Time of Flight Calculator

The Time of Flight Calculator determines how long a projectile remains airborne from launch to landing on level ground. Time of flight is a fundamental quantity in projectile motion that directly influences the horizontal range and is essential for timing-dependent applications such as sports strategy, fireworks choreography, and ballistic planning.

For a projectile launched and landing at the same height, the time of flight is: $$T = \frac{2v_0 \sin(\theta)}{g}$$ where $$v_0$$ is the initial speed, $$\theta$$ is the launch angle above the horizontal, and $$g$$ is gravitational acceleration. This formula follows directly from the vertical motion equation by finding when the projectile returns to its launch height.

The trajectory is perfectly symmetric about its midpoint: the time to reach maximum height equals exactly half the total flight time, $$t_H = T/2 = v_0 \sin\theta / g$$. At this moment, the vertical velocity is zero and the projectile transitions from rising to falling. This symmetry is a direct consequence of constant gravitational acceleration and the absence of air resistance.

Time of flight increases linearly with the vertical velocity component $$v_0 \sin\theta$$. Launching at 90° (vertically) maximizes flight time to $$T_{\max} = 2v_0/g$$, while a horizontal launch (0°) yields zero flight time (the object is already at ground level). Doubling the initial speed doubles the flight time, unlike range which quadruples.

In real-world applications, air resistance breaks the perfect symmetry: the descent takes longer than the ascent because drag decelerates the projectile going up but only partially counteracts gravity coming down. For a baseball, actual flight time might be 5-15% longer than the ideal calculation predicts, depending on speed and spin.

The impact speed for level-ground projectile motion equals the launch speed ($$v_0$$) in the ideal case, a consequence of energy conservation: the projectile returns to its launch height with the same kinetic energy. The velocity components at landing are the same magnitudes as at launch, but the vertical component is reversed.