There is a way to check the state of the battery using a voltmeter.
After a long drive (to make sure that the battery is fully charged) leave the car standing ~12 hours (over night).
Then measure the "open circuit voltage". Dont turn on the ignition! Just open the bonnet and measure the voltage. For the best measurements you should disconnect the cables from the battery to ensure there is absolutely no consumption from the car.
Measured voltage shows "state of charge".
100% - 12.65V
75% - 12.45V
50% - 12.24V
25% - 12.06V
0% - 11.89V
Your battery should keep at least 75% state of charge. If it is under that that is a sign that the battery is worn.
But those voltages are only valid at 20°C. If it is colder outside, then you must substract 0.022V/°C from your measured voltage.
So for instance, if there is 10°C outside, and you measured 12.3V with your voltmeter you should substract 0.22V. So the corrected value is 12.08V. And that is lower than 50% state of charge... time to think about new battery.