How can I know when my battery is fully charged?

When the red light turns off and only the green light is on that indicates that the battery pack is charged and the vehicle is ready to use. If the charger light stays green and there is no red light when the charger is plugged into the vehicle and into the wall this could be caused by many things.
https://support.electricscooterparts.com/support/solutions/articles/1000104443-charger-light-stays-green-when-charging

Hi testing battery voltage will not give an accurate reading on battery condition U need a BATTERY LOAD TESTER.it will check the condition & give U a true reading on there condition ,..if batteries r good the next thing to check is the control box the charger circuit runs into the control then to the batteries if control box is faulty this could b the problem .,with youre charger not charging . LOAD TESTER AVAILABLE ON E/BAY APROX COST $35 , Cheers

First measure the voltage of the batteries at the charging socket of the joystick.

Janice check your charger it could not be charging the batteries. Now always charge your batteries overnight while you sleep When you get up lights on the charger should be red and green if they are red and yellow then the charger hasn't fully charged the batteries and overnight should be more than enough time to charge fully. This could indicate a bad battery remember new doesn't always mean good. Like they say always charge before use and this goes for new batteries too you need to charge new batteries nightly for 10-15 days before they start operating at 100%. If when you plug in the charger before bed and the lights are red and green then there is a problem with the charger or the batteries or the charger circuit Hope this helps you

If you have an off-board charger that plugs into the joystick there are two lights on the charger one red(power on) and the other yellow (turns green when fully charged). Plug it into the chair and if the light is green then you have fully charged the batteries. Now if you have the on-board charger the charger meter on the rear of the chair will resd zero when fully charged. Hope this helps ya

Here is the manual:
http://toolboyworld.com/eBay/Ryobi_P120/P120_566_eng.pdf

Red = quick charge
yellow = evaluating
green = charged

CHARGING A COOL BATTERY PACK
If battery pack is within normal temperature range, the red LED on charger will come on.

Red LED should remain on for approximately 1 hour then the green LED will come on. Green LED on indicates battery pack is fully charged and charger is in maintenance charge mode.

the charger light detect the battery level charge, shows red when charging and green when fully charged.when the charger light is not lit,may be the battery dosnt hold any charge that means its likely that the battery is defective

Depends, is there another LED present that yuo would expect to light up? Not familiar with these chargers. Ours do a number of things to let you know what is going on. A dead battery lights up the charger with ared LED, it blicks red if the battery is defective, and goes green when fully charged. along the way I think there is an amber LED indicator but I am not sure what that does.
Your may go green or just blank out when fully charged.

When batteries are placed into the charge mode, the red light will come on.
When fully charged, on those units with a green light, the green light will be an indication that your batteries are charged and if your unit has no green light, the fully charged indication will be when the red light turns iff.

I would go to Radio Shack and have them explain the proper charging procedure as well as inquire about the red and green lights as not all chargers go green when fully charged-Normally red indicates a charging action and if a charger has no fully charged light, then a required charge time period is noted in the instructions. Batteries can be ruined by over charging!