user-1: As soon as I unplug my Arduino from USB and only use the VIN pin with my 9 V power supply, the analog readings from my Arduino start to get unstable, which means the value fluctuates much more than with USB connected. When I reconnect USB again, the readings are stable again.
I'm trying to build a load scale using a load cell, an INA125P and the Arduino, using this setup here: Instrument Amplifier Calibration.
Therefore I need stable readings. For example, I wrote some code to convert the analogRead() value to grams. While USB and VIN (9 V) connected, I get a stable reading of about 8.3 to 8.7 grams when I put a weight of 8.5 grams on the scale. As soon as I unplug USB, the LCD shows values from 7.8 grams up to 9 grams.
Unfortunately, I don't have any other power supply which I could use to test. I've already tried to use a 9 V battery with the same results. Do I maybe need some additional de-coupling capacitors?

user14238: I would say that this may be related to the analog reference. Try AnalogReference and see if it helps.

user-1: Does your arduino have a switch-mode regulator when converting 9V to 5V? If that's the case, then you must have some voltage ripple on your 5V power line. I'm guessing you are probably using analogRead which uses that 5V reference. If there is a ripple in your reference voltage, you will get a ripple in your readings.
Can you use the internal 1.1V reference of Atmega328p chip? That reference voltage is (as far as I know) the most stable you can provide for ADC. 
If that doesn't work, then you need to find a very stable 5V adapter for your 9V sources.

user33419: Load cell signals are very small and without proper shielding are be susceptible to noise. The USB power connector is likely earth grounded (the clue was battery operation is noisy, exact opposite of expectations!) I suggest testing this hypothesis:

Check with ohm meter if exposed metal on USB connector is connected to earth (chassis on your PC is usually earth connected).
Touch an earth grounded conductor to the signal ground of the load cell amplifier and see of the readings become more accurate.

The final solution is to use properly shielded signal wires between the load cell and the amplifier. Also the signal wires between load cell and amplifier should be a 'twisted pair' to further reduce noise.

user34320: I solved a similar issue by adding a pin from supply to AREF and it's now stable. This fixed a frustrating pH meter issue on my Mega that every time I plugged USB in it would be right, but as soon as I dropped the USB cable it changed the readings.

-1: <p>As soon as I unplug my Arduino from USB and only use the VIN pin with my 9&nbsp;V power supply, the analog readings from my Arduino start to get unstable, which means the value fluctuates much more than with USB connected. When I reconnect USB again, the readings are stable again.</p>

<p>I'm trying to build a load scale using a load cell, an INA125P and the Arduino, using this setup here: <a href="https://learn.adafruit.com/smart-cocktail-shaker/calibration" rel="nofollow noreferrer">Instrument Amplifier Calibration</a>.</p>

<p>Therefore I need stable readings. For example, I wrote some code to convert the <code>analogRead()</code> value to grams. While USB and VIN (9&nbsp;V) connected, I get a stable reading of about 8.3 to 8.7 grams when I put a weight of 8.5 grams on the scale. As soon as I unplug USB, the LCD shows values from 7.8 grams up to 9 grams.</p>

<p>Unfortunately, I don't have any other power supply which I could use to test. I've already tried to use a 9&nbsp;V battery with the same results. Do I maybe need some additional de-coupling capacitors?</p>
 14238: <p>I would say that this may be related to the analog reference. Try <a href="https://www.arduino.cc/en/Reference/AnalogReference" rel="nofollow">AnalogReference</a> and see if it helps.</p>
 -1: <p>Does your arduino have a switch-mode regulator when converting 9V to 5V? If that's the case, then you must have some voltage ripple on your 5V power line. I'm guessing you are probably using analogRead which uses that 5V reference. If there is a ripple in your reference voltage, you will get a ripple in your readings.</p>

<p>Can you use the internal 1.1V reference of Atmega328p chip? That reference voltage is (as far as I know) the most stable you can provide for ADC. </p>

<p>If that doesn't work, then you need to find a very stable 5V adapter for your 9V sources.</p>
 33419: <p>Load cell signals are very small and without proper shielding are be susceptible to noise. The USB power connector is likely earth grounded (the clue was battery operation is noisy, exact opposite of expectations!) I suggest testing this hypothesis:</p>

<ol>
<li>Check with ohm meter if exposed metal on USB connector is connected to earth (chassis on your PC is usually earth connected).</li>
<li>Touch an earth grounded conductor to the signal ground of the load cell amplifier and see of the readings become more accurate.</li>
</ol>

<p>The final solution is to use properly shielded signal wires between the load cell and the amplifier. Also the signal wires between load cell and amplifier should be a 'twisted pair' to further reduce noise.</p>
 34320: <p>I solved a similar issue by adding a pin from supply to AREF and it's now stable. This fixed a frustrating pH meter issue on my Mega that every time I plugged USB in it would be right, but as soon as I dropped the USB cable it changed the readings.</p>
