AngleWise / Triangle Solver
Right Triangle Solver:
Rise, Run & Any Angle
Nearly every cut on a job is a right triangle — stair rise and run, a roof slope, a brace across a corner. Give the solver any two pieces (two sides, or a side and an angle) and it fills in everything else, including the exact angle to set your saw.
Triangle Solver
The Terms, In Plain English
Rise (vertical leg)
The up-and-down side of the triangle — height, in plain terms. On stairs it's the step height; on a roof it's how far it climbs.
The up-and-down side of the triangle — height, in plain terms. On stairs it's the step height; on a roof it's how far it climbs.
Run (horizontal leg)
The flat, side-to-side side. The distance the triangle covers along the ground or the wall.
The flat, side-to-side side. The distance the triangle covers along the ground or the wall.
Hypotenuse
The long sloped side opposite the square corner. This is the length of the actual sloped piece you'll cut — a stringer, a rafter, a brace.
The long sloped side opposite the square corner. This is the length of the actual sloped piece you'll cut — a stringer, a rafter, a brace.
The two angles
The two corners that aren't the square 90° corner. They always add up to 90°, so if you know one, you know the other.
The two corners that aren't the square 90° corner. They always add up to 90°, so if you know one, you know the other.
How to Solve a Triangle, Step by Step
- Figure out what you already know. Two sides? A side and an angle? Pick the matching option in the solver.
- Enter your two values. The calculator only needs two pieces of a right triangle to find the rest.
- Read the slope length. The hypotenuse is the real length of the sloped board you're cutting.
- Read the base angle. That's what you set your saw or framing square to. The top angle is just 90° minus the base.
The Two Rules That Do All the Work
Behind the calculator, only two old rules are doing the heavy lifting:
- Pythagorean theorem. Rise² + run² = hypotenuse². It gives you the length of any sloped side from the two legs. The classic 3-4-5 triangle is this rule: 3² + 4² = 5².
- The angles add to 90°. In a right triangle the two non-square corners always total 90°, so finding one hands you the other for free.
The 3-4-5 trick on the job: to check that a corner is square without any math, measure 3 feet along one wall, 4 feet along the other, and if the diagonal between those marks is exactly 5 feet, the corner is a true 90°. Any multiple works too — 6-8-10, 9-12-15.
Common Mistakes
- Mixing up the leg and the slope. The hypotenuse is always the longest side. If your "slope" came out shorter than a leg, something's entered wrong.
- Using the run as the cut length. The board you cut is the hypotenuse length, not the run. Use the slope number.
- Forgetting the angles total 90°, not 180°. That's the whole triangle (180°) minus the square corner (90°).
- Entering an angle of 90° or more. A right triangle's other two angles are each less than 90°. If you're entering an angle, keep it under 90.
Frequently Asked Questions
- How do I find the angle from two sides?
- Divide rise by run and take the inverse tangent. A 3-and-4 triangle gives a base angle of about 36.87°. The solver does it for you.
- What is the hypotenuse?
- The long sloped side opposite the right angle, found with √(rise² + run²) — the Pythagorean theorem.
- Do the two angles always add to 90°?
- Yes. All three angles total 180°, and one is the 90° corner, so the other two always add to 90°.
- How is this used in carpentry?
- Stairs, roofs, braces — almost every angle cut is a right triangle. Two knowns give you the cut angle and the length of the sloped piece.
Be first to get the AngleWise app
This calculator is free here, forever. The AngleWise phone app adds offline access so it works with no signal, lets you save your projects, and builds full cut lists for the lumberyard. Leave your email and we'll notify you the moment it launches — no spam, just the launch.