Calculating angles for the gradient

 1cm on a 1:25000 map represents 250m on the ground. I have used arctan to calculate the gradients, having explained why it is tan on the previous post

Now the angle for the number of contours could be +-1 degree depending on whether the contours are just inside the edge of the 1cm or whether the next contour is only just beyond the edge. Looks like the rule of thumb is roughly double the number of contours to get the angle. I tested the theory on this photograph of Catstycam.

Using a protractor, the angle of the steepest part of the ridge disappearing into the cloud in 25 degrees. On the map that section has 12 contours in 1cm which comes out at 25 degrees.