Horizontal Projectile Motion Calculator
Time of flight, range, impact speed and angle for a horizontal launch, or the launch speed from a measured landing distance.
🏀 What is Horizontal Projectile Motion?
Horizontal projectile motion describes an object that leaves an edge with a purely horizontal velocity and then moves under gravity alone. Nothing pushes it sideways after launch, so its horizontal speed stays constant. Nothing pushes it up either, so it starts with zero vertical speed and gains downward speed at the rate g, about 9.81 m/s every second on Earth. Put the two motions together and the object follows the upper half of a parabola from the launch point down to the ground. Because the vertical motion is exactly the same as a dropped object, a ball rolled off a table and a ball dropped from the table edge hit the floor at the same moment.
This situation appears everywhere. A marble rolls off a lab table, a diver runs off a cliff, a stone is thrown sideways from a bridge, water pours out of a horizontal pipe, and a package is released from a level-flying aircraft. In each case the questions are the same. How long is the object in the air, how far does it travel horizontally, and how fast and at what angle does it arrive? The same relationships run in reverse in the classic school experiment: measure how far a ball lands from the table edge, and you can work out how fast it left the edge.
This page is the special case of the general projectile motion calculator with a launch angle of exactly zero degrees, and a direct application of the kinematic equations with zero initial vertical velocity. Setting the angle to zero collapses the general quadratic for time of flight to the single clean result t = sqrt(2h / g). The mass of the object does not appear anywhere, and neither does the launch speed in the fall time.
The calculator has two modes. The first takes a launch speed and height and returns time of flight, range, impact speed and impact angle, plus the exact position and speed at any time you choose. The second takes a measured landing distance and height and returns the launch speed that produced it. Both assume no air resistance and a flat landing surface, and both can use Earth, Moon, Mars or Jupiter gravity or a custom value.
📐 Horizontal Projectile Motion Formulas
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Ball rolling off a table
A ball leaves a 1 m table at 2 m/s on Earth. Where is it after 0.3 s?
Example 2 — Cliff diver
A diver runs off a 20 m cliff at 3 m/s
Example 3 — Stone thrown off a bridge
A stone is thrown sideways at 5 m/s from a bridge 45 m above the water
Example 4 — Moon versus Earth
The same 10 m/s horizontal throw from 20 m, on the Moon (g = 1.62 m/s²)
Example 5 — Table-edge lab: solve the launch speed
A ball lands 0.60 m from the table edge after falling 0.90 m
Example 6 — Cliff edge: speed needed to land 30 m away
How fast must an object leave a 45 m cliff to land 30 m from its base?
❓ Frequently Asked Questions
🔗 Related Calculators
What is horizontal projectile motion?
It is the motion of an object launched with a purely horizontal velocity from some height, then moving under gravity alone. The horizontal velocity stays constant while the vertical velocity grows from zero at g times t, so the path is half of a parabola ending at the ground.
What is the time of flight formula for a horizontal launch?
t = sqrt(2h / g), where h is the launch height and g is gravitational acceleration. It does not depend on the launch speed. From 20 m on Earth with g = 9.80665 m/s2, t = sqrt(40 / 9.80665) = 2.02 s.
How do you find the horizontal range of a projectile launched horizontally?
Multiply the constant horizontal speed by the time of flight: x = v0 x sqrt(2h / g). A ball leaving a 1 m table at 2 m/s lands 2 x 0.4516 = 0.90 m from the table edge.
How do you find the impact velocity?
The horizontal component is still v0. The vertical component is vy = g t = sqrt(2 g h). The impact speed is sqrt(v0 squared + vy squared), and the angle below horizontal is atan(vy / v0).
How do you find the launch speed from the landing distance?
Divide the horizontal distance by the fall time: v0 = x / sqrt(2h / g). For a lab ball that lands 0.60 m from the table edge after falling 0.90 m, v0 = 0.60 / 0.4284 = 1.40 m/s.
Does the mass of the object matter?
No. In the absence of air resistance every mass falls with the same acceleration, so time of flight, range and impact angle are independent of mass. Mass only matters for quantities such as kinetic energy or momentum.
Do a dropped ball and a horizontally thrown ball land at the same time?
Yes, if they start from the same height. The vertical motion is identical because the horizontal velocity has no effect on the fall, so both reach the ground after sqrt(2h / g) seconds.
How does this differ from the general projectile motion calculator?
This page is the special case of a launch angle of exactly zero degrees, with no upward velocity component. That simplifies everything to t = sqrt(2h / g). Use the general projectile motion calculator when the launch angle is not zero.
How does gravity on the Moon change the result?
With g = 1.62 m/s2 instead of 9.80665 m/s2, the fall time from the same height is about 2.46 times longer, so the range at the same launch speed is about 2.46 times larger. The impact speed is smaller.
Why is the impact angle never exactly 90 degrees?
The angle is atan(vy / v0). It would reach 90 degrees only if v0 were zero (free fall) or the drop were infinitely tall. For any real horizontal speed the object lands at a slant.
How accurate is this calculator for real objects?
It assumes no air resistance and a flat landing surface at height zero. For a dense object at modest speed it is a good estimate. Drag shortens the real range and lowers the impact speed, with a larger effect for light, fast or large objects.