Hi, I'm new to this and I am experimenting with an arduino and a analog pressure transducer.

Sensor:
Input: 0-10,34 bar(Gauge Pressure);
Output: 0.5-4.5V linear voltage output. 0 bar outputs 0.5V, 5,18 bar outputs 2.5V, 10,34 bar outputs 4.5V.
Wiring: Red: +5V; Black: ground; Blue: signal output;

int pressen = 0; // Set pressure sensor input on Analog port 0
void setup() {
}
void loop() {
// MEASUREMENT
int raw = analogRead(pressen); //Reads the pressure sensor raw value on analog port 0
float voltage = raw * 0.004887586;
float pressure = 0.0;
// MATH
{
pressure = voltage * 10,3/4.0; // it raises 10,3 bar over 4 volt faster => pressure = voltage * 2,575;
}
}

But this assumes output ranges from 0 to 5 v, how can I adjust this for 0,5 to 4,5 volt? My pressure will never get above 8 bar, does this mean I don't have to worry about the 4,5 volt?

The comma won't work here, use a decimal point:pressure = voltage * 10,3/4.0;

In any case, to calculate pressure from voltage, it is better to use all the information you have. The response of the gauge appears to be linear with an offset (as the attached plot shows), which would be better than what you have now. The best fit linear equation is shown in red on the plot and can be easily inverted to obtain pressure from voltage.

0.5V = 102.3
4.5V = 902.7
Range from 0 to 10.34 bar is 802.4

So:

//Measurement
float raw = analogRead(pressen); // I'm not sure what mixing int with float will do, so I've made this a float
//Math
float pressure = (raw - 102.3) * 10.34/802.4;

You won't get more than 3 digits of accuracy because you are only starting with 10 bits, and not even the entire 10 bits. There are ways to get more useful bits out of the Arduino's 10 bit ADC. There are also external 16 bit ADCs.

If you want speed, use unsigned int and use integer math by multiplying everything by 100, then merely display the decimal point in the appropriate place when you send it to the display. I reduced 1034/80240 by dividing both by 2 to get the largest number to fit in an unsigned int.

//Measurement
unsigned int raw = analogRead(pressen) * 100; //
//Math
unsigned int pressure = (raw - 10230) * 517/40120;

Thank you very much for catching that. I corrected the numbers as necessary below:

//Measurement
float raw = analogRead(pressen); // I'm not sure what mixing int with float will do, so I've made this a float
//Math
float pressure = (raw - 102.3) * 10.34/818.4;

//Measurement
unsigned int raw = analogRead(pressen) * 50; //
//Math
unsigned int pressure = (raw - 5115) * 517/40920;