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Right-Triangle Solver

Solve a right triangle from any two sides, or one side and one acute angle.

  • triangle
  • pythagoras
  • pythagorean
  • right angle
  • sin
  • cos
  • tan

About Right-Triangle Solver

A right triangle is fully determined by any two of its non-right pieces — two sides, or one side and one acute angle — and the rest can be found with the Pythagorean theorem and basic trigonometry. That makes right triangles the most common problem in carpentry, surveying, navigation, and any time you need to figure out a slope, a ramp, a diagonal cut, or the height of a tall thing you can stand next to.

This solver takes any valid combination of two inputs and computes everything else: the third side, both acute angles, the area, and the perimeter. A small diagram updates with the result so you can see which side and which angle is which. Angles are in degrees and follow the standard convention — C is the right angle (90°), c is the hypotenuse, A and B are the acute angles opposite legs a and b.

How to use

Pick what you're starting from using the "Given" dropdown: two legs, one leg and the hypotenuse, one leg and an acute angle, or the hypotenuse and an acute angle. The two input fields relabel themselves to match.

Enter your two values and the result panel updates instantly with all six pieces of the triangle (three sides plus the three angles), the area, and the perimeter. The diagram beside the cards shows a scaled drawing labelled with a, b, c, A, and B. "Copy all" gives you a single-line summary suitable for pasting into notes.

Frequently asked questions

  • What is the Pythagorean theorem?

    In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides — a² + b² = c². Given any two sides, the third is determined; the solver uses this for the "two legs" and "one leg + hypotenuse" modes.

  • What labelling convention does the solver use?

    The right angle is C (90°), and the hypotenuse opposite it is c. The two legs are a and b, and the acute angles opposite those legs are A and B respectively. A + B always equals 90°. This matches the convention used in most geometry textbooks.

  • Can I work in radians?

    The solver uses degrees throughout. To convert: 90° = π/2 ≈ 1.5708 radians; 45° = π/4 ≈ 0.7854; 30° = π/6 ≈ 0.5236. If your problem is in radians, multiply by 180/π first to get degrees before entering them here.

  • What if the hypotenuse is shorter than one of the legs?

    That's geometrically impossible — the hypotenuse must be the longest side. If you enter a hypotenuse shorter than the leg, the solver displays an error rather than producing nonsense. Re-check which side is the actual hypotenuse (it's always the one opposite the right angle).

  • How is the area calculated?

    Area = ½ × a × b, where a and b are the two legs (the sides that meet at the right angle). The hypotenuse never enters the formula. So a 3-4-5 right triangle has area ½ × 3 × 4 = 6 square units.

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