The calculation is a simple subtraction of two volumes.

1. Calculate Initial Volume: The calculator first finds the volume of the starting block by multiplying its length, width, and height.
2. Calculate Cutout Volume: It then finds the volume of the section being removed by multiplying the cutout's length, width, and height.
3. Subtract to Find Remainder: The cutout volume is subtracted from the initial volume to determine the final volume of the workpiece.
   Remaining Volume = Initial Volume - Cutout Volume

Example 1: Notching a Post. A 6" x 6" x 24" squared post holds 864 in³ of stock. You cut a 2" x 2" x 5" notch for a beam pocket, removing 20 in³. The remaining volume is 864 - 20 = 844 in³, or roughly 5.9 board feet (844 / 144).

Example 2: Hollowing a Blank. A 12" x 12" x 12" starting block is 1,728 in³. Removing a 4" x 4" x 4" core leaves 1,664 in³ of usable material. Multiply by the species density to estimate the finished weight, or divide by 144 for board feet.

• Mixing Units: Entering the block in inches but the cutout in another unit. Keep every dimension in the same unit so the subtraction is valid.
• Cutout Larger Than the Block: If the removed volume exceeds the starting block the result goes negative, which is physically impossible. Re-check your numbers.
• Ignoring Kerf: This tool subtracts only the ideal cutout volume. A real saw blade removes extra material, so your true remainder will be a little smaller.
• Overlapping Cutouts: The formula assumes one clean rectangular removal. Multiple intersecting pockets need to be combined before you subtract.

"Knowing the volume left after a cutout is really a material and weight question. When I size a carved panel or a jigged base, I subtract the voids first so I can quote how much stock to buy and what the piece will actually weigh once it is on the wall or the bench."

"For shipping and load planning this number matters more than people expect. A hollowed blank can be thirty percent lighter than the solid block it came from, and that difference changes how you brace, pack, and hang the finished part."

• Material Purchasing: Confirm how much usable stock remains after a pocket or rebate so you can repurpose the offcut instead of buying new board.
• Weight Estimation: Multiply the remaining volume by the species density to predict how heavy a carved or hollowed piece will be before you hang or ship it.
• Joinery Layout: Check that a mortise, notch, or dado leaves enough solid material around the void rather than thinning the workpiece to a fragile shell.
• Cost Accounting: Convert the leftover cubic inches to board feet to value scrap that still has life in it for jigs, shims, and small parts.

• Cuboid: A six-sided solid where every face is a rectangle; the shape this calculator models for both the block and the cutout.
• Volume: The three-dimensional space a piece of material occupies, expressed here in cubic units such as cubic inches.
• Board Foot: A lumber volume of 144 cubic inches, one foot long, one foot wide, and one inch thick.
• Density: Mass per unit volume, the figure you multiply a remaining volume by to estimate finished weight.