You've forgotten to mention the height of the room. (It will take more energy to heat a room with high ceilings than with low ones). You've also not stated what the power output of the radiators is.
Here's how to do it. Measure the height of your room, to the nearest foot. Then multiply the length width and height together. So, assuming that your room is around 8' high, the calculation so far is
13 x 18 x 8 (= 1872 in my example).
Now multiply that figure by 5 if it's a dining room or lounge. If it's a bedroom, multiply by 4 instead. If it's a kitchen, just multiply by 3.
If the room faces north, multiply the figure you've got by 1.15. (Otherwise, leave it unchanged).
If the room has French windows, multiply your current figure by 1.2. (Otherwise leave it unchanged).
If there's double-glazing, multiply your figure by 0.9.
The figure that you're left with will be the required heat output of the radiators in room, in BTU. The number of radiators you install will depend upon how important it is to have an even distribution of heat. What is important is to ensure that the total heat output, in BTU, is at least as great as the figure you've got from your calculations.
Chris
Source:
http://www.diydoctor.org.uk/projects/rads.htm