Free online projectile motion calculator. Enter initial velocity and launch angle to calculate max height, flight time, range, and optimal angle. Supports different gravity environments. Pure frontend calculation, no data upload.
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Projectile motion describes the motion of an object under the influence of gravity only (ignoring air resistance). Given initial velocity v₀, launch angle θ, initial height h, and gravitational acceleration g:
vₓ = v₀ × cos(θ) (horizontal, constant)
v_y = v₀ × sin(θ) (vertical, affected by gravity)
H = h + v_y² / (2g)
When initial height h = 0: T = 2 × v_y / g
When initial height h > 0: T = (v_y + √(v_y² + 2gh)) / g
R = vₓ × T
On level ground (h = 0), the angle that maximizes range is 45°.
When launched from a height, the optimal angle is less than 45°.
This calculator uses the ideal projectile motion model, ignoring air resistance for simplicity. In reality, air resistance significantly reduces range and max height. For high-speed objects like bullets or rockets, air resistance has a huge impact and requires complex ballistic calculations.
When initial height is zero, the range formula is R = v₀² × sin(2θ) / g. sin(2θ) reaches its maximum value of 1 at θ = 45°, making 45 degrees the optimal launch angle. When launching from a height, the optimal angle is slightly less than 45 degrees.
The only difference is the gravitational acceleration g. The Moon's g is about 1/6 of Earth's, so with the same initial velocity, range and height on the Moon are about 6 times greater. This tool supports switching between different planetary gravity environments.
A greater initial height means longer flight time and therefore greater range. This is why throwing an object from a high place goes farther than from ground level. Also, with an initial height, the optimal angle decreases from 45 degrees.