This is something I struggled with for a while and only recently have been able to do the math for. Purrmaster had asked how and most of this is my response to his question.
If you want the inside of the frame to be 8 inches in length then, with a board of 2 inch in width, you would add the width times 2. so with a 2 inch wide board the out side of your frame will be 12 inches.
However, if you want to account for the rabbet that you set the picture into then you have to do a bit more math. If with the same board you cut in a 1/8 rabbit then the space that the picture will be resting in will be the length of the inside edge plus a 1/4 inch (that’s twice the rabbet size) making the total space for the picture 8 1/4 inches In the picture below on the right side, that’s a 1/8 indicating the size of the rabbet.
if you wanted the space for the picture 8 inches, then you would make your frame 1/4 smaller. so instead of 12 inches you have 11 3/4.
Now my math mathematical to this is the following. (you will have to used this equation for both sides of the picture frame.
(length of picture) + 2[(width of board)-(width of rabbet)]= (outer length of frame)
length of picture) + 2(width of board)-2(width of rabbet)= (outer length of frame)
in a prettier version with
and to apply that to the situation i was talking about earlier with
But honestly, if you have the picture in front of you it’s a hell of a lot easier to go by eye and pencil marks. and it’s always important to take your time and make sure you have the miters going the correct way. I once cut a frame where all the miters where parallel to one another on each board. no fun.
Hope I helped