Horizontal Projectile Motion Calculator - Range, Time & Impact Speed

A horizontal projectile motion calculator is a classical-physics tool that takes the horizontal launch speed, the initial height above the landing surface, and the gravitational acceleration, then returns the time of flight, horizontal range, max height, impact vertical velocity, and impact speed for a projectile launched perfectly horizontally, so you can read off the standard no-air-resistance result without re-deriving the kinematics by hand.

• • Cliff, bridge, or platform drops: Estimate where a ball thrown from a 20 m cliff lands and how fast it moves on impact when launched at 15 m/s.
• • Package and payload air-drops: Predict the horizontal offset of a package released from a drone given the drop height and airspeed at release.
• • Sports and diving drills: Compare the landing distance for a cliff diver running off a 10 m platform at 3 m/s against a stationary drop.
• • Lunar and planetary comparisons: Re-run the same launch on the Moon (g = 1.62 m/s^2) or Mars (g = 3.71 m/s^2) by changing the gravity input.

Horizontal projectile motion is the special case of projectile motion where the launch angle is exactly zero degrees, so the initial velocity has no vertical component. Gravity still pulls the projectile straight down, which is why the same launch travels farther when the initial height is larger or the gravity is smaller.

This calculator covers only the horizontal-launch case. For launches with an upward or downward angle, see the general projectile motion or time-of-flight projectile motion calculators in the same Education and Academic category.

For launches that include an upward or downward angle rather than a pure horizontal launch, the Projectile Motion Calculator keeps the same inputs and adds a launch angle column.

The calculator solves the standard horizontal-launch kinematics in sequence. It computes the time of flight from the vertical fall equation, multiplies by the constant horizontal speed to get the range, then derives the impact vertical velocity and the magnitude of the impact velocity from the same time of flight.

• v₀ (initial horizontal velocity): Horizontal launch speed at the moment of release, in metres per second. Stays constant throughout the flight.
• h (initial height): Vertical distance from the launch point to the landing surface, in metres. Larger h means more time to fall.
• g (gravity): Gravitational acceleration in metres per second squared. Default 9.81 on Earth; use 1.62 for the Moon.
• t (time of flight): Time in seconds from release to impact, equal to sqrt(2h/g).
• R (horizontal range): Horizontal distance from launch to landing, equal to v₀ * t.
• Vy (impact vertical velocity): Downward vertical speed at impact, equal to g * t.
• |V| (impact speed): Magnitude of the total velocity at impact, equal to sqrt(v₀² + Vy²).

The time of flight depends only on the initial height and gravity, not on the horizontal launch speed. Two balls released from the same height hit the ground at the same instant, even if one lands many metres farther downrange.

According to OpenStax University Physics Volume 1 - 4.3 Projectile Motion, for a projectile launched horizontally from height h with horizontal speed v0, the time of flight is t = sqrt(2h/g), the horizontal range is R = v0 * t, and the impact vertical velocity is Vy = g * t downward.

When the same problem is phrased in SUVAT form with constant acceleration, the Kinematics Motion Calculator covers the matching linear kinematics with the same SI units.

Four ideas from kinematics that make the horizontal-launch formulas more than a list of equations.

The same horizontal-launch fall time t = sqrt(2h/g) shows up in cliff-diving safety, package-drop targeting, and the kinematics of a rolling object falling off a table.

When the flight time is the only output you need, the Time of Flight Projectile Motion Calculator returns the same t = sqrt(2h/g) value with a narrower input form.

Use the horizontal projectile motion calculator in five steps to find the time of flight, horizontal range, and impact speed for any horizontal launch.

1. 1 Enter the initial horizontal velocity v₀: Type the launch speed in metres per second at the moment of release, because horizontal speed does not change during the flight.
2. 2 Enter the initial height h: Type the vertical distance from the launch point to the landing surface, in metres.
3. 3 Enter the gravity g: Type the gravitational acceleration. Default is 9.81 m/s² on Earth; use 1.62 for the Moon, 3.71 for Mars, or 24.79 for Jupiter.
4. 4 Read the time of flight and range: The calculator returns time of flight in seconds and horizontal range in metres.
5. 5 Read the impact vertical velocity and impact speed: The calculator returns impact vertical velocity downward and impact speed as the vector magnitude.

For a ball thrown horizontally at 15 m/s from a 20 m cliff on Earth, enter v₀ = 15 m/s, h = 20 m, and g = 9.81 m/s². The calculator returns t = 2.019 s, R = 30.29 m, impact vertical velocity 19.81 m/s, and impact speed 24.85 m/s.

If you also want to size the launch thrust or landing impact force, the Forces and Newton's Laws Calculator applies F = m * a to the same horizontal-launch scenario.

Practical reasons to use this horizontal projectile motion calculator instead of working through the kinematics by hand.

• • All five horizontal-launch outputs from one input set: Enter launch speed, height, and gravity once and get time of flight, horizontal range, max height, impact vertical velocity, and impact speed in one view.
• • No manual derivation of fall time: The calculator handles the t = sqrt(2h/g) root and the subsequent range and velocity formulas for you.
• • Adjustable gravity for non-Earth scenarios: Change the gravity input to compare the same launch on Earth, the Moon, Mars, or Jupiter without rebuilding the kinematics.
• • Useful for both classroom and field use: The same formulas cover a tabletop ball rolling off a table and a drone package drop from 50 m.
• • Clear validation for impossible inputs: Zero or negative gravity returns zero outputs and an error, so you do not silently divide by zero.
• • Pairs with the general projectile calculator: Use this calculator for horizontal launches and switch to the general projectile motion calculator when the launch angle is non-zero.

The calculator is intentionally narrow: it solves the standard horizontal-launch kinematics with constant gravity and no air resistance.

What changes the time of flight, horizontal range, and impact speed this calculator returns, and what it cannot capture.

• • The calculator assumes no air resistance and a flat landing surface, so it does not capture draggy objects where drag dominates gravity.
• • The gravity input is treated as constant, which is a good approximation for short flights near Earth's surface but breaks down for long horizontal launches where Earth's curvature or the Coriolis effect matters.
• • The max height output equals the initial height because the launch is horizontal with no upward initial velocity.

According to HyperPhysics, the horizontal range for a projectile launched from height h with horizontal speed v₀ is R = v₀ * sqrt(2h/g) and the impact speed is |V| = sqrt(v₀² + 2gh), which the calculator evaluates directly from the same three inputs.

According to HyperPhysics - Projectile Motion (Horizontal Launch), for a projectile launched horizontally with speed v0 from height h, the horizontal range is R = v0 * sqrt(2h/g) and the impact speed is |V| = sqrt(v0^2 + 2gh).

According to Wikipedia - Projectile motion, in the idealised model of projectile motion, horizontal and vertical motions are independent, so a horizontally launched projectile keeps its horizontal speed constant while gravity accelerates it downward at g m/s^2.

To compare the launch kinetic energy against the impact kinetic energy and account for gravity as you fall, the Work-Energy-Power Calculator uses the same v₀ and impact speed in its energy equations.