Pressure Transducer Calibration and Transmission Factor Calculator

An electromechanical pressure transducer reports its output as a ratio signal in mV/V. Enter the six readings taken at each calibration pressure — three on ascending runs (columns 1, 3 and 5) and three on descending runs (columns 2, 4 and 6). The calculator fits one sensitivity through zero by least squares, gives the transmission factor that converts signal to pressure in bar, and works out the point sensitivity, its deviation from the fit, the relative hysteresis and the expanded uncertainty at every nonzero pressure, following the scheme of EURAMET cg-17 version 1.0 (2007). The fields start with the calibration data of Table E2b of that guide, with its example uncertainty budget (page 29) entered at each nonzero pressure, so a full result is visible before you enter your own data.

Calibration data

Coverage factor k (unitless)

Results

Results appear here as soon as every field is valid.

Least-squares sensitivity through zero, S₀

—

(mV/V)/bar

Transmission factor c = 1/S₀

—

bar/(mV/V)

Signal means, modelled pressure and point sensitivity

Pressure pbar	Ascending meanmV/V	Descending meanmV/V	Descending − ascendingmV/V	Overall meanmV/V	Modelled pressure c × meanbar	Sensitivity S = mean/p(mV/V)/bar	Deviation δ = S − S₀(mV/V)/bar

Uncertainty budget per point

Pressure pbar	w_refrelative, unitless	w_elecrelative, unitless	z/√12relative, unitless	b/√12relative, unitless	r/√12relative, unitless	Hysteresis hrelative, unitless	h/√12relative, unitless	wrelative, unitless	W = k × wrelative, unitless	U = \|S\| × W(mV/V)/bar	Error span U + \|δ\|(mV/V)/bar

Readings at 0 bar stay in the least-squares fit but have no sensitivity, deviation or relative uncertainty. No intermediate value is rounded; figures are displayed to 12 significant digits.

How to use the calculator

Enter the coverage factor k. It must be greater than 0; k = 2 is the common choice.
For each calibration pressure, enter the pressure in bar and the six raw output signals in mV/V, in run order: columns 1, 3 and 5 are the ascending runs, columns 2, 4 and 6 the descending runs.
At every nonzero pressure, enter the relative standard uncertainty of the reference pressure (w_ref) and of the electrical measurement (w_elec), and the full widths of the relative rectangular intervals for zero error (z), repeatability (b) and reproducibility (r). All five are relative values and cannot be negative. At 0 bar these fields are not used.
Use “Add pressure point” and “Remove point” to match your calibration sequence. Results update as you type; Calculate runs the same computation again.
Read S₀ and the transmission factor c, then the means, modelled pressure, sensitivity, deviation and uncertainty budget at each point.

Method

For each pressure p the calculator averages the readings:

ascending mean = (signal₁ + signal₃ + signal₅) / 3

descending mean = (signal₂ + signal₄ + signal₆) / 3

overall mean = (sum of all six signals) / 6

The signal is fitted against pressure with a least-squares straight line through zero, using every raw signal, so each pressure counts six times:

S₀ = Σ(p × signal) / Σ(p × p) in (mV/V)/bar

c = 1 / S₀ in bar/(mV/V); modelled pressure = c × overall mean

The guide describes a straight line fitted to the calibration data, with no intercept in its model; this calculator realises that line by least squares. At every nonzero pressure:

S = overall mean / p and δ = S − S₀

h = |descending mean − ascending mean| / |overall mean|

w = √( w_ref² + w_elec² + (z² + b² + r² + h²) / 12 )

W = k × w, U = |S| × W, error span = U + |δ|

If all pressures are zero, or if S₀ comes out as zero, no transmission factor exists and the calculator stops with a message. If the overall mean at a nonzero pressure is zero, the relative hysteresis and the uncertainty that depends on it are undefined.

Worked example

With the Table E2b data of the guide (pressures from 0 to 200.113 bar), S₀ = 0.010001506287 (mV/V)/bar and c = 99.9849393974 bar/(mV/V). At 100.056 bar the ascending mean is 1.0007 mV/V, the descending mean 1.00133 mV/V and the overall mean 1.001015 mV/V, giving a modelled pressure of 100.086424111 bar. With w_ref = 0.00005, w_elec = 0.000025, z = 0.00003, b = 0.00009, r = 0.00015 and k = 2: S = 0.0100045474534 (mV/V)/bar, δ = 0.0000030411663 (mV/V)/bar, w = 0.0001968704138, W = 0.0003937408276, U = 0.0000039391988 (mV/V)/bar and error span = 0.0000069803651 (mV/V)/bar. These agree with pages 26 and 29 of the guide at its printed precision.

Frequently asked questions

Why is the line fitted through zero?

The calibration model has no intercept. The output signal is taken as proportional to pressure, signal = S0 × p. A single factor then converts signal back to pressure, c = 1/S0, and the modelled pressure is c times the mean signal.

Do the zero-pressure readings change the fit?

They are kept in the sums, but every term at 0 bar is multiplied by p = 0, so they add nothing to Σ(p × signal) or Σ(p²) and do not move S0. A point sensitivity signal/p cannot be formed at zero pressure, so that point has no sensitivity, deviation or relative uncertainty.

Why are zero error, repeatability, reproducibility and hysteresis divided by 12?

Each is entered as the full width of a rectangular interval relative to the signal. A rectangular distribution of full width a has a standard deviation of a/√12, so its variance is a²/12.

What is the error span?

It is the expanded uncertainty of the point sensitivity, U = |S| × W, plus the magnitude of the deviation δ = S − S0. It describes how far the single value S0 may differ from the sensitivity at that pressure when S0 is used across the whole range.

When is the relative hysteresis undefined?

Relative hysteresis divides the difference between the descending and ascending means by the overall signal mean. If that mean is exactly zero the ratio does not exist, so h, w, W, U and the error span are reported as undefined at that pressure.

Does the calculator decide whether the transducer passes?

No. It reports the fitted factor, the point results and the uncertainties only. Any comparison with a specification or tolerance is left to you.

This calculator implements the calculation scheme of EURAMET cg-17 version 1.0 (2007), pages 18 and 25 to 30, as summarised above. It does not replace a documented calibration procedure, an accredited uncertainty evaluation or the guide itself, and it gives no statement of compliance. Check the results before using them in a certificate or a quality decision.