Time of Flight Calculator

Time of Flight Calculator gives the time a projectile stays in the air from its launch speed, angle and height, with the time to peak, the range and each step of the working shown.

What the Time of Flight Calculator Measures

Time of flight is how long a projectile stays in the air, from the moment of launch to the moment it lands. The Time of Flight Calculator finds it from the launch speed, the launch angle and the launch height. Air resistance is left out, so gravity is the only force on the projectile.

The Solve For menu also works backward. Enter a flight time you have measured, and the calculator returns the launch speed, the launch angle or the launch height that produces it. Every result shows the working line by line, so it serves as a time of flight calculator with steps for homework checks.

It runs in a phone or desktop browser, so there is no separate app to install. The Print Results button gives a page with the steps and both tables open, which can be saved as a PDF.

Time of Flight Formula for Projectile Motion

Only the vertical part of the motion decides the time. Split the launch speed v₀ at angle α into an upward part, v₀ sin α. On level ground, where the projectile lands at the height it left from, the time of flight formula is short.

$$t = \frac{2 v_0 \sin\alpha}{g}$$

This is the form given in OpenStax University Physics, which notes that the time rises in step with the vertical launch speed and falls as gravity gets stronger. Here t is in seconds, v₀ in m/s and g in m/s², with g set to 9.80665 m/s² for Earth.

The time of flight formula from height adds the drop h between the launch point and the landing point. The Time of Flight Calculator uses this form whenever the two heights differ.

$$t = \frac{v_0 \sin\alpha + \sqrt{(v_0 \sin\alpha)^2 + 2 g h}}{g}$$

For a horizontal projectile the angle is zero, so the upward speed is zero and the formula shrinks again. Launch speed drops out completely. A ball rolled off a table and a ball dropped from the same height land at the same moment.

$$t = \sqrt{\frac{2h}{g}}$$

The Horizontal Projectile Motion Calculator covers that level-launch case in more detail, and the Free Fall Calculator handles a plain drop. For any angle, enter 0 as the landing height and the launch height as h.

How to Derive Time of Flight

Start from the height of the projectile at time t. It begins at height h, rises with its upward launch speed and is pulled back by gravity. Setting that height to zero marks the landing.

$$0 = h + v_0 \sin\alpha \, t – \frac{1}{2} g t^2$$

This is a quadratic in t, and the quadratic formula gives two roots. One is negative and describes a moment before the launch, so it is discarded. The positive root is the from-height formula above. Setting h to zero turns it into the level-ground formula.

The same equation is one of the constant-acceleration set, with u = v₀ sin α and a = −g. The SUVAT Calculator solves it directly if you prefer to work with the vertical motion alone.

Worked Example With Steps

The Time of Flight Calculator opens with a launch at 30 m/s and 53° from a point 100 m above the landing level. The upward launch speed is 30 × sin 53° = 23.96 m/s. Putting that into the from-height formula gives (23.96 + √(574.04 + 1,961.33)) ÷ 9.80665 = 7.58 seconds.

The cards break that time down. The projectile climbs for 2.44 s, which is 32.24% of the flight, and peaks at 129.27 m. The fall from the peak takes the other 5.13 s. It lands 136.81 m away, moving at 53.49 m/s.

The note under the cards compares this with flat ground. The same launch would last 4.89 s if it landed at launch height, so the 100 m drop adds 2.69 s. From a raised launch the way down always takes longer than the way up.

A textbook check confirms the math. For the OpenStax fireworks shell, fired at 70 m/s and 75°, the calculator gives 6.89 s to the peak and a peak height of 233.1 m. The book prints 6.90 s and 233 m, using g = 9.80 m/s².

Maximum Flight Time and Launch Angle

For a fixed launch speed, the longest time in the air comes from throwing straight up, at 90°. The sine of the angle is then 1, its largest value. The angle table in the Time of Flight Calculator shows this for your own launch. These rows are for 30 m/s from 100 m.

Maximum time and maximum distance do not happen at the same angle. The longest flight here is at 90°, yet it goes nowhere sideways. Of the angles listed, 30° carries farthest from this height, at 163.62 m. The Projectile Range Calculator finds the best angle for distance.

To reach the peak height that goes with each flight time, use the Maximum Height Calculator. Both tools start from the same upward launch speed, so their time to peak always agrees.

Finding Speed, Angle or Height From a Time

A stopwatch is often easier to use than a speed gun. Time a throw, then let the Time of Flight Calculator work backward. The three other choices in the Solve For menu each take a flight time and two known values.

The height row is the classic cliff or well problem. A stone thrown level that lands after 2 seconds fell 19.61 m, whatever its speed. The calculator also explains inputs that cannot work, such as a flight time shorter than the climb to the peak.

Checkpoint Height, Raised Landings and Planets

The lower section holds three extra settings. Checkpoint Height reports how long the projectile stays above a chosen level, such as a wall, a net or a rim. In the opening example it is above 120 m for 2.75 s, from 1.07 s on the way up to 3.82 s on the way down.

Landing Height handles a target above or below the ground. OpenStax sets a problem with a tennis ball hit at 30 m/s and 45° and caught 10 m above the launch point. Enter 0 as the launch height and 10 m as the landing height, and the Time of Flight Calculator returns 3.79 s. It also notes that the ball first passes that height going up, at 0.54 s.

The gravity field carries presets for the Moon, Mars, Venus and Jupiter. The last card compares them without changing any setting. The 7.58 s flight on Earth would last 33.66 s on the Moon, 16.27 s on Mars and 4.16 s on Jupiter.

Time of Flight in Class 11 and Other Uses

What is the time of flight formula in Class 11 physics?

Class 11 projectile motion uses the level-ground form, T = 2 v₀ sin θ ÷ g, for a projectile that lands at the height it was thrown from. It is paired with the time to reach maximum height, v₀ sin θ ÷ g, which is exactly half of it. In the Time of Flight Calculator, set the launch and landing heights equal to get this case.

How do you calculate total flight time in physics?

Add the time going up to the time coming down. The climb lasts v₀ sin α ÷ g. The fall lasts √(2H ÷ g), where H is the drop from the peak to the landing point. In the worked example that is 2.44 s plus 5.13 s, which matches the 7.58 s from the single formula.

On level ground the two parts are equal, so the total is twice the time to peak. The Projectile Motion Calculator gives the flight time together with the range and the full path of the launch.

How do you calculate plane flight time or travel time?

That is a different meaning of flight time. For a trip, time equals distance divided by speed, so 2,000 km at 800 km/h takes 2.5 hours. For an aircraft the speed that counts is the speed over the ground, which wind changes. The Ground Speed Calculator works that out from airspeed and wind.