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Projectile Motion From a Height Calculator

Find time of flight, range, max height, and impact velocity for an object launched at an angle from above ground level — like throwing something off a cliff or a building.

Time of flight
2.9237 s
Horizontal range
37.9798 m
Maximum height above ground
22.867 m
Impact velocity
24.8475 m/s

How it works

This generalizes this site's existing Projectile Motion calculator (which only lands back on flat ground) to a launch point a height h above the ground it lands on. For an object launched at speed v and angle θ above horizontal, the vertical position is y(t) = h + v·sin(θ)·t − ½gt². Solving y = 0 for its positive root gives the time of flight t = (v·sin(θ) + √((v·sin(θ))² + 2gh)) ÷ g, and the horizontal range is R = v·cos(θ)·t.

Maximum height above the ground is reached when the vertical velocity hits zero, at h + (v·sin(θ))² ÷ (2g). Impact velocity comes from energy conservation — the drop converts height into speed exactly the way this site's Free Fall calculator does — giving v_impact = √(v² + 2gh).

Setting the height to zero recovers this site's flat-ground Projectile Motion calculator's results exactly, since this is the same physics with one extra starting height added in.

FAQ

What does a launch angle of 0 mean?

A perfectly horizontal launch — the classic case of throwing or sliding something off a ledge with no upward angle at all. The object still falls under gravity the whole time; it just starts with no vertical velocity.

Does this account for air resistance?

No — like this site's Projectile Motion and Free Fall calculators, this assumes a vacuum (no drag), so it's exact for the idealized physics problem but will overstate real-world range, flight time, and impact speed for light or irregularly shaped objects, especially over longer falls.

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