Coefficient of Restitution Calculator

Analyze collisions using velocity or height data quickly. Compare energy loss and rebound speed easily. Get clear restitution results for lab reports instantly today.

Calculator Inputs

Velocity Method Data

Bounce Height Method Data

Formula Used

Velocity method:

e = |v₂ - v₁| / |u₁ - u₂|

Here, u₁ and u₂ are initial velocities. v₁ and v₂ are final velocities. The numerator is separation speed. The denominator is approach speed.

Bounce height method:

e = √(rebound height / drop height)

Energy ratio from restitution:

Relative energy retained = e² × 100

Kinetic energy:

KE = 0.5 × mass × velocity²

Momentum:

p = mass × velocity

How to Use This Calculator

  1. Select the velocity method for two moving objects.
  2. Select the height method for a simple bounce test.
  3. Choose the units used in your experiment.
  4. Enter initial and final velocities, or enter drop and rebound heights.
  5. Add masses when energy, momentum, and impulse results are needed.
  6. Press the calculate button.
  7. Review the result shown above the form.
  8. Use the CSV or PDF button to save your result.

Example Data Table

Test Type Input Values Formula Estimated Result
Two cart collision u₁ = 5 m/s, u₂ = -2 m/s, v₁ = -1 m/s, v₂ = 3 m/s |3 - (-1)| / |5 - (-2)| 0.5714
Ball bounce Drop = 2 m, Rebound = 1.28 m √(1.28 / 2) 0.8000
Elastic reference Approach speed = 6 m/s, Separation speed = 6 m/s 6 / 6 1.0000

About the Coefficient of Restitution

The coefficient of restitution measures how lively a collision feels. It compares the speed after impact with the speed before impact. A value near zero means the objects stick or rebound weakly. A value near one means the rebound keeps most relative motion. Values above one can appear when stored energy is released during impact.

Why This Calculator Helps

This calculator supports two common test styles. The velocity method works well for carts, balls, and moving objects. Enter each object's velocity before and after impact. The height method works for bounce tests. Enter the drop height and rebound height. The tool then reports restitution, energy retention, energy loss, and a simple collision class.

Practical Measurement Tips

Use the same direction sign for every velocity. A rightward velocity can be positive. A leftward velocity can be negative. This keeps the relative speed correct. For bounce tests, measure height from the same reference point. Use meters, feet, or centimeters consistently. Repeat the test several times. Average results reduce random error.

Interpreting Results

A perfectly inelastic collision has a coefficient of zero. The bodies have no separation speed after impact. A partially elastic collision has a value between zero and one. Most real sports balls and materials fall here. An elastic collision has a value near one. Superelastic results need review. They may mean extra energy entered the system. They may also reveal measurement mistakes.

Energy and Momentum Notes

Restitution is not the same as energy efficiency. It is based on relative speed. Energy depends on mass and velocity squared. That is why this calculator also accepts optional masses. When masses are entered, it estimates kinetic energy before and after impact. It also reports momentum change for each object. These values help compare materials, surfaces, and test conditions.

Best Use Cases

Use it for classroom experiments, lab reports, product checks, and coaching analysis. It can compare rubber balls, steel balls, carts, packaging drops, and rebound surfaces. Keep inputs realistic. Clean the test surface. Record temperature when materials are sensitive. Review the warning messages when the approach speed is too small, because tiny speed differences can create unstable answers. Save each result to document your testing process later clearly.

FAQs

What is the coefficient of restitution?

It is a ratio that compares separation speed after impact with approach speed before impact. It helps describe how elastic a collision is.

Can the coefficient be greater than one?

Yes. A value above one can happen when extra stored energy is released. It can also happen because of measurement errors.

What does a value of zero mean?

A value of zero means there is no rebound separation speed. The collision behaves as perfectly inelastic in the measured direction.

What does a value near one mean?

A value near one means the collision keeps most relative speed. It is close to elastic behavior, though real losses may still exist.

Which method should I use?

Use the velocity method for two moving objects. Use the bounce height method when dropping one object and measuring its rebound height.

Do I need mass values?

No. Mass is not needed for the basic coefficient. Add mass values when you want energy, momentum, and impulse estimates.

Why are direction signs important?

Velocity has direction. Use positive and negative signs consistently. This keeps approach and separation speeds meaningful for head-on collisions.

Is bounce height accurate for every collision?

It is useful for vertical rebound tests. It may not suit angled impacts, spinning objects, rough surfaces, or tests with strong air resistance.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.