Angle of Impact Calculator
Calculate impact angles, exit velocity, and energy loss for any collision scenario involving surfaces.
Enter the initial velocity, angles, coefficient of restitution, and mass to instantly analyse collision dynamics.
Angle of Impact Calculator
Calculate impact angles, exit velocity, and energy loss for any collision scenario involving surfaces.
About the Angle of Impact Calculator
The angle of impact is the angle at which a moving object meets a surface, measured from the plane of that surface. It is a fundamental quantity in classical mechanics, governing how objects rebound, how much energy is transferred during a collision, and what happens to the trajectory after contact. Understanding impact angles is essential across many disciplines — from sport science and automotive safety engineering to forensic analysis, ballistics, and industrial process design.
When an object travelling at a known velocity meets a surface, the velocity vector can be decomposed into two perpendicular components: the normal component (perpendicular to the surface) and the tangential component (parallel to the surface). The normal component is responsible for the compression and rebound force, while the tangential component — assuming no friction — remains unchanged throughout the collision. The ratio between the rebound normal velocity and the incoming normal velocity is defined as the coefficient of restitution (e), a dimensionless number between 0 and 1. A value of 1 represents a perfectly elastic collision with no energy loss, while 0 represents a perfectly inelastic impact where the normal component of velocity is completely absorbed.
The calculator uses these principles to compute the exit velocity and exit angle after impact. The normal component of velocity after the collision is e × vₙ (reversed), and the tangential component vₜ remains the same. The resulting exit velocity is √(vₙ_out² + vₜ²) and the exit angle is derived from the arctangent of the ratio of these components, adjusted back to the horizontal reference frame using the surface angle.
Kinetic energy loss is calculated from the difference in kinetic energy before and after the collision: ΔKE = ½m(v² − v_out²). Expressing this as a percentage of the initial kinetic energy gives a clear measure of collision inelasticity. A billiard ball has a coefficient of restitution around 0.9, meaning only about 19% of kinetic energy is lost in a typical bounce. A car crashing into a rigid barrier may have e ≈ 0.1–0.3, losing 91–99% of kinetic energy.
Practical applications of impact angle analysis include automotive crash testing, where engineers model barrier collisions to evaluate crumple zones; sports engineering, where tennis court surfaces and billiard table cushions are optimised for specific rebound characteristics; ballistic trajectory analysis for forensic reconstruction; and industrial conveyor design, where material drop angles are calculated to minimise wear on chutes and hoppers. Biomechanical studies also use impact angle analysis to understand how joints absorb shock during running and jumping.
This calculator assumes a two-dimensional, rigid-body collision with no friction along the contact surface and a fixed, immovable surface. Real-world collisions may involve surface deformation, spin, aerodynamic forces, and multi-axis motion. For most educational, engineering estimation, and sports-science purposes, however, the two-dimensional model provides accuracy well within practical tolerances.
Worked Examples
Load any example to see the impact angle, exit velocity, and energy loss calculated instantly.
| Scenario | Impact angle / Exit vel. | Notes |
|---|---|---|
| Billiard ball: v=3 m/s, θ=30°, surface=0°, e=0.9, m=0.17 kg | 30° impact / 2.93 m/s exit / 4.8% energy loss | High-elasticity collision. Only the normal velocity component is attenuated by e=0.9; the large tangential component is preserved, so overall energy loss is only about 5%. |
| Tennis ball: v=25 m/s, θ=15°, surface=0°, e=0.75, m=0.057 kg | 15° impact / 24.63 m/s exit / 2.9% energy loss | Very shallow impact angle means nearly all velocity is tangential. The ball exits almost flat with only about 3% kinetic energy lost to the normal restitution. |
| Car crash: v=15 m/s, θ=45°, surface=0°, e=0.2, m=1500 kg | 45° impact / 10.82 m/s exit / 48% energy loss | Low restitution with a 45° impact; about half the kinetic energy is absorbed by the crumple zone and barrier deformation. |
| Physics lab: v=5 m/s, θ=60°, surface=30°, e=0.85, m=0.01 kg | 30° impact / 4.82 m/s exit / 7% energy loss | Inclined surface at 30°. The effective impact angle is θ_vel − θ_surface = 30°. Exit angle from horizontal is about 56°. |
How to Use the Angle of Impact Calculator
- Enter the initial velocity of the object in metres per second — this is the speed of the object just before it hits the surface.
- Set the velocity angle in degrees, measured from the horizontal. For a downward-travelling projectile striking a flat floor, this is the angle below the horizontal.
- Set the surface angle in degrees from horizontal. A flat floor is 0°; a ramp tilted at 30° would be 30°.
- Enter the coefficient of restitution (0 to 1). Use 0.9 for hard rubber balls, 0.75 for tennis balls, 0.2–0.4 for typical automotive crashes.
- Enter the object mass and click Calculate. The results show impact angle, exit velocity, exit angle, and the percentage of kinetic energy lost.
Frequently Asked Questions
What is the angle of impact?
The angle of impact is the angle between the velocity vector of the approaching object and the plane of the surface it strikes. A 90° impact is a head-on collision perpendicular to the surface; a very shallow angle (near 0°) means the object nearly grazes the surface. The angle of impact directly determines how much of the velocity acts to compress the surface versus slide along it.
What is the coefficient of restitution?
The coefficient of restitution (e) is a ratio between 0 and 1 that measures how much of the normal velocity component is retained after a collision. A value of 1 means a perfectly elastic bounce with no energy loss in the normal direction. A value of 0 means the object does not bounce at all. Most real materials fall between 0.1 and 0.95 depending on the speed, temperature, and material properties.
How is exit velocity calculated?
The exit velocity is calculated by decomposing the incoming velocity into normal (perpendicular to surface) and tangential (parallel to surface) components. The normal component is multiplied by the coefficient of restitution and reversed; the tangential component is kept unchanged. The exit velocity is then the vector sum of these two components: v_out = √(vₜ² + (e × vₙ)²).
Why does a glancing (low-angle) impact lose less energy?
At a low impact angle, most of the velocity is tangential (parallel to the surface) and very little is normal (into the surface). Since energy loss only occurs in the normal direction (governed by the coefficient of restitution), a glancing blow dissipates very little energy. This is why shallow-angle bullets ricochet and why spacecraft re-entries use shallow angles to spread heat.
What real-world factors does this calculator not account for?
This calculator assumes a rigid, immovable surface; no friction along the surface; a point mass with no rotation; and a two-dimensional geometry. Real collisions may involve surface deformation, spin transfer, three-dimensional trajectories, aerodynamic effects, and variable restitution at different speeds. For detailed engineering analysis, finite element simulations should supplement the results from this tool.
How does surface angle affect the results?
The surface angle shifts the reference frame for the collision. The actual impact angle used in the physics is the velocity angle minus the surface angle. A steeper surface reduces the effective impact angle, which can make a high-speed collision behave more like a glancing blow. The exit angle is then computed relative to the surface and converted back to horizontal by adding the surface angle, giving the true trajectory after the bounce.