calculating tension

[ScienceGirl502]

is there a basic formula for calculating tension?

like the tension in a cable or string holding up a sign, etc.

[Galileo]

You have to look at the particular problem for calculating the tension.

In equilibrium problems, the basic idea is that the tension in a string at one end is of that magnitude as to keep the object at that end stationary.
If there's a lamp of mass m hanging down from a cable vertically,
then gravity acts on the lamp with a force -mg (I take up as the positive direction).
Since the net force on the lamp is zero, the tension in the cable at that end is mg.
The tension in the cable where it is attached to the ceiling is greater, since the combined gravitational force acting down is -g(m+m_c). Where m_c is the mass of the cable.

If the cable is massless, the tension always has the same magnitude throughout.

In general, every problem needs its own ideas to solve (eg. for the tension). The important thing is to understand the concept and being able to apply it. Not just learning formulas and plugging in the data.

[arildno]

"If the cable is massless, the tension always has the same magnitude throughout."
For accelerating systems, this is not always correct (for example a rope not moving relatively to a rotating pulley, or when there is kinetic friction between the rope&pulley).