Angle Cut Calculator
ConstructionCalculate the cut length along an angled face and the extra board length needed for a miter-style cut. Free tool for carpenters, framers, and DIY woodworkers.
Cut Length
4.95
Extra Length Needed
3.5
What is a Angle Cut?
An Angle Cut Calculator computes the cut length along an angled face of a board and the extra length the angled cut consumes beyond the board's straight-across width, based on the board's width and the cut angle. This is the core trigonometry behind miter-box style angled cuts used throughout carpentry, trim work, and fabrication.
Pair this calculator with the Rafter Length Calculator when the angled cut is part of a roof rafter, or the Roof Pitch Calculator if you need to derive a cut angle from rise and run measurements first.
How to use this Angle Cut calculator
- Enter your Board Width in inches — the actual (not nominal) width of the stock being cut.
- Enter your Cut Angle in degrees, measured from square (a straight 90-degree cut is 0 degrees on this scale).
- Review the Cut Length result for the distance to mark and cut along the angled face.
- Review the Extra Length Needed result to plan how much additional stock the angled cut will consume.
Formula & Methodology
The calculator applies standard right-triangle trigonometry to the board's width and cut angle: Cut Length = Board Width ÷ cos(Cut Angle) Extra Length Needed = Board Width × tan(Cut Angle) Worked example: For a 3.5 in wide board cut at a 45-degree angle: Cut Length = 3.5 ÷ cos(45°) = 3.5 ÷ 0.7071 ≈ 4.95 in Extra Length Needed = 3.5 × tan(45°) = 3.5 × 1.0 = 3.5 in
Frequently Asked Questions
The cut length along an angled face is calculated by dividing the board's width by the cosine of the cut angle: Cut Length = Board Width ÷ cos(Angle). This gives the distance along the angled cut line, which is always longer than the board's straight-across width for any angle greater than 0 degrees.
Extra length needed is how much additional board length beyond the straight-across width the angled cut consumes, calculated as Board Width × tan(Angle). This is useful for figuring out how much longer your starting stock needs to be to accommodate the angled cut without running short.
A standard 90-degree corner miter joint (like a picture frame corner) uses a 45-degree cut angle on each piece, so the two 45-degree angled faces combine to form the 90-degree corner. For other corner angles, the cut angle on each piece is generally half of the total corner angle.
As the cut angle approaches 90 degrees, the cosine of the angle approaches zero, which means the cut length (board width divided by cosine) grows very large — at extreme angles, a small width can require a very long angled cut, which is why this calculator caps the angle input below 90 degrees.
This calculator computes geometry based on the cut angle measured from square (perpendicular to the board's edge) — matching how a miter saw's angle scale is typically read, where 0 degrees is a straight square cut and larger angles tilt the cut line more sharply across the board.
This calculator covers a single-axis angled cut (a standard miter cut across the board's width), while a compound miter cut combines both a miter angle (across the width) and a bevel angle (through the thickness) simultaneously, which requires a more complex calculation involving both angles together — common for crown molding and similar trim work.
Yes — the underlying trigonometry applies to any rectangular stock being cut at an angle across its width, whether it's a wood board, metal bar stock, or plastic trim, as long as you enter the correct width for your material.
Board width is the straight-across dimension of the board perpendicular to its length — for a standard 1x4, this is the actual (not nominal) width, typically 3.5 inches, since nominal lumber dimensions are larger than actual finished dimensions.
Knowing the extra length an angled cut consumes helps you buy enough stock to avoid running short partway through a project, especially when cutting several angled pieces from a single board where the angled ends each consume more length than a square cut would.
Common framing and trim angles range from shallow cuts around 15 to 30 degrees for some roof and stair applications up to 45 degrees for standard corner miters, though the specific angle always depends on your project's geometry — check your plans or use the [Roof Pitch Calculator](/roof-pitch-calculator/) to derive a roof-related cut angle from rise and run.
Use this Angle Cut Calculator for general angled board cuts, then check the [Rafter Length Calculator](/rafter-length-calculator/) or [Roof Pitch Calculator](/roof-pitch-calculator/) for roof framing angles, or the [Birdsmouth Cut Calculator](/birdsmouth-cut-calculator/) for the notched seat cut where a rafter meets a wall plate.
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