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)

More info

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.

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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.

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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}

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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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