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What is the pythagoras-based formula for the distance between two points for a 3D vector?

2 years ago

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Madeline Mcglynn


2 Answers

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It follows a very similar format to the pythagoras formula in 2D, in 3D it is: sqrt((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2)

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Simon Profile Picture
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Sussex University graduate who just can't get enough of maths!

Hi Madeline!


If your two points are (x₁, y₁, z₁) and (x₂, y₂, z₂), then the formula is:

Distance = √[(x₁x₂)² + (y–y)² + (z–z)²]


For example, let's say you want to find the distance between the points (–6, 4, –15) and (2, –5, –3):

Distance = √[(–6–2)² + (4–(–5))² + (–15–(–3))²]

= √[(–8)² + (9)² + (–12)²]

= √[64 + 81 + 144]

= √[289]

= 17


Simon


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