Vector Magnitude Calculator

An online calculator for finding the magnitude (length, norm) of a vector, with steps shown.

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Find the magnitude (length) of $$$\mathbf{\vec{u}} = \left\langle 3, 4, 12\right\rangle$$$.


The vector magnitude of a vector is given by the formula $$$\mathbf{\left\lvert\vec{u}\right\rvert} = \sqrt{\sum_{i=1}^{n} \left|{u_{i}}\right|^{2}}$$$.

The sum of squares of the absolute values of the coordinates is $$$\left|{3}\right|^{2} + \left|{4}\right|^{2} + \left|{12}\right|^{2} = 169$$$.

Therefore, the magnitude of the vector is $$$\mathbf{\left\lvert\vec{u}\right\rvert} = \sqrt{169} = 13$$$.


The magnitude is $$$13$$$A.