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Projectile Motion Calculator

Solve for time of flight, maximum height, and range of a projectile launched at an angle.

m/s
deg
0° 90°
m
Leave at 0 for ground launch.
m/s²

Results

Time of Flight
0.00 s
Maximum Height
0.00 m
Total Range
0.00 m
Trajectory Visualization

Understanding Projectile Motion

Projectile motion is a form of motion experienced by an object or particle (a projectile) that is thrown near the Earth's surface and moves along a curved path under the action of gravity only. This curved path was shown by Galileo to be a parabola.

The Physics Formulas

To calculate the parameters of motion, we split the initial velocity into horizontal ($v_x$) and vertical ($v_y$) components.

vx = v0 · cos(θ)
vy = v0 · sin(θ)

1. Time of Flight

The total time the object stays in the air depends on the vertical component of velocity and gravity. If launched from ground level ($h=0$):

t = 2 · v0 · sin(θ) / g

If launched from an initial height ($h > 0$), we solve the quadratic equation for time when vertical displacement is zero.

2. Maximum Height

The maximum height is reached when the vertical velocity becomes zero.

H = h0 + (v0 · sin(θ))² / (2 · g)

3. Range

The horizontal distance traveled is the horizontal velocity multiplied by the total time of flight.

R = v0 · cos(θ) · t