Wood Triangle Calculator: Rise, Run, and Diagonal Cuts
Enter the rise and run of any right-triangle woodworking layout — a rafter, brace, gusset, or angled cut — and this calculator uses the Pythagorean theorem (c = square root of rise squared plus run squared) to find the diagonal length and both non-right angles.
Quick Answer
Enter the rise and run of any right-triangle woodworking layout — a rafter, brace, gusset, or angled cut — and this calculator uses the Pythagorean theorem (c = square root of rise squared plus run squared) to find the diagonal length and both non-right angles.
Wood Triangle Calculator: Rise, Run, and Diagonal Cuts
Enter your values below for an instant result, then see the formula, worked example, and common mistakes.
Enter rise and run, then click calculate.
How to Use This Calculator
Rise is the vertical leg of your right triangle (like the vertical height of a brace or the vertical rise of a roof); run is the horizontal leg. Use the same unit (inches or feet) for both.
Type your rise and run measurements into the two fields. These can be any positive numbers — the calculator works the same whether you’re in inches, feet, or centimeters, as long as both fields use the same unit.
The hypotenuse is the actual length of material you need to cut for a diagonal brace, rafter, or angled panel connecting the two legs.
The calculator gives both non-right angles of the triangle, useful for setting a miter saw or bevel gauge to the correct cutting angle.
If you want to verify a corner is exactly 90 degrees rather than calculate a diagonal, measure 3 units down one side and 4 units down the other — the diagonal between those two points should measure exactly 5 units (or any multiple, like 6-8-10 or 9-12-15) if the corner is square.
Formula
Hypotenuse (c) = square root of (rise2 + run2). Angle from the run = arctangent(rise / run), and the second angle equals 90 degrees minus that value, since the three angles of any triangle sum to 180 and one angle is already 90.
Reference Table: Common Pythagorean Triples
| Rise | Run | Diagonal (hypotenuse) |
|---|---|---|
| 3 | 4 | 5 |
| 6 | 8 | 10 |
| 5 | 12 | 13 |
| 8 | 15 | 17 |
| 7 | 24 | 25 |
Common Mistakes to Avoid
- Mixing units — entering rise in inches and run in feet gives a meaningless diagonal length; always convert both to the same unit first.
- Confusing pitch notation with degrees — a “6/12 pitch” is not 6 degrees, it means 6 inches of rise per 12 inches of run, which works out to about 26.57 degrees.
- Using the diagonal formula when you actually need to check squareness — for checking a corner is 90 degrees, use the 3-4-5 (or 6-8-10) method by measuring along both legs and checking the diagonal, rather than solving for an unknown angle.
- Forgetting that doubling both rise and run doubles the diagonal too, but does not change the angles — the triangle’s shape (and therefore its angles) depends on the ratio of rise to run, not their absolute size.
- Rounding intermediate results before the final calculation, which compounds small errors — keep full decimal precision until the final cut length or angle is set on your saw.
When the Estimate May Be Wrong
This calculator solves a right triangle given its two legs (rise and run), which is the most common woodworking scenario for rafters, braces, and diagonal cuts. It assumes a true right angle between rise and run; if your structure is not actually square at that corner, the calculated diagonal will not match reality. For roof rafter calculations specifically, remember to also account for birdsmouth cuts, ridge board thickness, and overhang, which this basic triangle calculation does not include.
FAQs
How do you find the diagonal length of a right triangle in woodworking?
Use the Pythagorean theorem: the diagonal (hypotenuse) equals the square root of the rise squared plus the run squared, provided the angle between rise and run is a true 90 degrees.
What is the 3-4-5 rule used for in woodworking and construction?
It is a quick way to verify a corner is square: measure 3 units along one side and 4 units along the other from the corner, and the diagonal between those two points should measure exactly 5 units (or any proportional multiple) if the corner is a true right angle.
How do I convert a roof pitch like 6/12 into degrees?
Take the arctangent of rise divided by run — for a 6/12 pitch, arctan(6/12) = about 26.57 degrees from horizontal.
Does this calculator work for angles other than 90 degrees?
No, this calculator assumes rise and run meet at a true right angle, since that is the standard setup for rafters, braces, and most cut-layout tasks in woodworking.
Sources and Methodology
Pythagorean theorem application and 3-4-5 squaring method sourced from ConstructCalc’s Pythagorean Theorem Calculator and ThisIsCarpentry’s “Finding the Right Angle” guide, both standard references for construction and woodworking right-angle layout.
