Projectile Time of Flight Calculator
From a launch speed, an angle, and gravity, get the time of flight, the horizontal range, and the maximum height — the three numbers that describe any ground-launched throw.
Three inputs, three answers
Enter the launch speed, the angle, and gravity and the calculator returns the time of flight (2v·sinθ/g), the horizontal range (v²·sin2θ/g), and the maximum height (v²·sin²θ/2g) at once.
Ground level, no drag
The formulas assume the projectile launches and lands at the same height and that air resistance is ignored — ideal for textbook problems, an approximation for the real world.
What is a projectile time of flight calculator?
Speed, angle, and gravity in, full trajectory out
A projectile time of flight calculator turns three measurements — the launch speed, the launch angle, and the strength of gravity — into the numbers that describe a ground-launched throw: how long it stays in the air (time of flight), how far it travels horizontally (range), and how high it climbs (maximum height). Gravity is the only force acting after launch, so once you know the initial velocity and the angle, the whole arc is fixed. That makes those inputs all you need for a thrown ball, a fired arrow, a fountain jet, a long jump, or any physics homework involving a launch from level ground.
Enter the speed, angle, and gravity to get the time of flight, range, and maximum height instantly.
Three short formulas, all built from the launch speed v, the angle θ, and gravity g. The angle is first converted from degrees to radians (θ = angle × π / 180).
time = 2 × v × sin θ / gThe time of flight comes from the vertical motion: gravity decelerates the upward speed v·sinθ, brings it to rest at the top, then accelerates it back down, so the total airtime is 2v·sinθ/g. The horizontal range is v²·sin(2θ)/g, which is largest at 45°. The maximum height, v²·sin²θ/(2g), is how high the projectile climbs before falling back.
Suppose you launch a projectile at 20 m/s and an angle of 45° on Earth (g = 9.81 m/s²).
Time of flight
2 × 20 × sin 45° / 9.81 = 2 × 20 × 0.7071 / 9.81 = 2.883208 s — the airtime.
Horizontal range
20² × sin 90° / 9.81 = 400 × 1 / 9.81 = 40.774720 m — how far it lands.
Maximum height
20² × sin²45° / (2 × 9.81) = 400 × 0.5 / 19.62 = 10.193680 m — the peak.
The three outputs answer three different questions about the same arc. The time of flight (about 2.88 s for 20 m/s at 45°) is how long the projectile spends in the air — useful for hang time, for timing a catch, or for working out when a jet of water lands. The single most useful insight is that the range is largest at exactly 45°: any steeper and the throw climbs high but lands short; any flatter and it travels fast but low. Two complementary angles — say 30° and 60° — give the same range, one with more height and airtime, the other flatter and quicker. The maximum height (about 10.19 m here) is the peak of the arc, reached at the halfway point of the flight, and it grows with the square of the vertical speed component v·sinθ. Gravity ties it all together: the same g links speed and angle to time, range, and height, which is why the same throw covers far more ground on the Moon (g ≈ 1.62) than on Earth.
The formulas are exact for an idealised projectile, but a couple of practical points are worth keeping in mind.
No air resistance, level launch and landing
These formulas describe an ideal projectile fired from ground level that lands at the same height, with gravity as the only force — air resistance, wind, lift, and spin are all ignored. Real throws fall short of the no-drag range, especially at high speeds, and launching from a cliff or hitting a raised target changes the time of flight. The inputs are also in SI units (m/s, degrees, m/s²), so the time comes back in seconds and the range and height in metres — keep speed in metres per second to get a meaningful answer.