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, which is what you need for 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) ≈ 361.25 in (30.10 ft). Barely longer than the run, since the 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.

Reading the slope back out

The two legs also give you the angles, and on this page the angles are usually the point. The one at the base of leg b is atan(a ÷ b). Three ways of quoting the same thing:

• As a ratio, 1:12, the form ramp codes use.
• As a percent grade, rise ÷ run × 100, the form road signs use. A 1:12 ramp is 8.3%.
• As a pitch, rise per 12 of run, the form roofers use. A 6:12 roof is 26.57°.

For accessible ramps the US ADA limit is 1:12, which is 4.76°, and it caps a single run at 30 inches of rise before you must put in a landing. Steeper than 1:12 is not a slightly worse ramp, it is a ramp that fails inspection.

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 and 9-12-15, is the site shortcut for laying out a square corner without a protractor. Measure 3 along one string and 4 along the other, and when the diagonal reads exactly 5 the corner is true.