To calculate actual distance (d) off of a topo map. Determine the horizontal distance taveresed (x), count up the number of contour lines you cross (n), and the vertical distance between each contour line (h). Plug into this equation:

d = x/sin(arctan(n*h/x))

if you don't like arctan and sin's you can use the alternate formulation:

d = square root(x^2 + (n*h)^2)

With topo map software you could easily develop a cubic spline algorithm to get a more accurate estimate of distance traversed. I would be surprised if commercially available topo software didn't include that feature.