# Distance between Two Points Calculator

For two given points, the calculator will find the distance between them, with steps shown.

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If you have two-dimensional points, set the third coordinates equal to $0$ or leave them empty.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

Find the distance between $P = \left(-2, 3\right)$ and $Q = \left(5, 1\right)$.

## Solution

The distance between two points $P = \left(p_{x}, p_{y}\right)$ and $Q = \left(q_{x}, q_{y}\right)$ is $d = \sqrt{\left(q_{x} - p_{x}\right)^{2} + \left(q_{y} - p_{y}\right)^{2}}$.

We have that $p_{x} = -2$, $p_{y} = 3$, $q_{x} = 5$, $q_{y} = 1$.

Thus, $d = \sqrt{\left(5 - \left(-2\right)\right)^{2} + \left(1 - 3\right)^{2}} = \sqrt{53}$.

$d = \sqrt{53}\approx 7.280109889280518$A