Special Right Triangle Calculator

They are the 45-45-90 and 30-60-90 triangles. Their angles are fixed, so their side lengths always follow the same ratios no matter how large or small the triangle is scaled.

In a 45-45-90 triangle the sides are in the ratio 1 to 1 to the square root of 2. In a 30-60-90 triangle they are 1 to the square root of 3 to 2, meaning short leg to long leg to hypotenuse.

For 45-45-90 you can enter a leg or the hypotenuse. For 30-60-90 you can enter the short leg, the long leg, or the hypotenuse. Switching triangle type resets the side choice to the first valid option.

The hypotenuse is always exactly twice the short leg. The long leg is the short leg times the square root of 3, which is about 1.732 times longer, and it sits opposite the 60 degree angle.

The two legs are equal because the two acute angles are both 45 degrees. The hypotenuse is a leg times the square root of 2, so from the hypotenuse you divide by the square root of 2 to get each leg.

The area is half the product of the two legs, since they meet at the right angle. The perimeter is the sum of all three sides. Both use the sides derived from your one input.

The ratios themselves are exact, but the square roots of 2 and 3 are irrational, so the side lengths, area, and perimeter are shown rounded to four decimal places for readability. The angles are always the whole numbers of the type.

Use this tool when you already know the triangle is a 45-45-90 or 30-60-90 and want a fast answer from one side. For any other right triangle, or when you have two arbitrary values, use the general right triangle calculator.

Yes. The calculation runs locally in your browser, so nothing is uploaded. A JSON API is also available, taking type, knownSide, and value.