Time of Flight Calculator

Time of Flight Calculator: How Long Does a Projectile Stay Airborne?

The time of flight of a projectile — the duration from launch to landing — governs everything from the range of a thrown ball to the hang time of a long jumper. This Time of Flight Calculator computes total flight time, time to peak height, horizontal range, and maximum height from launch speed, angle, and launch height, updating in real time. A built-in angle comparison table shows how different launch angles affect flight duration at the same speed.

The Time of Flight Formula

On level ground, the vertical position is y(t) = vy × t - ½g × t², where vy = v × sin(θ). Setting y = 0 and solving: T = 2vy / g = 2v sin(θ) / g. When launched from height h above the landing level, the equation becomes h + vy × t - ½g × t² = 0, solved by the quadratic formula: T = (vy + sqrt(vy² + 2gh)) / g. For a 20 m/s launch at 45° from ground level: vy = 14.14 m/s, T = 2 × 14.14 / 9.81 = 2.88 s. These derivations follow directly from the vertical SUVAT equations, as documented in the HyperPhysics projectile motion reference.

Launch Angle and Flight Duration

All values for v = 20 m/s, g = 9.81 m/s², level ground.

The Role of Launch Height

Launching from an elevated position always increases time of flight for a given speed and angle, because the projectile must fall further before reaching the landing level. From a 10 m cliff at 45° and 20 m/s: vy = 14.14 m/s, using T = (14.14 + sqrt(14.14² + 2 × 9.81 × 10)) / 9.81 = (14.14 + sqrt(200 + 196.2)) / 9.81 = (14.14 + 19.90) / 9.81 = 3.47 s, compared to 2.88 s on level ground. The extra 0.59 s comes from the additional descent time from the 10 m height. The Khan Academy projectile motion review covers both flat and elevated cases with worked examples.

Time of Flight in Sports Science

Time of flight is a key performance metric in multiple sports. In athletics, a high jumper's hang time determines maximum crossbar clearance height — the athlete must be at peak height when crossing the bar, so the timing of the jump relative to the bar position matters as much as the total height reached. In cricket, a fast bowler's delivery flight time (typically 0.35–0.50 s for a 90 mph delivery over 22 yards) determines how long a batsman has to react. In American football, a punter optimises flight time to allow coverage teams to reach the landing zone — longer hang time is preferred over maximum range, which is why punts are kicked at steeper angles (55–65°) than the range-maximising 45°. The Sports Engineering Journal publishes detailed analyses of these optimisation problems.

Gravity's Effect on Time of Flight

Since time of flight scales as 1/g, reducing gravity dramatically extends flight time. On the Moon (g = 1.62 m/s², one-sixth of Earth), flight time is sqrt(9.81/1.62) = 2.46 times longer than on Earth for identical launch conditions. A 20 m/s kick at 45° on the Moon would produce T = 17.4 s and a range of 245 m. On Mars (g = 3.72 m/s²), the same kick gives T = 7.56 s and range = 107 m. This calculator makes it straightforward to explore these scenarios using the gravity input field.

Practical Applications: Targeting and Interception

Time of flight is central to any ballistic targeting problem. Artillery gunners use it to set fuze delay timings — a shell that bursts too early or too late misses its intended altitude. Air traffic controllers use flight time calculations to ensure separation between aircraft on approach. In robotics and drone delivery, time of flight of thrown objects determines the feasibility of catch-and-release manipulation. Knowing the flight time also tells you when to deploy a device: if a sensor package is dropped from a drone at 50 m height horizontally (angle = 0°, height = 50 m), T = sqrt(2 × 50 / 9.81) = 3.19 s — the exact time the receiving system must be ready to catch it.

Connecting to Other Kinematics Tools

Time of flight is one of four key outputs from full projectile analysis. Use the projectile motion calculator for a complete breakdown including impact speed and trajectory table. The projectile range calculator lets you solve for the launch speed or angle needed to achieve a specific range — the inverse of the range calculation done here. For the vertical component alone, the SUVAT calculator solves the same equations with explicit variable selection.

Time of Flight on Flat vs. Inclined Surfaces

All the examples above assume the landing surface is horizontal. On an inclined surface — a ski jump, a mountain slope, or a ramp — the effective range and impact point are different from the flat-ground calculation, but the time of flight formula is unchanged: it still depends only on the vertical launch velocity, launch height above the impact point's elevation, and gravity. The key adaptation is to calculate the elevation of the landing point on the slope as a function of horizontal distance, then find the intersection of the trajectory curve with that slope line. This calculator treats the landing level as flat at the height you specify. For slope problems, set the height to the elevation difference between launch and the expected impact zone on the slope, then verify the result by checking that the horizontal range matches the distance along the slope.

Metric and Imperial Notes

Launch speed can be entered in m/s, km/h, or mph. The calculator converts internally to m/s for all calculations. Time is always in seconds, heights and ranges always in metres. To convert range to feet, multiply by 3.281. To convert range to yards (useful for golf and American football), multiply by 1.094. For artillery problems, range in kilometres is the range in metres divided by 1,000. Note that the air resistance correction — not modelled here — typically reduces actual range by 10–40% depending on the projectile. The vacuum trajectory calculated here sets the theoretical upper limit; real-world range will be shorter. For a golf ball at 70 m/s and 15°, the vacuum range is 498 m while actual drive range is around 270–300 m, showing that aerodynamics halves the theoretical range for a relatively light, small ball at high speed. For a shot put (very dense, low surface area), the correction is much smaller — under 5%.