how many measurable dimensions are known in the space and time?

Four.

Length

Height/Depth

Width

These spacial dimensions can be measured with a ruler if they are small enough.

Time

This is measured with a watch.

Edit

LE Grant raises a good point the word "dimension" means something different to different people. A mathematician's definition of a dimension (from Linear Algebra) is not the same as what a physicist would argue is a dimension.Einstein popularised the concepts of the four dimensions of space-time as a co-ordinate system involving the co-ordinates (x,y,z,t) that is three perpendicular (or orthogonal) directions in space and then time. Giving us the length, width, height (or depth) and time. In dimensional analysis we think in terms of independent measurable values for example, mass, length, electric charge and absolute temperature. Note these dimensions are abstract concepts unlike kilogrammes, metres, coulombs and kelvin which are arbitrary scales.

As L E Grant's answer demonstrates though the word dimension doesn't have a universally accepted definition and means something different to a mathematician than to a physicist and both are different to that understood by a layman.

3+1=4

Measurable dimensions span the Universe as we perceive. here Measure is Euclidean measure that is the root mean square value & is called distance.

LE Grant' answer doesn't address that. Mass, time, length & direction are all connected by Mathematical formulae that are relevant like the equation for Gravity. But they can't form the framework in which Euclidean distance (measure) makes sense.

When Einstein introduced 'time' as the fourth dimension he needed to fit into our all too familiar 3D Universe. He did it by roping in the speed of light as the linking factor since

c = s/t________

& r = √x²+y²+z²,

and the distance is ____________

distance=√(s²+r²)=√x²+y²+z²+(ct)².

The point to remember is to bring all the components into the same units, that alone mathematically spans the Space.

Only four. three spatial dimensions and one temporal dimension!!

four: mass, time, length and direction

I believe they are working on an 11th one.