor signal to density without hiding extrapolation
Use two documented signal and density endpoints to calculate a linear transfer function, live density, span fraction, sensitivity, and out-of-range status.
- Copy lower and upper signal endpoints from the transmitter configuration.
- Copy the matching lower and upper density range values.
- Use one signal type and one density unit throughout the mapping.
- Enter the live corrected signal and inspect extrapolation status.
- Verify the mapped result against a known check point before operational use.
Signal-to-density quantities
Upper range value
Density assigned to the upper signal endpoint.
Span fraction
Live signal position between signal endpoints.
Sensitivity
Density change per signal unit.
Extrapolation
Linear result outside the calibrated signal span.
Result interpretation
Read endpoint mapping and extrapolation
A fraction from 0 to 1 is inside the declared signal span. Values outside that interval are extrapolated even if the arithmetic remains finite. Sensitivity may be negative for an intentionally reversed density mapping; do not silently reorder endpoints.
Calculation method
Map a live signal through calibration endpoints
Subtract lower signal from the live signal and divide by signal span. Multiply that fraction by density span and add the lower density endpoint. Calculate sensitivity as density span divided by signal span and preserve the original orientation.
Evidence checks
Endpoint and extrapolation checks
Calibration identity
Endpoints must belong to the same transmitter range, configuration revision, and output mode.
Signal correction
Account for loop offsets, scaling in acquisition hardware, or digital raw counts before applying this mapping.
Linear-response assumption
A linear transfer function is valid only when the sensor or transmitter output is configured linearly in density.
Reversed mapping
A falling density with rising signal is allowed mathematically but should be confirmed against configuration.
Extrapolation response
Out-of-range output may represent overrange, fault current, or saturation rather than a valid density.
Independent checkpoint
A midpoint or certified-fluid check can reveal endpoint transcription or configuration error.
Process validity
Correct signal mapping does not guarantee the sensor is free of coating, bubbles, temperature bias, or installation effects.
Visual explanation
Two-axis signal-to-density calibration line with live marker
Signal runs horizontally and mapped density vertically. Endpoint markers define the calibration line; the live marker remains on the line but changes status when it leaves the declared signal interval.
Detailed calculation process
Signal fraction and engineering-unit substitution
fraction = (S − SLRV)/(SURV − SLRV); ρ = ρLRV + fraction(ρURV − ρLRV); sensitivity = (ρURV − ρLRV)/(SURV − SLRV)
| Symbol | Meaning | Required unit |
|---|---|---|
| S | live corrected signal | selected signal unit |
| SLRV,SURV | signal endpoints | selected signal unit |
| ρLRV,ρURV | density endpoints | selected density unit |
| fraction | signal span position | dimensionless |
| sensitivity | density per signal | density/signal unit |
| ρ | mapped density | selected density unit |
- Waiting for current inputs.
- Waiting for current inputs.
- Waiting for current inputs.
- Waiting for current inputs.
- Waiting for current inputs.
- Waiting for current inputs.
Reconciliation:Waiting for current inputs.
Defaults and assumptions
Linear transmitter span
Defaults demonstrate a 4–20 mA loop mapped from 600 to 1200 kg/m³ with a 12 mA live signal. Confirm the actual transmitter configuration before use.
| Check | Current value A | Current value B | Decision role |
|---|
Decision analysis
Use the mapped value only inside its calibration scope
Use an in-range mapped value for monitoring after calibration and installation checks. Route extrapolated or fault-region signals for instrumentation review instead of treating them as valid process density.
Validate the complete signal chain rather than only the endpoint arithmetic. A control-system tag can apply its own raw-count scaling, square-root extraction, offset, damping, or engineering conversion before the value reaches this page. Confirm where the entered live signal is measured and ensure the two calibration endpoints refer to that same stage. Compare the mapped midpoint with an independent configured checkpoint, because swapped density endpoints or an obsolete transmitter range can still produce a smooth line. Interpret overrange according to device documentation: some transmitters continue measuring beyond nominal range, while others use specific high or low currents for fault status. Do not report a numerically extrapolated density when the signal actually represents fault, saturation, open circuit, or diagnostic mode. If sensitivity is negative, confirm that the reverse orientation is intentional and preserved through alarms and displays. Correct transfer-function mapping also does not remove process error from coating, bubbles, vibration, temperature, pressure, installation, or sample nonrepresentativeness. Retain transmitter tag, range revision, loop location, signal quality, and checkpoint evidence with every operational use of the mapped density.
Evidence and data lineage
Retain endpoint certificates and signal source
Retain transmitter tag, serial number, configuration revision, signal type, endpoint units, density range, live timestamp, correction chain, check-point evidence, and extrapolation status.
Limits and exclusions
What a linear scale cannot validate
The model excludes nonlinear sensor response, temperature compensation, digital protocol status, loop fault conventions, damping, calibration uncertainty, and process installation effects.
Reliable sources
References for Map a live sensor signal to density without hiding extrapolation
Calibration terms
Worked cases
Density transmitter decisions
4–20 mA densimeter
The 12 mA signal maps to the midpoint density and agrees with a certified-fluid checkpoint.
Fault-region signal
A 22 mA input extrapolates numerically but is routed to instrument diagnostics instead of reported as density.
Important note
Map a live sensor signal to density without hiding extrapolation: scope before action
A valid equation can translate an invalid instrument signal. Interpret device status and configured fault behavior before using the mapped number.
Map a live sensor signal to density without hiding extrapolation FAQ
Can density endpoints decrease as signal rises?
Yes, but confirm the reversed configuration intentionally.
What if signal endpoints are equal?
The transfer function is undefined and the inputs are rejected.
Does the calculator assume mA?
No. Signal labels are generic; all three signals must share one unit.
Can I use voltage?
Yes for a documented linear voltage output.
Can I use raw digital counts?
Yes when endpoint counts and preprocessing are documented.
What does 50% fraction mean?
The signal is halfway between declared endpoints.
Does 120% mean a valid measurement?
No. It is extrapolated and may be overrange or fault.
Why retain negative sensitivity?
It preserves an intentionally reversed endpoint orientation.
Does this calibrate the sensor?
No. It applies entered calibration endpoints.
Can it correct temperature?
No. Use the transmitter’s validated compensation or a separate model.
Why verify a midpoint?
Two correct-looking endpoints can still be transcribed from the wrong range.
Does rounding affect status?
No. Unrounded fraction controls extrapolation.
Can I map specific gravity instead?
Only if both endpoints and output are explicitly specific gravity.
What must the PDF show?
It records endpoints, live signal, mapped density, sensitivity, and range status.