One-Dimensional Collision Calculator
Calculate signed velocities after a collision from masses, incoming velocities and a restitution coefficient. Compare momentum and kinetic energy before and after contact.
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Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Conserve total linear momentum and set the relative separating speed to e times the relative approaching speed. Resolve each final velocity around the centre-of-mass velocity.
v1=Vcm−m2 e(u1−u2)/(m1+m2); v2=Vcm+m1 e(u1−u2)/(m1+m2)
Worked example
Two equal 1 kg bodies with incoming velocities 2 m/s and 0 m/s exchange velocities in an elastic collision (e=1). At e=0 they both leave at 1 m/s and 1 J of translational kinetic energy is converted to other forms.
Assumptions and input details
Isolated one-dimensional point-body collision, with no external impulse, rotation or deformation model. Positive velocity points right; body 1 is initially left of body 2. Require u1≥u2 so the bodies approach or move together; e is 0–1. Masses are positive 1e−9–1e12 kg; signed velocities within ±1e9 m/s. e=0 gives equal final velocity; e=1 conserves translational kinetic energy. An entered coefficient is a scenario, not a measured material property. This does not calculate impact force, injury or structural damage.
References: OpenStax one-dimensional collisions
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
The 19 mass definitions distinguish avoirdupois and troy measures, metric and regional measures. Japanese kin is 600 g; mainland Chinese shijin is 500 g.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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