Proper Way To Handle Gravity?

I have been thinking about a proper way to handle gravity in a 3d shooter.

Imagine your character is 16 units in height. The average human is say… 2 meters tall. This means that 1 meter is 8 units. the ratio is 1:8.

If gravity is expressed as 9.81 m/s^2 I believe then it would be equal to 78.48 units/s^2

However, this is only your acceleration per second…

If a game is running at 60 frames per second, this is where I become quite shaky, because you cannot just divide the gravity (78.48) by 60, and treat it as normal…

Assuming this conventional way of handling gravity is correct:

velocity.z += gravity;
z -= velocity.z;

How would you take into account there being 60 calculations per second?

Yes, I have tried dividing the 78.48 by 60, but it does not feel correct…