Vector magnitude formula
For v = (x,y), |v| = √(x²+y²). For v = (x,y,z), add z². The same square-sum rule extends to every additional dimension.
Calculators / Quick tool
Vector Magnitude Calculator
Calculate the Euclidean magnitude of a finite numeric vector.
● Processed locally in your browser
How to useHow to use Vector Magnitude Calculator ⌄
Calculate the Euclidean magnitude of a finite numeric vector.
- 1
Paste content, enter parameters or choose the files you need in “Vector components”.
- 2
Choose “Calculate magnitude” for the job. Processing runs in this browser.
- 3
Review the result under “Vector magnitude”, then copy or download it after checking the output.
Result guide
What Vector Magnitude Calculator calculates
Enter between 2 and 100 comma-separated numeric components. The calculator evaluates the Euclidean norm |v| = √(v₁² + … + vₙ²) and shows the exact squared-component substitution.
Worked 3–4–12 example
For v = (3,4,12), |v| = √(3²+4²+12²) = √169 = 13. Negative components produce the same contribution after squaring.
Magnitude is never negative
A Euclidean magnitude is a length, so it is always zero or positive. Only the zero vector has magnitude zero. This tool does not calculate signed scalar magnitude or non-Euclidean norms.
Frequently asked questions
How do I enter a 2D or 3D vector?
Enter components separated by commas, such as 3,4 for 2D or 3,4,12 for 3D. Do not include parentheses or variable names.
Is vector magnitude the same as distance?
It is the distance from the origin to the vector endpoint. To find the distance between two arbitrary points, subtract their coordinates first or use the related coordinate-distance calculator.
Can the calculator handle negative and decimal components?
Yes. Each finite component may be signed or decimal. The calculator squares every component before adding and taking the square root.
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