Angle of Impact Calculator — Projectile Landing Angle
Enter the initial launch speed, launch angle, and height above the landing level to calculate the angle of impact — the steepness of the velocity vector at the exact moment the projectile hits the ground.
m/s
°
m
Angle the velocity vector makes with the horizontal at the moment of landing
- 1
Horizontal velocity
vx = 20 × cos(30°) = 17.32Remains constant throughout the flight (no air resistance). - 2
Initial vertical velocity
vy₀ = 20 × sin(30°) = 10 - 3
Discriminant
vy₀² + 2 × g × h₀ = 10² + 2 × 9.81 × 10 = 296.2 - 4
Time of flight
(10 + √296.2) ÷ 9.81 = 2.77Positive root of the height quadratic — time until the projectile hits the ground. - 5
Vertical speed at impact
|10 − 9.81 × 2.77| = 17.21 - 6
Angle of impact
arctan(17.21 ÷ 17.32) = 44.82
How does this calculator work?
Impact angle = arctan(|vy_impact| / vx). Horizontal velocity vx = v₀·cos(α) is constant; vertical speed at landing is |vy₀ − g·t| where t = (vy₀ + √(vy₀² + 2g·h₀))/g. For same-level launch the impact angle equals the launch angle. Higher launch height or lower horizontal speed steepens the impact. No air resistance assumed.
Formula
How this is calculated
A projectile launched with speed v₀ at angle α above horizontal from height h₀ follows a parabolic path under gravity (g = 9.81 m/s²). The horizontal velocity vx = v₀·cos(α) remains constant throughout the flight (no air resistance). The vertical velocity starts at vy₀ = v₀·sin(α) and decreases linearly: vy(t) = vy₀ − g·t.
The projectile lands when the height equation H₀ + vy₀·t − ½g·t² = 0 is satisfied. Solving the quadratic gives the time of flight t = (vy₀ + √(vy₀² + 2g·H₀)) / g. At that moment the downward speed is |vy_impact| = |vy₀ − g·t|, and the angle of impact is arctan(|vy_impact| / vx).
For a launch and landing at the same height (h₀ = 0), the impact angle equals the launch angle — the trajectory is symmetric. A greater launch height steepens the impact angle because the projectile has a longer fall to accumulate downward speed. Air resistance, spin, and aerodynamic effects are not modelled; results are most accurate for dense, slow-moving objects and shortest ranges.
Frequently asked questions
With more altitude to fall through, gravity accelerates the projectile downward for longer, so the downward velocity component at impact grows larger relative to the constant horizontal component. The ratio |vy_impact| / vx increases, making arctan larger and the impact steeper.
At 0° launch angle the initial vertical speed is zero. The impact angle is arctan(√(2g·h₀) / vx). A ball thrown horizontally from 10 m at 15 m/s hits at arctan(√(196.2)/15) = arctan(14.0/15) ≈ 43°.
No — this is ideal projectile motion. For dense, compact, slow-moving objects (shot put, heavy ball) results are close to reality. For lighter or faster objects (tennis ball, football) air drag significantly reduces range and modifies the impact angle. Real trajectories are asymmetric, with a steeper descent than ascent.
Also known as
TG we-Calculate Editorial Team. (2026). Angle of Impact Calculator — Projectile Landing Angle [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/angle-of-impact-calculator
TG we-Calculate Editorial Team. "Angle of Impact Calculator — Projectile Landing Angle." TG we-Calculate. 2026. https://we-calculate.com/calculator/angle-of-impact-calculator.
TG we-Calculate Editorial Team, "Angle of Impact Calculator — Projectile Landing Angle," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/angle-of-impact-calculator
@misc{wecalculate_angle_of_impact_calculator, title = {Angle of Impact Calculator — Projectile Landing Angle}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/angle-of-impact-calculator}}, year = {2026}, note = {TG we-Calculate} }
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