Enter vector components and calculate the magnitude
Enter 2 to 12 vector components, separated by commas or spaces, then press Calculate. Use decimal values such as 2.5 or fractions such as 3/4. For example, enter 3, 4 to calculate a 2D vector's magnitude.
The calculator uses the Euclidean magnitude formula for the components you provide and displays the result with its calculation steps.
Use the calculator controls
- Enter the components in the Components (2 to 12, separated by commas or spaces) field.
- Choose an optional value from Unit (label only - no conversion is performed), or leave it set to None / unitless.
- Press Calculate to show the result.
- Use Copy result to copy the displayed report, or use Download result (.txt) to save it as a text file.
- Press Reset to clear the components and unit selection and hide the result.
Read the result and formula steps
The result panel shows the magnitude, the vector dimension, and the parsed vector. Its Formula & steps section lists each component squared, the sum of squares, and the final square-root calculation. The magnitude is formatted to six decimal places.
The calculation assumes orthonormal Cartesian components and uses:
|v| = sqrt(v1^2 + v2^2 + ... + vn^2)
Input rules and validation
- Enter between 2 and 12 components.
- Separate components with commas, spaces, or both.
- Use plain numbers or simple fractions, such as
-3,2.5, or3/4. - Empty, unparseable, or out-of-range input is rejected before calculation.
- A fraction with a zero denominator, such as
1/0, is rejected.
Assumptions and limitations
- Use components from an orthonormal Cartesian coordinate system.
- Enter all components in compatible units. The unit field labels the result only; it does not convert or rescale values.
- A zero vector has a magnitude of exactly 0 and is treated as a valid result.
- Fraction calculations are converted to JavaScript
Numbervalues before the square root is calculated. Unusually large inputs may therefore be affected by JavaScript numeric limits, and the calculator has no separate overflow warning. - Copy result uses browser clipboard access. If that access is unavailable or rejected, the tool displays
Copy failed..
Privacy and local processing
Vector parsing and calculation happen in your browser, and the calculator does not submit the vector input as part of its calculation workflow. The page also loads analytics and includes a subscription form that sends email data to /assets/subscribe.php.
Frequently Asked Questions
What formula does this calculator use?
It uses the standard Euclidean norm: |v| = sqrt(v1^2 + v2^2 + ... + vn^2), the square root of the sum of the squares of the vector's components in an orthonormal (Cartesian) basis.
Can I calculate the magnitude of a vector with more than 3 components?
Yes. Enter any number of components (up to 12) separated by commas or spaces, and the calculator applies the same sum-of-squares formula regardless of dimension.
Does the unit selector convert units?
No. The unit selector only labels the result for readability (for example, m or N). It performs no unit conversion - all components must already be entered in the same unit.
What happens if I enter a zero vector?
A zero vector (all components 0) has a magnitude of exactly 0. The calculator reports this directly - it is a valid, well-defined result, not an error.