The confusion comes from nominal vs. actual dimensions of dimensional lumber.
Typically a solid wood board sold in customary/imperial units is slightly smaller along its thickness and width, the thickness being the smallest dimension. For example, a "2x4" is actually 1.5in x3.5in and a "1x3" is actually 0.75in x 3.5in.
To convert from customary units to metric, subtract 1/2in from the thickness and width, then multiply by 25.4 to get millimeters (1 inch = 2.54cm = 25.4mm), and round to the nearest mm. This is called a "soft conversion" according to the American Wood Council.
Here are a few common equivalents:
2x4 = 38x89mm
2x6 = 38x140mm
2x8 = 38x184mm
2x10 = 38x235mm
2x12 = 38x286mm
Once you've converted the nominal customary dimensions to actual metric dimensions, you can convert the actual customary length to the actual metric length. If the customary length is expressed in feet, multiply by 12 to get inches. Once you have the length in inches, multiply by 2.54 to get cm, then divide by 100 to get meters (or simply multiply by 0.0254 to convert directly from inches to meters).
If you need to go in the other direction, simply work backwards.
Starting with desired final dimensions of 45mm x 46mm x 1.6m, let's convert to nominal customary units:
- Thickness: 45mm / 25.4mm/in + 0.5in = 2.27in
- Width: 46mm / 25.4mm/in + 0.5in = 2.31in
- Length: 1.6m / 0.0254m/in = 62.99in / 12in/ft = 5.25ft
Depending on the lumber sizes available, you may need to buy either a 3x3 x 6ft or 4x4 x 8ft.
Another solution is to adjust the dimensions of your finished parts to be slightly smaller so you don't have to resaw or waste so much material.
Yet another solution, especially if you have difficulty finding 3x3s or 4x4s, is to buy, you could buy thinner material such as 2x4s or 1x3s, and laminate (glue) them together. If you can find 3 perfectly flat 1x3s, your finished laminated board will have dimensions of 2.25in x 2.5in--just a hair under your 2.27in x 2.31in preferred size in terms of thickness.
A couple final tips:
- Because most boards are not straight and flat when you buy them, you should buy slightly oversized (even if laminating) so you can mill them flat and trim them to their final dimensions.
- Always start with a plan, but leave some extra material that you can trim away as-needed (not as-planned) during final dimensioning. You will almost never be able to cut all your parts to final dimensions and have them fit perfectly in the end. Instead, dimension your parts relative to one another, and adjust as necessary as you're cutting the parts. This is called relative dimensioning, and it allows you to make and account for minor mistakes along the way without ruining the final fit of the entire project.