Norma Vetor 3D
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
About this calculator
The 3D vector norm calculator computes the magnitude (or length) of a three-dimensional vector based on x, y, and z coordinates. The result is derived using the Euclidean norm formula: square each component, sum them up, and take the square root. This value represents the vector's distance from the origin in 3D space.
To use the calculator, simply input the vector's three components. The tool automatically performs calculations: squaring each component, adding them, and calculating the square root. Ensure inputs are in compatible units, especially when the vector represents physical quantities like force or velocity.
This tool is useful in physics, engineering, and computer graphics, where 3D vector magnitudes are commonly required. For example, when determining the strength of a tridimensional force or an object's velocity in motion. It's also applied to verify if vectors have equal lengths, such as in normalization processes.
Note: The calculator uses the standard Euclidean norm (L²). For non-Euclidean geometries or alternative norms (like L¹ or L∞), this tool won't be suitable. Negative component values don't affect the result, as they're squared during calculation.
Frequently asked questions
Why use the Euclidean norm instead of other norms?
The Euclidean norm is standard for 3D vectors as it represents actual physical distance. Other norms like L¹ are used in specific contexts, but L² is conventional in physics and mathematics.
What happens if vector components are negative?
Negative values don't affect the result because they are squared. The norm depends only on the absolute values of the components.
Can I calculate the norm if some components are zero?
Yes. If x, y, or z are zero, the formula remains valid. The norm will be the square root of the sum of the squares of the non-zero components.
How is this calculation applied in physics problems?
For 3D vectors representing forces, velocities, or accelerations, the norm indicates the total magnitude of the vector quantity.