Right Triangle Calculator

Right Triangle is is a triangle with one right angle. Using the Pythagorean theorem, if two side lengths are given, the remaining side can be calculated. The circumcenter of a right triangle lies at the midpoint of its hypotenuse, meaning the midpoint of the hypotenuse is equidistant from all three vertices.

Right Triangle Calculation Method

For a right triangle, if any two of the hypotenuse, height, base, non-right angle, and area are given, all remaining values can be derived.

When the base and height are known

Formula for the hypotenuse of a right triangle

The triangle height (h) is 0 .

The base (a) of the triangle is 0 .

The hypotenuse (b) of the triangle is 0 .

The angle ab (θ) of the triangle is 0 .

The area (S) of the triangle is 0 .

About This Calculator

A right triangle has one 90° angle. The Pythagorean theorem links its three sides, and trigonometry links its sides to its angles — the two facts behind most surveying, construction and navigation math.

Enter any two sides to find the third and the area, or use the angle functions to solve for unknown sides.

A right triangle satisfies a² + b² = c² with c as the hypotenuse: legs of 3 and 4 give 5, and 5 and 12 give 13. The two acute angles add up to exactly 90°, and the altitude drawn to the hypotenuse splits the triangle into two smaller triangles that are similar to the original.

Key Formula:a² + b² = c² · Area = ½ × base × height

Frequently Asked Questions

What is the Pythagorean theorem?

In any right triangle the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides: a² + b² = c². A 3-4-5 triangle is the classic example.

How do I find an angle from two sides?

Use the inverse trigonometric functions: sin⁻¹(opposite/hypotenuse), cos⁻¹(adjacent/hypotenuse) or tan⁻¹(opposite/adjacent). Those three relate any pair of sides to the angle between them.

What are special right triangles?

The 45-45-90 triangle has sides in the ratio 1 : 1 : √2, and the 30-60-90 triangle has sides in the ratio 1 : √3 : 2. Memorising these ratios lets you solve many problems without a calculator.

How do I test whether a triangle is right-angled from its sides?

Compare the square of the longest side with the sum of the squares of the other two. For 8, 15 and 17 the sum 64 + 225 = 289 = 17², so the triangle is right-angled; if the sum is smaller the angle is obtuse.

What are the trigonometric ratios in a right triangle?

Sine is opposite over hypotenuse, cosine adjacent over hypotenuse and tangent opposite over adjacent. At 30° these take the simple values 0.5, 0.866 and 0.577, which is why the 30-60-90 triangle appears so often.

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Sources & last update

2026-10-19