How this instrument works
At the moment a projectile lands, its velocity has two components: a horizontal one (vx) that stayed constant throughout the flight, and a vertical one (vy) that grew the whole way down under gravity. Those two components form the legs of a right triangle, with the actual velocity vector as the hypotenuse — and the angle between that vector and the ground is simply the arctangent of vy divided by vx, the same trigonometry used for any right-triangle slope.
The result tells you how steep or shallow the landing is. An angle close to 90° means the object is falling almost straight down, with very little horizontal component — think of something dropped from directly overhead. An angle close to 0° means it's skimming in almost flat, with a large horizontal component relative to its vertical drop — think of a flat, fast throw. Everything in between describes the full range of real projectile landings, from lobbed arcs to grazing shots.
This calculator only needs the two velocity components at the instant of impact, not the full trajectory that produced them. If you only know a launch angle, launch speed, and height, you'd first work out vx and vy at landing with a separate projectile-motion or trajectory tool, then plug those two numbers in here to get the impact angle itself.
- Enter Vertical velocity component (vy) — the speed the projectile is moving up or down at the moment it lands.
- Enter Horizontal velocity component (vx) — the constant sideways speed of the projectile.
- Read Angle of impact — the angle, in degrees from horizontal, at which the object strikes the surface.
- Keep both components in the same speed unit (both m/s, or both ft/s); the angle only depends on their ratio, not on which unit you picked.
Worked example — a classic 3-4-5 velocity pair
Enter 30 into Vertical velocity component (vy) and 40 into Horizontal velocity component (vx) — a projectile landing with 30 units of vertical speed against 40 units of horizontal speed. Angle of impact reads 36.8699 degrees: atan(30 ÷ 40) = atan(0.75).
These two numbers form a scaled-up 3-4-5 right triangle, so the total landing speed works out to a clean 50 units (√(30² + 40²) = 50) — a tidy check that the geometry lines up, even though the angle itself, 36.8699°, isn't one of the 'nice' textbook angles like 30°, 45° or 60°.
Questions
What angle results when vy and vx are equal?
Exactly 45 degrees. When the vertical and horizontal components match — say vy = 10 and vx = 10 — their ratio is 1, and the arctangent of 1 is precisely 45°, the midpoint between a flat, skimming landing and a straight-down drop.
What happens if the horizontal velocity is zero?
The formula breaks down, since dividing by zero has no defined result — this calculator asks for a nonzero horizontal component rather than guessing. Physically, vx = 0 describes a straight-down impact (a 90° angle), so if that's your case, enter a very small nonzero vx to get a reading extremely close to 90° instead.
Is the impact angle the same as the launch angle?
Only when the projectile lands at the same height it was launched from and air resistance is negligible — in that idealized case, the impact angle mirrors the launch angle exactly. Once the landing point is higher or lower than the launch point, or drag is significant, the two angles diverge, and the impact angle typically ends up steeper than the launch angle because of accumulated vertical speed.
Does the projectile's mass affect the angle of impact?
No — the angle depends only on the ratio between the vertical and horizontal velocity components at landing, not on how heavy the object is. Mass affects how quickly air resistance slows an object down, which can indirectly change vx and vy over a real flight, but given the same two components at impact, two objects of any mass land at the same angle.
What real-world situations use angle of impact?
It comes up anywhere the steepness of a landing or collision matters: ballistics and forensic reconstruction, sports like javelin and long jump, engineering assessments of falling-object risk, and physics or game-engine simulations that need a realistic bounce or splash angle. In each case, the same two-component arctangent relationship applies.