The coefficient of restitution is a dimensionless quantity used to describe the elasticity of a collision between two objects. It represents the ratio of the relative velocity of separation after the collision to the relative velocity of approach before the collision.

The formula for the coefficient of restitution (e) is:

e = (Relative Velocity of Separation) / (Relative Velocity of Approach)

Since the coefficient of restitution is a dimensionless quantity, its dimensional formula is simply "1" or "dimensionless." This means it has no physical units and is independent of the system of units used to measure velocity or any other relevant parameters involved in the collision.