Coefficient of Restitution Calculator
Compares relative separation and approach speeds along the impact line. On this Coefficient of Restitution page, changing an entry updates the result and visible checking path.
Measurements for Coefficient of Restitution
Coefficient of restitution
Following e = separation speed / approach speed
The worked case uses Relative approach speed = 5 m/s, Relative separation speed = 4 m/s. These values provide a reproducible example, and no unannounced unit conversion is applied to them.
Arrange e = separation speed / approach speed symbolically before substitution. That order makes an inverted ratio, omitted exponent, or misplaced number easier to identify.
What this result represents for Coefficient of Restitution
Compares relative separation and approach speeds along the impact line. In machine-performance studies, this relationship is meaningful only when the reference frame, direction convention, and units remain consistent.
The named fields are relative approach speed, relative separation speed. Each belongs in a defined position within e = separation speed / approach speed; writing values beside the symbols helps catch a transposition.
For coefficient of restitution, coefficient of restitution is treated as a nonnegative magnitude. If an entered combination produces a negative value, revisit the physical domain instead of reading the sign as a direction.
Reading coefficient of restitution in context
The calculator reports coefficient of restitution in ratio. If that number enters a later formula, keep guard digits until the final operation.
Compare coefficient of restitution with the scale of the coefficient of restitution scenario. A metric-prefix mistake or inconsistent time unit can produce tidy arithmetic that is physically implausible.
For reproducibility, record relative approach speed, relative separation speed, their units, the reference direction, and e = separation speed / approach speed rather than storing only the final numeral.
A second conservation check for Coefficient of Restitution
Start the dimensional check with e = separation speed / approach speed. After cancellation, the surviving dimension needs to correspond with ratio; a mismatch means the setup needs correction.
Then change one input by a controlled amount and predict how coefficient of restitution is expected to respond before recalculating. Direction and sensitivity provide separate checks on the arithmetic.
Conditions the equation calls for for Coefficient of Restitution
The Coefficient of Restitution model uses the stated one-dimensional quantities. Conservation requires negligible external impulse during the event, while rotation, deformation, sound, heat, or off-axis motion can change coefficient of restitution.
The precision of coefficient of restitution is limited by the least precise measurement. Extra displayed digits aid verification, but safety-critical work calls for validated data and a suitable engineering procedure.
A related quantity after Coefficient of Restitution
Useful follow-up calculations include one-dimensional elastic collision calculator, ballistic pendulum calculator.
Use coefficient of restitution in a later page only when its units, reference, and assumptions remain compatible.
Understanding Coefficient of Restitution
What does the coefficient of restitution represent?
It is coefficient of restitution under e = separation speed / approach speed and the field definitions printed on this page.
How can the Coefficient of Restitution output be checked?
Rearrange e = separation speed / approach speed to recover one entered quantity, then confirm that the remaining unit is ratio.
Do these inputs need consistent units?
Yes. Match every value to the unit beside its field before evaluating e = separation speed / approach speed.
Why could another coefficient of restitution differ?
Gravity choice, rounding, sign conventions, reference frames, or different assumptions can shift the reported coefficient of restitution.
Should the coefficient of restitution be negative?
No. The coefficient of restitution model reports a magnitude, so a negative value points to inputs outside its physical domain or an inconsistent setup.