Right Triangle Area Calculator

A right triangle has one 90° angle. The two sides forming that right angle are called the legs (a and b); the longest side, opposite the right angle, is the hypotenuse (c).

A = ½ × a × b

Because the legs are perpendicular to each other, one leg is the base and the other is the height. No separate measurement needed.

Bonus: hypotenuse from Pythagoras

c = √(a² + b²)

If you measured both legs, you also know the hypotenuse — useful for figuring out diagonal cuts, brace lengths, and ramp lengths.

Real-world right triangles:

• A roof gable end where the rafter meets the wall is a right triangle. Legs: half the building width (run) and the roof height (rise). Doubling the area gives you the whole gable wall.
• A wheelchair ramp footprint: leg 1 is the rise (height change) and leg 2 is the run (horizontal distance). The hypotenuse is the ramp surface. For a 4 in rise over 48 in of run, the ramp surface is √(16 + 2304) = 48.17 in — barely longer than the run.
• The corner brace on a gate or shelf. A 12 in × 12 in brace covers 72 sq in of plywood and has a 16.97 in diagonal.

Common practical case — finding rise from slope:

You want a 1:12 wheelchair-accessible ramp slope and you have 30 in of vertical rise to overcome. Run = 12 × 30 = 360 in (30 ft). Ramp footprint is a right triangle with legs 30 in and 360 in. Hypotenuse (ramp length): √(900 + 129,600) ≈ 360.5 in (30.04 ft). Negligibly longer than the run — slope is so shallow.

Worked example — calculating sheathing for a gable end:

House is 24 ft wide. Roof pitch is 6:12 (6 in of rise per 12 in of run). Roof rise from the eaves to the peak: 6/12 × 12 = 6 ft. Half the gable triangle area is 0.5 × 12 × 6 = 36 sq ft. Doubled for the full gable: 72 sq ft of sheathing per gable end.

Sign convention reminder:

Area is always positive. If you’re plugging numbers into a CAD tool that gives a negative value, you’ve described the triangle with reversed orientation. Take the absolute value.

The 3-4-5 triple (and its multiples like 6-8-10, 9-12-15) is a useful right-triangle shortcut for laying out square corners on a building site — no protractor needed.