Right Triangle Calculator

Calculate sides, angles, area, perimeter, and altitude of a right triangle with step-by-step solutions

Check Right Triangle Calculator

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Formula result

Copy-ready result handoff

Use this after finding hypotenuse, missing leg, area, perimeter, or acute angles.

Common searches
right triangle calculatorPythagorean calculatorhypotenuse calculator
Input check

Confirm the hypotenuse is opposite the 90 degree angle.

Assumption

The calculator assumes one right angle and consistent length units.

Right triangle result note

Copy this after replacing the bracketed result with the value shown by the calculator.

Right triangle result: [paste hypotenuse, legs, acute angles, area, and perimeter].
Inputs checked: Confirm the hypotenuse is opposite the 90 degree angle.
Assumption: The calculator assumes one right angle and consistent length units.
Use case: Geometry homework, construction measurement, slope check, or trig review.
Next check: Use Pythagorean Theorem Calculator for a focused a^2 + b^2 = c^2 check.

Pick the input mode that matches what you know: two legs, a leg with the hypotenuse, or a leg with an acute angle. The result includes all sides, both acute angles, area, perimeter, and altitude to the hypotenuse.

How the result is built

Formula, Variables, And Worked Example

a^2 + b^2 = c^2
area = a * b / 2, perimeter = a + b + c
sin(theta) = opposite / hypotenuse

a and b are the legs, c is the hypotenuse, and theta is one acute angle.

Worked example

For legs 5 and 12, c = 13, area = 30, perimeter = 30, and the angle opposite 5 is arcsin(5 / 13), about 22.62 degrees.

Assumptions and common mistakes
  • The triangle must contain exactly one 90 degree angle.
  • Opposite and adjacent sides depend on which acute angle you choose.
  • Do not mix degrees and radians when entering or reading angles.
  • The hypotenuse is always opposite the right angle and is the longest side.
Input mode guide
  • Two legs: best when base and height are known.
  • Leg plus hypotenuse: use when the diagonal is known.
  • Leg plus angle: use trigonometry to solve all remaining values.
Related checks
Pythagorean theoremTriangleDistanceSlope

Right Triangle Formulas, Assumptions, And Mistakes

What this right triangle solver returns

The calculator solves the missing side lengths, both acute angles, area, perimeter, and altitude to the hypotenuse. It also detects common special right triangles when the angle pattern matches 30-60-90 or 45-45-90.

Pythagorean theorem and trig together

When two sides are known, the Pythagorean theorem gives the missing side. When an angle and a side are known, sine, cosine, and tangent connect the angle to the opposite, adjacent, and hypotenuse lengths.

Special right triangles

A 45-45-90 triangle has equal legs and a hypotenuse equal to leg * sqrt(2). A 30-60-90 triangle has side ratio 1:sqrt(3):2, with the shortest side opposite the 30 degree angle.

When to use a different triangle page

If the triangle does not have a 90 degree angle, use the Triangle Calculator instead. If you only need the missing side from two right-triangle sides, the Pythagorean Theorem Calculator is the faster focused option.

References & Sources

Common result checks

Questions about this tool

What inputs are enough to solve a right triangle?
Two compatible measurements are enough when at least one is a side. This calculator supports two legs, one leg plus hypotenuse, or one leg plus one acute angle.
What is the difference between opposite and adjacent?
Opposite and adjacent depend on the acute angle you choose. The opposite side is across from that angle, and the adjacent leg touches that angle.
Can I enter angles in radians?
Yes. In leg plus angle mode, choose degrees or radians before entering the acute angle.
Why must the hypotenuse be longer than the leg?
The hypotenuse is opposite the right angle and is always the longest side of a right triangle.