Tools logoTools/
Math & Science/Right Triangle Calculator

Right Triangle Calculator

All sides, angles, area, and perimeter of a right triangle from any two known values.

Runs locally·Free, no signup·Updated May 6, 2026
Loading tool…
How it works

A walkthrough, end to end.

  1. 1

    Pick what two values you know: two legs, a leg + hypotenuse, or a leg + an acute angle.

  2. 2

    The calculator solves for all sides, both acute angles, area, and perimeter using SOH-CAH-TOA and Pythagorean theorem.

  3. 3

    Common cases: 30-60-90 and 45-45-90 special right triangles.

Reference

Right triangle relationships

Two acute angles sum to 90°. Pythagorean: a² + b² = c². Trigonometry: sin(A) = a/c, cos(A) = b/c, tan(A) = a/b. Area = ½ × a × b.

Use cases

What you can do with this.

30-60-90 special triangle

Sides in ratio 1 : √3 : 2. Knowing one side gives the others. Common in geometry, hex grids, and engineering.

45-45-90 isoceles right triangle

Two legs equal; sides in ratio 1 : 1 : √2. Standard for square diagonals and roof valleys at 45° pitch.

Solve from two legs

Legs 5 and 12 → c = 13, angles 22.6° and 67.4°. Most common case in carpentry/construction problems.

Solve from leg + angle

Leg 8, opposite angle 35° → hypotenuse = 8/sin(35°) = 13.95. Useful for navigation and surveying.

Roof rafter calculation

Rise (vertical leg) and run (horizontal leg) of the roof give rafter length (hypotenuse). The calculator handles standard roof framing math.

Inclined plane physics

Incline length, height, and base form a right triangle. Use to compute vertical/horizontal components of motion or force.

Trig sin/cos/tan calculation

Quick way to verify trig values for specific angles. Calculator's reported sin/cos/tan agree to several decimal places with calculator/spreadsheet trig functions.

Right triangle calculator 2026 — what's current

Foundational geometry, unchanged. Calculator wins for speed and avoiding mental SOH-CAH-TOA mistakes.

FAQ

Frequently asked.

  • Mnemonic for trig: Sin = Opposite/Hypotenuse, Cos = Adjacent/Hypotenuse, Tan = Opposite/Adjacent. Standard high-school trig.

  • It uses degrees. To convert: degrees × (π/180) = radians. Standard scientific calculators offer mode switch; this one is degrees-only for simplicity.

  • You need either a second side OR an angle. One side alone is insufficient — there are infinite right triangles with one side at any length.

  • No. Calculations run entirely in your browser.