The following shows a basic formula for scaling a negative up to print size. It is important to note that a 35mm frame will correctly scale proportionately to a 4x6in and 8x12in print.**
Scaling formula: (final image width X printer DPI)/original size = scanner resolution
For example, if you want to print a 4x6in print at 300 dpi on the printer from a 35mm negative, first calculate the width:
4in x 300 printer DPI = 1200, then divide by original 0.9448 inch = 1270 (custom scanner dpi)
Then, just to be sure, calculate the height:
6 inch x 300 dpi = 1800, then divide by original 1.417 inch = 1270 (custom scanner dpi)
To scale to either 5x7 inch or 8x10 inch you should calculate using the larger dimension to avoid having to crop the photo (eg 7 for 5x7 and 10 for 8x10). Use the lower value if you want exactly 5x7 inch or 8x10 inch but plan on cropping in your photo editor.
** A 35mm frame is 24x36 mm. This is approximately equivalent to 0.9448x1.417 inch.