Using the Vector Magnitude Calculator
Enter 2 to 12 components, then click Calculate. The result shows the vector, its dimension, each squared component, the sum of squares, and the magnitude. You can attach a unit label, copy the report, or download it as a text file.
- Enter values in Components (2 to 12, separated by commas or spaces), such as
3, 4. Commas and spaces can be mixed. - Choose a label in Unit (label only - no conversion is performed), or leave
None / unitlessselected. - Click Calculate to display
|v|, the dimension, the parsed vector, and the calculation steps. - Click Copy result or Download result (.txt) to keep the report. Use Reset to clear the input and hide the result.
The vector magnitude formula
The calculator uses the Euclidean norm for components in an orthonormal Cartesian basis:
|v| = sqrt(v1^2 + v2^2 + ... + vn^2)
Input: 3, 4
Squares: 3^2 = 9, 4^2 = 16
Sum: 25
Magnitude: 5.000000For this input, the report shows the parsed vector, its dimension, and a magnitude of 5.000000. The magnitude always displays six decimal places. The component squares and their sum stay visible in the steps.
Accepted vector components
Enter 2 to 12 values, separated by commas, spaces, or both. Each value can be a signed whole number, a decimal such as -2.5, or a fraction such as 3/4. Text that does not match those forms, more than 12 components, and a fraction with a zero denominator such as 1/0 produce an error.
A zero vector is valid: 0, 0 produces a magnitude of exactly 0. The script keeps fraction components and intermediate squares as fractions, then converts the sum to a JavaScript Number for the square root and displayed magnitude.
What the Unit selector changes
The Unit selector adds a label such as m, m/s, or N to the displayed magnitude and report. It leaves the component values unchanged, so all components must already use the selected unit. Vector parsing and calculation happen in the browser, with no request that sends the component input to a server.
Examples the calculator accepts
- Enter
3, 4for a 2D vector. The magnitude is5.000000. - Enter
1, -2, 2for a 3D vector. The result reports a 3D dimension and can carry them/slabel. - Enter more than three components to see the same sum-of-squares steps for a higher-dimensional vector, up to 12 components.
Choosing another math calculator
Use Math Calculators to browse equation, geometry, sequence, matrix, vector, and number theory tools. The Vector Calculator handles addition, subtraction, dot product, cross product, projection, and other vector operations. The Distance Formula Calculator takes two coordinate points and finds the distance between them. For a right triangle with two known sides, the Pythagorean Theorem Calculator finds the missing side.
Frequently asked questions
How do I find the length of a vector?
Enter its components and click Calculate. The result is the square root of the sum of their squares, and the report shows each squared component and the sum used.
Can I calculate a 3D vector magnitude?
Yes. Enter three values such as 1, -2, 2. The result reports a 3D vector and the calculator accepts up to 12 components.
Can I enter fractions in the vector magnitude calculator?
Yes. A fraction such as 3/4 is accepted as one component. A fraction with a zero denominator is rejected.
Does the Unit selector change the vector magnitude?
The selector adds a label to the result and leaves the magnitude calculation unchanged. All components must already use compatible units.