Coefficient of Restitution Calculator

How it is calculated

The tool divides the speed at which two bodies move apart after impact by the speed at which they approached: e = vsep / vapp. Both are relative speeds along the line of impact, in the same unit (m/s, km/h or mph all work, because the unit cancels). The approach speed must be above zero and the separation speed cannot be negative. The separation speed also cannot exceed the approach speed, since e above 1 would mean the collision created energy; such an input gives no result. The answer is a pure number between 0 and 1 shown to four decimals: 1 is perfectly elastic and 0 means the bodies do not separate at all. For a ball dropped on a fixed floor, e can also be found from heights as √(hbounce / hdrop).

Common mistakes

• Using heights instead of speeds: a ball that bounces to 70% of its drop height has e of about 0.84, not 0.70, because speed varies with the square root of height.
• Entering the speeds of two moving bodies separately instead of relative speeds. For a head-on collision, add the two speeds before impact, and the two after.
• Swapping approach and separation. For a normal bounce this gives a value above 1, which the tool rejects with no result.
• Mixing units, such as approach in m/s and separation in km/h.
• Reading e as the share of energy kept. The energy kept is e², so e = 0.7 retains about 49% of the kinetic energy.