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Projectile Motion Calculator

Find time of flight, maximum height, and horizontal range for an object launched at an angle, using standard kinematics — in metric (m/s) or imperial (ft/s) units.

Time of flight
2.8832 s
Maximum height
10.1937 m
Horizontal range
40.7747 m

How it works

This models ideal projectile motion (no air resistance) for an object launched at an angle θ above flat, level ground with initial speed v: time of flight t = 2v·sin(θ) ÷ g, maximum height h = v²·sin²(θ) ÷ (2g), and horizontal range R = v²·sin(2θ) ÷ g, where g is the gravitational acceleration.

Velocity and gravity just need to share the same length unit — switch the toggle to see both fields relabeled and rescaled together, and the results come out in that same unit (seconds for time either way, since only length converts). Gravity defaults to Earth's standard 9.81 m/s² but is a normal input you can change, so this also works for other bodies (the Moon's ~1.62 m/s², Mars' ~3.71 m/s²) or to model g in ft/s².

The horizontal range is maximized at a 45° launch angle for a given speed — that's why 45° is the default — and drops toward zero as the angle approaches 0° (a flat, grazing shot) or 90° (straight up, where all the motion is vertical).

FAQ

Why does the range go to zero at 90 degrees?

At a 90° launch angle, sin(2×90°) = sin(180°) = 0, so the range formula gives zero — physically, launching straight up means there's no horizontal velocity component at all, so the object comes straight back down where it started (ignoring wind and air resistance).

Does this account for air resistance?

No — like most closed-form projectile motion formulas, this assumes a vacuum (no drag). Real-world range and height, especially for light or irregularly shaped objects, will be somewhat less than this calculator's ideal-physics result.

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