lighting plot software

...Being a computery kinda guy, I'm inclined to try to plan the hang in software; is there anything that does that that doesn't cost a million and a half bucks? ...
$0.00. LX Free

... but I don't know how to figure the floor ovals/cones based on beam width and pipe position, by hand. ...
You're (probably) not lighting the floor, you're lighting the face plane, which is ~ +5'-0", depending on how tall the cast members are. As @kicknargel said so eloquently above,
... Faces are more important than feet. ...
. Whether on computer or by hand, divide the playing area into multiple 8'-12' lighting areas. If a realistic box set, the areas may be determined by furniture placement, a sofa area, a table area, and so on. One of the biggest mistakes of the novice lighting designer is rushing to draft a light plot before they've seen a run-thru and know how the director and actors are using the space. Never trust a director when he tells you, "You don't need to light that area, no one ever goes there." Best to have an odd number of areas left to right, as DSC is probably an important area that may need to be isolated. Likewise DSL and DSR. Put a capital letter or (old) Roman numeral in the center of each area--these become your focus points. Then use the Pythagorean Theorem to determine the throw distance from each mounting position. This will tell you whether you need a 19°, 26°, 36°, WFL, NSP etc. The McCandless Method would have, minimally, frontlights at 45° angle of elevation and 45° L&R, sidelights L&R, a backlight, and possibly a downlight FOR EACH AREA. You obviously don't have enough equipment for all that, so part of your job as Lighting Designer is to determine where/how compromises can be made. If you're lighting a very large stage, you may only have enough fixtures for frontlight, and only one color at that. Cheap LEDs with narrow 10-15° beams are not particularly useful here.

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The cheapest computer based program that I know of is 'Softplot'. It runs about $300.

IT is not the standard of the industry by any means, and as fairly awkward in a number of aspects, but you get what you pay for, and it is not a bad value.
 

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