Time of Flight Calculator - Projectile Motion
Find how long a projectile stays in the air, split into the climb and the descent, or work out the flight time needed to hit a target distance.
⏱️ What is Time of Flight?
Time of flight is the total time a projectile spends in the air, from the instant it leaves the launcher to the instant it first touches the landing surface. Throw a ball, kick a football, fire a cannonball or jump off a ledge and the clock you would run with a stopwatch is the time of flight. In the ideal model, where only gravity acts, it depends on just three things: the vertical part of the launch velocity, the height of the launch point above the landing level, and the strength of gravity.
The key idea is that horizontal and vertical motion are independent. Sideways, nothing changes the speed, so the horizontal velocity stays constant for the whole flight. Vertically, gravity pulls with the constant acceleration g. The projectile rises until its vertical speed reaches zero at the apex, then falls back down. Because the stopwatch only cares about the vertical motion, a ball dropped from a balcony and a ball thrown horizontally from the same balcony land at the same moment, and so do two throws with different horizontal speeds but the same vertical speed.
This calculator is built for questions about time. Physics students use it to check homework on hang time, apex time and flight time from a cliff. Coaches use it to compare a high, lofted kick with a flat drive. Anyone with a stopwatch measurement can work backwards: on level ground, the time of flight gives the vertical launch speed as g t / 2. The first mode takes speed, angle and height and returns the time of flight, the time up, the time down, the range, the peak height and the impact speed. The second mode takes a target distance, an angle and a height, and returns the flight time together with the launch speed needed.
On level ground the flight is symmetric: the climb and the descent take equal times, and the projectile lands with the same speed it left with. From a raised launch point the descent is longer than the climb and the impact is faster. The chart in each mode shows how time of flight changes with launch angle. The upper limit is a vertical throw at 90 degrees, which stays up longest and goes nowhere sideways. All results assume no air resistance. For the full trajectory, see the projectile motion calculator, or use the horizontal projectile motion calculator for throws launched exactly sideways.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — A Thrown Baseball
v₀ = 30 m/s at 35° from a 1.8 m release height on Earth
Example 2 — Dropped Ball vs Ball Thrown Horizontally
A ball thrown at 15 m/s exactly horizontally (0°) from a 20 m balcony on Earth
Example 3 — A Long Jump
v₀ = 9 m/s at 20°, treated as level ground on Earth
Example 4 — A Launch from a 50 m Cliff
v₀ = 20 m/s at 30° from a cliff 50 m above the landing level on Earth
Example 5 — Flight Time to Land 60 m Away
Target 60 m at 40° from a 2 m release height on Earth
❓ Frequently Asked Questions
🔗 Related Calculators
What is the time of flight formula for a projectile?
On level ground, t = 2 v0 sin(theta) / g. When launched from a height h0 above the landing level, t = (v0 sin(theta) + sqrt((v0 sin(theta))^2 + 2 g h0)) / g. Here v0 is the launch speed, theta the launch angle above the horizontal and g the gravitational acceleration. Air resistance is ignored.
How do you calculate time of flight from speed and angle?
Multiply the launch speed by the sine of the angle to get the vertical speed, then divide twice that number by g for level ground. A 20 m/s launch at 30 degrees has a vertical speed of 10 m/s, so t = 2 x 10 / 9.80665 = 2.04 s. The calculator does this and handles launch heights too.
Does horizontal speed affect time of flight?
No. Horizontal and vertical motion are independent when air resistance is ignored. Time in the air depends only on the vertical launch speed, the launch height and g. A faster sideways throw lands farther away, but at exactly the same moment as a slower one.
How long does a ball dropped take compared with one thrown horizontally?
They take the same time. Both start with zero vertical speed and fall the same height, so t = sqrt(2 h / g). From 20 m on Earth that is 2.02 s whether the ball is dropped or thrown sideways at 15 m/s. The thrown ball just lands 30.29 m away.
What launch angle gives the longest time of flight?
90 degrees, a straight vertical throw. The vertical speed v0 sin(theta) is largest there, so the time of flight peaks at (v0 + sqrt(v0^2 + 2 g h0)) / g. The chart marks this limit. The tradeoff is that a vertical throw has no range at all.
How do you find time to the top of the trajectory?
The vertical speed falls to zero at the apex, so the time to the top is t = v0 sin(theta) / g. For a 30 m/s launch at 35 degrees that is 1.75 s. On level ground this is exactly half of the total time of flight.
Why is the climb shorter than the fall when launching from a height?
The projectile has to fall back through the launch height and then keep falling to the lower landing level. The climb still takes v0 sin(theta) / g, but the descent covers more distance. A 20 m/s, 30 degree launch from a 50 m cliff climbs for 1.02 s and falls for 3.35 s.
How do you find the flight time for a given horizontal range?
Once the launch speed is known, t = R / (v0 cos(theta)). When the speed is not known you can use t = sqrt(2 (h0 + R tan(theta)) / g), which follows from the launch speed that lands exactly at R. The Reach a range mode applies this and also reports the required speed.
How does gravity change the time of flight?
Time of flight is inversely proportional to g. With g = 1.62 m/s2 on the Moon, a level ground flight lasts 9.80665 / 1.62 = 6.05 times as long as on Earth. Mars, at 3.721 m/s2, gives about 2.64 times the Earth time. Pick a planet or enter a custom g.
Does mass change the time of flight?
Not in the ideal model. Gravity gives every mass the same acceleration, so a heavy and a light object launched alike stay up equally long. In real air, drag matters more for light, large objects, which shortens their time of flight.
Why does this calculator not accept 90 degrees in the range mode?
A vertical throw has zero horizontal velocity, so it can never land at a nonzero horizontal distance. The needed launch speed grows without limit as the angle nears 90 degrees. In the first mode, 90 degrees is allowed and gives the vertical-throw time of flight.