Hypot function

Calculator and formula for the Hypot function

Hypot calculator

What is calculated?

This function computes the square root of the sum of squares of a series of numbers. It is particularly useful to compute the hypotenuse of a right triangle.

Input values


Number series
Result
The result is shown with the selected number of decimal places

Hypot function info

Properties

Hypot function:

  • Computes √(a₁² + a₂² + ... + aₙ²)
  • Avoids overflow/underflow
  • Numerically stable
  • Range: [0, ∞)

Application: Mainly used to compute the hypotenuse in right triangles and to determine distances between points.

Examples
hypot(3, 4) = 5
Classic 3-4-5 triangle
hypot(1, 1) ≈ 1.414
Diagonal of a square
hypot(5, 12) = 13
Another Pythagorean triple
hypot(1, 1, 1) ≈ 1.732
Space diagonal of a cube

Formula of the Hypot function

General form
\[h = \sqrt{a_1^2 + a_2^2 + \ldots + a_n^2}\] Hypot for n numbers
Two numbers (classic)
\[c = \sqrt{a^2 + b^2}\] Pythagorean theorem
Three dimensions
\[d = \sqrt{x^2 + y^2 + z^2}\] Spatial distance
Euclidean norm
\[\|\vec{v}\| = \sqrt{\sum_{i=1}^{n} v_i^2}\] Vector norm

Calculation example

Example: Hypotenuse of a right triangle

Given:

  • Leg a = 3
  • Leg b = 4

Calculation:

\[c = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5\]

Result: The hypotenuse length is 5 units.

Description of the Hypot function

Definition

The hypotenuse is the side opposite the right angle of a triangle. The length of the hypotenuse of a right triangle can be determined using the Pythagorean theorem.

Extended application

The derived Hypot function computes the square root of a series of numbers by adding the squares. This is especially useful in vector calculations and multidimensional distance computations.

Numerical stability

The Hypot function is implemented to avoid numerical overflows and underflows that can occur when computing √(a² + b²) directly if a or b have very large or very small values.

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Exponential function base 10x  •  Exponential function base ex  •  Exponential function base xy  •  Modular Exponentiation (PowMod)  •  Logarithm to base 10 (Log)  •  Logarithm to base e (Ln)  •  Logarithm to base a (Loga)  •  Square root (sqrt)  •  Cubic root (cbrt)  •  nth root  •  Hypot  •