What is magnitude?

Magnitude means the size or amount of something, without regard to direction.

In everyday language it just means "how big" an earthquake of magnitude 7 is larger than magnitude 5.

In mathematics and physics, some quantities have both size and direction — these are called vectors (e.g., velocity: "60 km/h heading north"). The magnitude of that velocity is simply 60 km/h the direction is removed. Magnitude is always a positive number or zero.

Calculating magnitude: for a 2D vector with components (x, y):

Magnitude = √(x² + y²) This is simply the Pythagorean theorem applied to the vector's components.

Examples:

• Magnitude of a force vector → how strong the force is
• Magnitude of a displacement vector → how far something moved (distance, not direction)
• In astronomy, magnitude = brightness of a star (higher magnitude = dimmer star a historical convention)