Reference · Math

math.hypot

math.hypot(num...) -> float

What it does

The Euclidean length of a vector given as separate numbers: the square root of the sum of their squares, as a float, as Python's math.hypot. With two numbers it is the hypotenuse of a right triangle; with more, the length in that many dimensions. The squares are never formed outright, so very large and very small numbers neither overflow nor underflow.

Examples

print(math.hypot(3, 4), math.hypot(1, 1))print(math.hypot(1, 2, 2), math.hypot(3, 4, 12))

5.0 1.41421356237309513.0 13.0

Edge cases

• Signs do not matter; one number gives its absolute value, and no numbers give 0.0.
• math.sqrt(x * x + y * y) overflows for 1e200; math.hypot does not, and 1e-200 does not vanish either.
• An infinity gives inf, even next to a NaN. Otherwise a NaN gives NaN, as in Python.
• The numbers are separate arguments, not a list: for a list use vec.norm, and for two points math.dist.

print(math.hypot(-3, -4), math.hypot(-5), math.hypot())print(math.isfinite(math.hypot(1e200, 1e200)), math.hypot(1e-200, 1e-200) > 0)print(math.hypot(math.inf, math.nan), math.hypot(math.nan, 1), math.hypot(math.nan, 0))print(vec.norm([3, 4]), math.dist([0, 0], [3, 4]))

5.0 5.0 0.0true trueinf NaN NaN5.0 5.0

Errors

There is no domain error. An argument that is not a number, a list included, is a runtime error, not an error value: it stops the request.

print(math.hypot([3, 4]))

line 1: `math.hypot` expects a number as argument 1, got list

print(math.hypot(3, null))

line 1: `math.hypot` expects a number as argument 2, got null

Chaining

In a pipeline the first number comes first, so x | math.hypot(y) is the length of (x, y):

print(3 | math.hypot(4))print([[3, 4], [5, 12]] | map((p) => math.hypot(p[0], p[1])))

5.0[5.0, 13.0]

See also

math.dist, vec.norm, math.sqrt, math.atan2

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