Right Triangle Calculator
Solve any right triangle from any 2 known values — sides or angles. Get every side, both acute angles, area, perimeter, and the altitude to the hypotenuse, plus a live diagram.
a²+b²=c²
Hypotenuse
½ab
Area
90°
Angle C
Choose what you know:
Known: Leg a and Leg b
Enter both legs of the right triangle. The right angle (C = 90°) is always known.
Quick presets
Right Triangle
5 cm
Hypotenuse c
6 cm²
Area
36.87°
Angle A
53.13°
Angle B
Full Triangle Breakdown
3 cm
Leg a
4 cm
Leg b
5 cm
Hypotenuse c
36.87°
Angle A
53.13°
Angle B
90°
Angle C
12 cm
Perimeter
6 cm²
Area
2.40 cm
Altitude to hyp.
Solving a Right Triangle
A right triangle is any triangle with one interior angle locked at exactly 90° — here that’s always angle C, opposite the longest side, the hypotenuse (c). The two shorter sides are called legs (a and b), and the two remaining angles (A and B) are always acute and always sum to 90°. That fixed 90° corner is what makes right triangles special: it guarantees the Pythagorean relationship a² + b² = c², and it’s the anchor that every trig ratio is measured against. Because of that extra structure, only 2 known values (as long as at least one is a side) are needed to solve the whole triangle — one fewer than a general triangle needs.
SOH-CAH-TOA: Trig Ratios for Right Triangles
For any acute angle in a right triangle, three ratios stay constant no matter how big or small the triangle is drawn, because every right triangle with that same angle is a scaled copy of every other. Sine is the opposite leg divided by the hypotenuse, cosine is the adjacent leg divided by the hypotenuse, and tangent is the opposite leg divided by the adjacent leg — remembered together as SOH-CAH-TOA. Flip a ratio around with its inverse function (arcsin, arccos, arctan) and you can go the other direction too, recovering an angle from a pair of side lengths, which is exactly how the “Legs a+b” mode above finds angle A.
SOH-CAH-TOA and Right Triangle Formulas
SOH: sin(α) = opposite/hypotenuse = a/c · CAH: cos(α) = adjacent/hypotenuse = b/c · TOA: tan(α) = opposite/adjacent = a/bFrom legs (a,b): c=√(a²+b²), α=arctan(a/b), β=90°−αFrom a+c: b=√(c²−a²), α=arcsin(a/c), β=90°−α · From b+c: a=√(c²−b²), α=arccos(b/c), β=90°−αFrom a+α: b=a/tan(α), c=a/sin(α), β=90°−α · From c+α: a=c·sin(α), b=c·cos(α), β=90°−αArea = (a×b)/2 · Perimeter = a+b+c · Altitude to hypotenuse: h = (a×b)/cTwo angles alone are never enough. Since angle C is fixed at 90° and A + B always equals 90°, knowing both acute angles just confirms that constraint — it says nothing about how big the triangle actually is. Every valid combination on this calculator needs at least one side length, paired with either a second side or one acute angle.
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