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Right Triangle Calculator

Solves a right triangle from any two of its sides (two legs, or one leg and the hypotenuse) using the Pythagorean theorem, and returns all sides, the two acute angles in degrees, area, perimeter and the altitude to the hypotenuse.

When to use

You know two sides of a right-angled triangle and need the third side, the angles or the area.

Do not use when: The triangle has no right angle (use triangle-solver) or you only need the hypotenuse length (pythagorean gives just that).

Formula

hypotenuse² = leg_a² + leg_b²; angle_a_deg = atan(leg_a / leg_b); angle_b_deg = 90 − angle_a_deg; area = leg_a × leg_b / 2; altitude = leg_a × leg_b / hypotenuse

Inputs

Parameter	Type	Unit	Required	Description
`leg_a`	number	units	no	First leg (side adjacent to the right angle). Range: > 0
`leg_b`	number	units	no	Second leg (side adjacent to the right angle). Range: > 0
`hypotenuse`	number	units	no	Side opposite the right angle; must be longer than either leg. Range: > 0

Outputs

Output	Type	Unit	Description
`leg_a`	number	units	First leg.
`leg_b`	number	units	Second leg.
`hypotenuse`	number	units	√(leg_a² + leg_b²).
`angle_a_deg`	number	degrees	Acute angle opposite leg_a = atan(leg_a / leg_b).
`angle_b_deg`	number	degrees	Acute angle opposite leg_b = 90 − angle_a_deg.
`area`	number	units²	leg_a × leg_b / 2.
`perimeter`	number	units	leg_a + leg_b + hypotenuse.
`altitude_to_hypotenuse`	number	units	Height from the right angle onto the hypotenuse = leg_a × leg_b / hypotenuse.

Example

Legs 3 and 4: {"leg_a":3,"leg_b":4} → {"hypotenuse":5,"angle_a_deg":36.8699,"angle_b_deg":53.1301,"area":6,"perimeter":12,"altitude_to_hypotenuse":2.4}

Leg 5, hypotenuse 13: {"leg_a":5,"hypotenuse":13} → {"leg_b":12,"angle_a_deg":22.6199,"angle_b_deg":67.3801,"area":30,"perimeter":30}

GET https://tttkmbb.com/api/v1/calculate/right-triangle?leg_a=3&leg_b=4

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/right-triangle (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/right-triangle · Markdown: https://tttkmbb.com/geometry/right-triangle.md · JSON definition: https://tttkmbb.com/geometry/right-triangle.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="right-triangle"
OpenAPI operationId: solve_right_triangle
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

Wikipedia – Right triangle (reference)
Wikipedia – Pythagorean theorem (reference)
Wolfram MathWorld – Right Triangle (reference)

FAQ

Which angle is angle_a_deg?

The angle opposite leg_a (at the vertex where leg_b meets the hypotenuse). The two acute angles always add up to 90°.

What if I enter all three sides?

They must satisfy leg_a² + leg_b² = hypotenuse² (to 0.01 %); otherwise an INVALID_PARAMETER error is returned. Give just two sides to avoid this.

Related calculators

Triangle Solver — Solve triangles that are not right-angled.
Triangle Area Calculator — Area only, by any of three methods.
Pythagorean Theorem Calculator — Just the hypotenuse or a leg from the Pythagorean theorem.