The pressure error term in the formula to compute the sensor error is quoted in kPa, that's what made
me think the error term was in kPa, overall you show the error as +/- 1.25 kPa so I will use that.
If I use your above calculations and plug in the voltage I get off the sensor at 6 kPa I get
the following
P(Vout) = (Vout / (Vs x 0.018) - 0.04/0.018) +/- 1.25kPa
P(Vout) = (0.583/(5 x 0.018) - 0.04/0.018) +/- 1.25kPa
P(Vout) = (0.583/0.09) - 2.22 +/- 1.25kPa
P(Vout) = 6.48 - 2.22 +/- 1.25kPa
P(Vout) = 4.26 kPa +/- 1.25kPa
I would be great if we always knew the actual pressure (6 kPa) but then we wouldn't need the sensor
to measure it. In this case the sensor reading indicates 4.26 kPa and its off by 1.74 kPa, not 0.5 kPa.
Regarding your question ( voltage at 12.95 kPa)
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Applying 12.95 kPa I read a voltage of 1.02 Volts.
Using the same method I and a reading of 1.02 Volts
P(Vout) = (1.02/0.09) - 2.22 +/- 1.25kPa
P(Vout) = 11.33 - 2.22 +/- 1.25kPa
P(Vout) = 9.12 +/- 1.25kPa
Since in this case we know the pressure ahead of time is 12.95 and the sensor is reads 9.12 +/- 1.25 kPa
it is off by 3.83 kPa which is much larger than the error term of 1.25 kPa.
Even if I could somehow know to add the error so that the sensor reads 9.12 kPa + 1.25 = 10.37 kPa,
it's still off by 2.6 kPa.