Hypotenuse Calculator

Professional hypotenuse calculator for students and professionals. Calculate right triangle sides, angles, area using Pythagorean theorem with detailed step-by-step solutions and interactive charts.

Two Sides
Angle & Side
Area & Side

Right Triangle Legs

Formula

c = √(a² + b²)

Enter the lengths of both legs to calculate the hypotenuse using the Pythagorean theorem.

Known Parameters

Formula

c = a / cos(α) or c = b / sin(α)

Use trigonometric ratios when you know one side and one acute angle.

Known Values

Formula

b = (2 × Area) / a
c = √(a² + b²)

Calculate the other leg from area, then find the hypotenuse.

Instant results No signup required Standard formulas Free to use

Frequently Asked Questions about Hypotenuse Calculator

What is the difference between the hypotenuse and the legs of a right triangle?

The hypotenuse is always the longest side of a right triangle, located directly opposite the 90-degree right angle. The legs are the two shorter sides that form the right angle. In the formula a² + b² = c², 'c' always represents the hypotenuse. This tool automatically identifies which side is the hypotenuse based on your inputs.

Can I use this hypotenuse calculator for non-right triangles?

No, the Pythagorean theorem only applies to right triangles (triangles containing a 90-degree angle). For oblique triangles (acute or obtuse), you would need to use the Law of Cosines. However, if you know the height or can split the shape into two right triangles, this calculator can help with those components.

Is it possible to calculate the hypotenuse if I only know the area?

Yes, but only if you also know at least one leg. The “Area & Side” tab is designed for this exact scenario. You provide the total area of the right triangle and the length of one leg. The tool calculates the other leg using b = (2 * Area) / a, and then finds the hypotenuse using the standard theorem.

Does the tool handle negative numbers or zero values?

Negative lengths are physically impossible, so the input fields only accept positive numbers or zero. If you enter zero for both legs, the result will be zero because a triangle cannot exist. The “Load Example” button uses a classic 3-4-5 triangle to demonstrate valid inputs.

How accurate are the angle and area results?

The calculations use JavaScript’s native Math functions, which provide double-precision floating-point accuracy (about 15 decimal digits). Angles are displayed rounded to one decimal place by default, but the internal calculation uses the full precision. The area is accurate to the square unit you selected, and the solution steps show the exact formulas used.

Why do I see different units on the result page?

The result page displays the hypotenuse, legs, and area using the unit you selected for the input. However, the internal calculation normalizes everything to a base unit (e.g., meters or inches) to ensure mathematical consistency. You can mix feet and centimeters in the input; the tool will convert everything automatically before applying a² + b² = c².

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