Physics · Live
Projectile Motion Calculator
Enter launch speed, angle, and height to get time of flight, max height, range, and landing speed for any projectile — instantly, with a plotted flight path.
Inputs
Launch conditions
Leave at 0 for ground-level launches.
Quick examples
Trajectory results
Time of flight
3.6
s
Max height
15.93
m
Range
63.71
m
Landing speed
25
m/s
Landing angle
45
° below horizon
Horiz. / vert. velocity
17.7 / 17.7
m/s
Flight path
Height vs. distance
Formula reference
The kinematics used
Time of flight
t = [vy₀ + √(vy₀² + 2gh₀)] / g
Max height
H = h₀ + vy₀² / (2g)
Range
R = vₓ · t
Landing speed
vf = √(vₓ² + vy₀² + 2gh₀)
Physics guide
How projectile motion works — and how this calculator solves it.
Projectile motion describes anything launched into the air and left to gravity alone — a thrown ball, a kicked soccer ball, a fired artillery shell, a long jumper leaving the ground. Given an initial speed, a launch angle, and a launch height, this calculator predicts exactly how long the object stays airborne, how high it climbs, how far it travels, and how fast it's moving the instant it lands. It's the standard tool for introductory physics coursework and quick real-world estimates alike.
Splitting velocity into components
The trick to projectile motion is that horizontal and vertical motion are entirely independent of each other. Gravity only ever acts vertically — it slows the object's rise and eventually pulls it back down — while its horizontal speed never changes (again, ignoring air resistance). Splitting the initial velocity into components makes this explicit:
vy₀ = v₀ · sinθ (vertical, steadily eroded by gravity)
Worked example
Take a ball thrown at 20 m/s at a 40° angle from a 2-meter-high wall. vₓ = 20cos40° ≈ 15.32 m/s and vy₀ = 20sin40° ≈ 12.86 m/s. Solving t = [vy₀ + √(vy₀² + 2·g·h₀)] / g with g = 9.81 m/s² gives a flight time of about 2.77 seconds. Multiply that by the constant horizontal speed and the ball lands roughly 42.4 meters away, after climbing to a maximum height of about 10.4 meters — and it hits the ground at about 20.96 m/s, landing at a slightly steeper angle (≈43°) than it was thrown, because the 2-meter drop added a little extra downward speed on the way in.
Why 45° isn't always optimal
For a launch and landing at the same height, exactly 45° squeezes the most range out of a given speed — the horizontal and vertical components are perfectly balanced for that case, and any angle above or below it “wastes” speed in one direction or the other. The moment the launch point sits higher than the landing point, though, that balance shifts: the object already gets extra time in the air from the drop itself, so a slightly flatter angle — trading a little height for more horizontal speed — actually covers more ground. The higher the launch point relative to the range, the further below 45° the optimal angle drifts.
Units and gravity
Toggle between metric (m/s, meters, g = 9.81 m/s²) and US units (ft/s, feet, g = 32.2 ft/s²) — the calculator uses whichever gravity value matches the unit system, so every number stays internally consistent without any manual conversion.
What this doesn't model
Like virtually every introductory projectile-motion tool, this calculator assumes an idealized vacuum: no air resistance, no spin, no wind. That's the honest standard for this category of tool, and it's exactly what's taught in physics coursework — but it also means real-world outcomes for things like a thrown baseball, a golf drive, or an artillery shell will differ, sometimes substantially, once drag and spin are factored in. Treat the numbers here as the theoretical baseline, not a substitute for a full ballistics model.