Three basin properties which apply to all basins;
       Linear properties - one dimension
       Areal properties - two dimensions
       Relief properties - three dimensions

Linear Properties
The linear parts of a river basin are the channels themselves. Water falling within the boundaries of a river basin eventually enters the stream channel and the stream transports the material which the slope processes bring to the bottom of the valley. The size of rivers and basins varies greatly, thus they are classified and ordered.
The ordering system was developed by A.N.Strahler. All the streams which flow from a source and have no tributaries are classified as first order streams. The confluence of two first order streams produces a second order stream, and the confluence of two second order streams produces a third order stream etc.
The relationships between the number of streams and order is known as Horton’s Law of Stream Numbers. It states that:
‘there is a geometric ration between the number of streams of one order and the next’
This ratio is known as the Bifurcation Ratio.

The bifurcation ration of large basins is generally the average of the bifurcation rations of the stream orders within it. Most natural stream systems have a ration of between 3 and 5.
There is also an informal relationship between stream length and order. Higher order basins generally have longer rivers.

Areal Properties
By introducing a second dimension, the areal properties of a basin can be measured. It is possible to delimit the area of the basin which contributes water to each stream segment. The watershed can be traced from where the stream has its confluence with the higher order stream along hillcrests to pass upslope of the source and return to the junction. This line separates slopes which feed water towards the streams from those which drain in to other streams.If the area of the 1st order basin is found in this way, it is possible to calculate the mean area of the basins. If the watersheds of the second basins are traced in the same way, it will be seen that there are areas which drain directly in to the second order stream. These are called inter basin areas, and they mean that the area of the second order basin is not the sum of the areas of the first order basins.
(i)    Density
The average length of channel per unit area of the drainage basin is called the drainage density.

Drainage density = SL / SA

where SL is the total length of streams in the basin, and SA is the total area of the whole basin.

This indicates how frequently streams occur on the land surface. Factors affecting drainage density include geology and density of vegetation. The vegetation density influenced drainage density by binding the surface layer, thus preventing overland flow from concentrating along definite lines and from eroding small rills which might become small channels. The vegetation slows down the rate of overland flow, and stores some of the water for short periods of time.
The effect of lithology on drainage density is marked. Permeable rocks with a high infiltration rate reduce overland flow, and consequently drainage density is low. Groundwater flow is important. Example; chalk areas of the South East.
Impermeable rocks with little vegetation, with heavy downpours will produce high drainage densities. Example; Badlands of Arizona.

(ii) Shape
Shape is important. Long basins have flatter hydrographs and take longer to achieve a throughflow of water from a rain storm. The most efficient basin would be one in which the watershed is circular and all the water disappears down a hole in the middle. Two measures have been devised to assess shape.
(a) Basin circularity compares the area of the basin to the area of a circle of the same circumference.

Basin circularity = 4p SA / P2.

where SA is the total area of the basin, and P is the length of the basin perimeter of watershed.
The closer the number is to 1, the more like a circle the watershed is.
(b) Basin elongation compares the longest dimension of the basin to the diameter of a circle of the same area as the basin.

Basin elongation = Dlp 4SA

where Dl is the longest dimension of the basin, and SA is the total area of the basin. This indicated how nearly circular the area of the basin is. The nearer 1, the greater the correspondence to a circle.

Relief Properties
All the above features have been considered to lie on a plane surface. The third dimension introduces the concept of relief. By measuring the vertical fall from the head of each stream segment to the point where it joins the higher order stream and dividing the total by the number of streams of that order, it is possible to obtain the average vertical fall. If this is plotted against the average stream length of that order, then the average gradient is obtained.
The average gradients of streams of each order when linked together produce an average long profile of the basin. Generally, these long profiles illustrate that the lower order tributaries are steeper than those of the higher orders. This relationship is well established in geomorphology.