What is the cost of movement on roads and railroads in Civilization 5?

Question

The manual states (page 52):

As long as the unit moves from one tile containing a road/railroad into another tile containing a road/railroad, the unit will expend just a fraction of the normal cost to move.

It doesn't say, however, what are the exact values of the fractions. Does moving along a road takes the underlying terrain into account? Is there any place these numbers are written?

Answer 1

I did a quick test using a couple different saves I had available to me, and found the following:

Route                   |  Cost (Movement points)
Road                    |   1/2
Road, with Machinery    |   1/3
Railroad for fast unit  |   1/3
Railroad for slow unit  |  3/10

More info

• Each unit lists how many movement points it has remaining in the bottom left when it is selected. The movement points are normally shown as rounded whole numbers only, but you can see the decimal number if you mouse over it.
• What terrain a road/railroad is on makes no difference. Roads on open terrain, hills, and forest all cost the same to move across.
• I tested both slow (2 movement point) and fast (4 movement point) units on each type f route. Railroad was the only one that showed a difference for different units.
• 3/10 (0.3) is an odd number, but its actually what I found.
• Going from road to rail or rail to road costs the slower 1/3.
• Remember roads do not bridge rivers until you get construction.

Edit: In my first test, I had an extra movement point on my units due to playing as Persia in a golden age. (I did not remember where it came from, thanks bwarner) I've tested again and got the same results.

Edit2: I incorrectly listed the tech that increase road movement speed as Construction. Construction is important here because it builds bridges, but the one that affects the speed of roads is Machinery.

Answer 2

Source: https://civilization.fandom.com/wiki/Movement_(Civ5)

In this table, "Unit Speed" is the number of movement points that the unit gets each turn (ex. a worker has 2, where a horseman has 4); MP/Tile is the amount of movement points it takes for a unit to move one tile with that improvement.

Improvement	Unit Speed	MP/Tile
Road, pre-Machinery	N/A	0.5
Road, post-Machinery	N/A	0.333...
Railroad	2	0.2
Railroad	3	0.3
Railroad	4+	0.333...

Notes:

• Roads do not cross rivers until Engineering is researched
• Railroads give units a minimum movement of 10 tiles/turn
• Railroads do not give any benefit (relative to roads) to units with speed 4 or higher, as they can already move 12 tiles/turn on roads
• Helicopters do not benefit from roads or railroads