Speed vs Velocity

This is a short page aiming to differentiate between speed and velocity. For more detailed information on either of those topics, view their respective main pages.

The Main Idea

Speed ([math]\displaystyle{ v }[/math]) and velocity ([math]\displaystyle{ \vec{v} }[/math] or v) are similar concepts, and as a result, the terms are often confused and interchanged incorrectly in everyday conversation. The key difference between them is that velocity is a vector quantity that describes both how fast and in which direction an object is moving, while speed is a scalar quantity that describes only how fast an object is moving. Speed is the magnitude of the velocity vector. Velocity is the more descriptive of the two, as it contains all of the information speed contains and then some. It is easy to tell the speed of an object given only its velocity, but it is impossible to tell the velocity of an object given only its speed because one has no way of knowing the object's direction of travel.

Both speed and velocity have the same units because a vector always has the same units as its magnitude. Both are measured in units of distance over units of time. The SI unit for both speed and velocity is the meter per second (m/s).

Mathematical Relationship Between Speed and Velocity

The following formulas describe the relationship between speed and velocity and can be helpful when converting between the two:

[math]\displaystyle{ v = |\vec{v}| }[/math]

[math]\displaystyle{ v = \sqrt{v_x^2 + v_y^2 + v_z^2} }[/math] (in 3 dimensions)

[math]\displaystyle{ \vec{v} = v\hat{v} }[/math], where [math]\displaystyle{ \hat{v} }[/math] is the direction of travel.

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