Horizontal Projectile Motion Calculator

Calculate trajectory, time of flight, and horizontal range

Solve horizontal projectile motion problems with unit switching and bidirectional calculation.

Last updated: December 23, 2025

CreatorFrank Zhao

Parameters

Velocity (v)

More info

m/s

Initial height (h₀)

More info

Time of flight (t)

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sec

Distance (x)

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1Time of Flight

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

2Horizontal Range

R = v_x \cdot t = v_x \sqrt{\frac{2h}{g}}

3Initial Height

h = \frac{gt^2}{2}

4Initial Velocity

v_x = \frac{R}{t}

tTime of Flight

hInitial Height

v_xHorizontal Velocity

RRange

What is a horizontal projectile motion calculator?

This horizontal projectile motion calculator solves a special (and very common) case of projectile motion: an object is launched straight sideways from a height. That means the initial vertical velocity is zero — and gravity takes over immediately.

The nice part: you only need two inputs. Enter any two of $v$ , $h_0$ , $t$ , or $x$ — and the rest updates instantly.

You’ll also see a trajectory plot under the results, which is great for intuition (and for checking whether your answers “look right”). If you’re curious about the general case with a launch angle, you may also like our Projectile Range Calculator.

Horizontal projectile motion equations

In a horizontal launch, the initial velocity points along the ground. So the horizontal and vertical components start as:

v_x = v

\quad

v_{y0} = 0

Distance (position)

x = v\,t

\quad

y = h_0 - \frac{1}{2} g t^2

Here $x$ is the horizontal distance, $y$ is the height above the ground, $h_0$ is the starting height, and $g$ is gravitational acceleration.

Velocity & acceleration

v_x = v

\quad

v_y = -g t

a_x = 0

\quad

a_y = -g

Trajectory (eliminate time)

y = h_0 - \frac{g\,x^2}{2v^2}

This is why the path is a parabola.

Time of flight

The object hits the ground when $y=0$ .

t = \sqrt{\frac{2h_0}{g}}

Range (horizontal distance)

Multiply the time by the horizontal speed.

x = v\,t = v\sqrt{\frac{2h_0}{g}}

If you want to compare “pure drop” motion (no horizontal speed), try our Free Fall Calculator.

How to use this calculator (quick start)

The calculator uses bidirectional solving: the last two fields you edit are treated as your “given” values. Everything else updates automatically.

Pick any two known values

For example: $v$ and $h_0$ .

Choose units that match your problem

Switch between meters/feet, seconds/minutes, and common speed units.

Read the results

The calculator returns $t$ (time of flight) and $x$ (horizontal distance), and the trajectory plot updates below.

Solve “in reverse” if you need to

For example, if you know a target distance $x$ and a height $h_0$ , enter those and the calculator can determine the required speed $v$ .

Example of horizontal projectile motion calculations

Let’s do a simple (but memorable) example: a ball is thrown horizontally from a tall platform. Suppose the horizontal speed is $v=7\ \text{m/s}$ and the starting height is $h_0=276\ \text{m}$ .

Step-by-step

Compute the time of flight

t = \sqrt{\frac{2h_0}{g}} = \sqrt{\frac{2\cdot 276}{9.80665}} \approx 7.50\ \text{s}

Compute the horizontal distance

x = v\,t = 7\cdot 7.50 \approx 52.5\ \text{m}

How to interpret this:

The time depends only on $h_0$ (free-fall), while the range scales with speed $v$ . If you double $v$ , you double $x$ — but $t$ stays the same.

Want to ask the reverse question (“what speed do I need to reach $x=100\ \text{m}$ from this height?”)? Enter $h_0$ and $x$ and let the calculator solve for $v$ .

Tips & best practices

Use consistent units (or let the calculator convert for you):

Switching between meters and feet is fine — just don’t mix “m” thinking with “ft” labels.

Common mistakes to avoid

•Entering a negative height $h_0$ (physically it usually means your reference level is different).
•Forgetting air resistance in real-world long ranges — the ideal model can overestimate distance.
•Using a very small height with very large speed and expecting a long flight time (time is set by $h_0$ , not $v$ ).

Quick sanity check: if you increase $h_0$ by a factor of 4, time increases by a factor of 2 because $t\propto\sqrt{h_0}$ .

If you’re also looking at energy changes (height → speed), our Potential Energy Calculator can be a helpful companion.

FAQs

How do I calculate horizontal distance in projectile motion?

First compute the flight time from height: $t = \sqrt{\frac{2h_0}{g}}$ Then multiply by horizontal speed: $x = v\,t$ . In one line, the range is $x = v\sqrt{\frac{2h_0}{g}}$ .

How do I calculate time of flight for a horizontal launch?

The time depends only on $h_0$ and $g$ : $t = \sqrt{\frac{2h_0}{g}}$ . Horizontal speed does not change the flight time in the ideal model.

Is there horizontal acceleration in projectile motion?

In the ideal case (no air resistance), no. That’s why $a_x = 0$ and the horizontal speed stays constant.

What is the vertical acceleration when projected horizontally?

It is the acceleration due to gravity, downward: $a_y = -g$ with $g \approx 9.8\ \text{m/s}^2$ near Earth.

Does mass affect the range in a horizontal launch?

Not in this simplified model. With no air resistance, objects fall at the same rate regardless of mass. Mass starts to matter in real life mainly through drag.

Limitations & disclaimers

This calculator uses an ideal model (no air resistance, no wind, flat ground).
Gravity is treated as constant: $g=9.80665\ \text{m/s}^2$ .
Results are for learning and estimation. For engineering or safety-critical work, verify with a more detailed model.

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