To calculate air density you need the temperature, pressure, humidity and the gas constant, but it can get more complicated than you might think. Our density calculations page has the formulas and other information you'll need to find air density using either metric or American units. If the balloon is filled with helium, it is less dense then the air surrounding the balloon. This is why the balloon rises. If the balloon is filled with air and if it has sat long enough for the air inside to reach same temperature as the air surrounding the balloon, then the air inside will be a little more dense than the outside air.
Air density depends on the temperature, the pressure and the humidity.
In free air, the density decreases as temperature and humidity go up and increases as the pressure goes up. The air inside the balloon is at a higher pressure than the air outside, and is therefore more dense. We know the air inside is at a higher pressure because it is pushing outward on the balloon in order for the balloon to hold its shape. Another way to put it. The elastic balloon is exerting a force toward the center of the balloon.