Projectile Motion Calculator
Range, maximum height, flight time and impact speed for a projectile launched at a speed and angle from any height, no air resistance, with a trajectory table.
Where and when the projectile lands, how high it goes, how fast and at what angle it hits — plus its position at equal time steps — with the kinematic equations and g stated.
Example: Launched at 20 m/s and 45° from ground level: range 40.79 m, apex 10.20 m after 1.44 s, flight time 2.88 s. From 10 m up the same throw flies 3.47 s and lands 49.10 m away at 24.4 m/s.
Two motions
that do not talk to each other.
The equations, why 45° is only best on level ground, and what the model ignores.
The kinematics
The launch velocity is split into a horizontal part vₓ = v₀ cos θ, which stays constant, and a vertical part v_y = v₀ sin θ, which gravity reduces by g every second. Height is y = h₀ + v_y t − ½gt²; the apex is reached at t = v_y/g and sits v_y²/2g above the launch point. Setting y = 0 gives the flight time t_f = (v_y + √(v_y² + 2gh₀))/g, and the range is vₓ t_f. Impact speed combines vₓ with the vertical speed at t_f. The table lists position and vertical velocity at equal time steps.
Angle and gravity
On level ground the range is v₀² sin 2θ / g, greatest at 45° and the same for complementary angles (30° and 60°); the page reports that 45° figure for comparison. From a height the best angle is lower than 45°, and a horizontal (0°) launch still travels. g is prefilled with standard gravity, 9.80665 m/s², the value fixed by the 3rd CGPM in 1901; change it for another body — the fixture uses 1.62 as a labelled lunar sample.
What is ignored
No air resistance, no spin, no wind, flat ground and uniform gravity: the textbook model. Real objects fall short of these figures, badly so for light or fast ones, and the page says so on every result. Inputs are in metres and metres per second. Nothing leaves the browser; the same four anonymous usage counts as the rest of the site apply.
SOURCES
- CGPM, 3rd meeting (1901) — standard acceleration of gravity g_n = 9.80665 m/s²
- Constant-acceleration kinematics — any introductory mechanics text (e.g. Halliday, Resnick & Walker, Fundamentals of Physics, ch. 4)
Last reviewed 19 September 2026. How results are checked: How we verify.