SuperDevTools
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Triangle calculator for right and oblique triangles

Enter any two values, at least one of them a side, and everything else is worked out. The right angle is at C, and the hypotenuse c lies opposite it.

Examples
Scale drawing of the triangle
Triangle drawn to scale. Each vertex A, B, C lies opposite the side a, b, c with the same letter.
Calculation steps

    Your last values stay saved on this device.

    Solve any triangle from the values you know

    This triangle calculator fills in every missing measurement. Give it two values for a right triangle or three for any other triangle, and it returns the sides, the angles in degrees and radians, the area, the perimeter and the altitudes. It draws the triangle to scale and lists each formula it used, handy for checking homework or a layout on site.

    How to use it

    1. Pick a tab: “Right triangle”, “Any triangle” or “Is it a right triangle?”.
    2. For a right triangle, fill in two boxes among “Side a”, “Side b”, “Hypotenuse c” and angles A and B, with at least one side. The right angle is at C.
    3. For any triangle, fill in three boxes with at least one side. Angle A sits opposite side a, B opposite b, C opposite c.
    4. Read the results, the drawing and the “Calculation steps”.

    Pythagorean theorem and right triangle trig

    In a right triangle, the square of the hypotenuse equals the sum of the squares of the two legs: c² = a² + b². With a = 3 and b = 4, c = √25 = 5. Angle A is arctan(3 ÷ 4) ≈ 36.8699° and angle B is 90° − A ≈ 53.1301°. The area is a × b ÷ 2 = 6, the perimeter 12 and the altitude to the hypotenuse a × b ÷ c = 2.4.

    With one side and one angle, SOH CAH TOA does the work: a = c × sin A and b = c × cos A. For c = 10 and A = 30°, a = 5 and b ≈ 8.6603.

    Oblique triangles: law of cosines, law of sines, Heron

    The tool spots the case on its own: SSS, SAS, ASA, AAS or SSA. The law of cosines, a² = b² + c² − 2bc cos A, turns sides into angles; the law of sines, a ÷ sin A = b ÷ sin B = c ÷ sin C, finds the missing sides. The area comes from Heron's formula, √(s(s − a)(s − b)(s − c)), where s is the semi-perimeter.

    Example: sides 7, 8 and 9 give s = 12 and an area of √720 ≈ 26.8328. The angles A, B and C are about 48.1897°, 58.4119° and 73.3985°.

    SSA is the ambiguous case. With a = 8, b = 10 and A = 40°, sin B ≈ 0.8035, so B is either 53.4641° or 126.5359°, and side c is either 12.4230 or 2.8978. Both triangles are shown.

    Everyday uses

    • Ladder against a wall: the 4-to-1 safety rule puts a ladder at about 75°. A 13 ft ladder at 75° reaches 13 × sin 75° ≈ 12.557 ft, with its foot 3.3646 ft from the wall.
    • Room diagonal: a 16 ft by 12 ft room has a diagonal of √400 = 20 ft.
    • TV screen size: a 55-inch 16:9 screen is about 47.94 in wide and 26.96 in tall.
    • Squaring a corner with 3-4-5: for a deck or a foundation, mark 3 ft along one line and 4 ft along the other; the diagonal must read 5 ft. If you measure 5.02 ft, the “Is it a right triangle?” tab shows a 0.4% difference and an angle of 90.4784°, accepted with the default “Tolerance (%)” of 0.5.

    Frequently asked questions

    How do I know if a triangle is a right triangle?

    Use the converse of the Pythagorean theorem: if the square of the longest side equals the sum of the squares of the other two, the triangle is right. For 5, 12 and 13, 169 = 25 + 144, so the answer is yes.

    How do I find the hypotenuse?

    Square both legs, add them and take the square root: √(6² + 8²) = √100 = 10.

    Why does SSA sometimes give two answers?

    The side opposite the known angle can meet the other arm of that angle at two points. If it is too short, no triangle exists and the tool says so.

    Are my values saved?

    Yes, on this device only. “Clear all” removes them.