Maximum Height Calculator – Projectile Motion
The maximum height calculator is a tool for finding the maximum vertical position of a launched object in projectile motion. Whether you need the max height formula for an object starting directly off the ground or from some initial elevation – we've got you covered. If you're still wondering how to find the maximum height of a projectile, read the two short paragraphs below, and everything should become clear.
How to find the maximum height of a projectile?
The maximum height of the object is the highest vertical position along its trajectory. The object is flying upwards before reaching the highest point – and it's falling after that point. It means that at the highest point of projectile motion, the vertical velocity is equal to $0$ ($v_y = 0$).
From that equation we can find the time $t_{\mathrm{h}}$ needed to reach the maximum height $h_{\mathrm{max}}$:
The formula describing vertical distance is:
So, given $y = h_{\mathrm{max}}$ and $t = t_{\mathrm{h}}$, we can join those two equations together:
And what if we launch a projectile from some initial height $h$? No worries! Apparently, the calculations are a piece of cake – all you need to do is add this initial elevation!
Let's discuss some special cases with changing angle of launch:
 If $\alpha = 90\degree$, then the formula simplifies to:
And the time of flight is the longest.
If, additionally, $v_y = 0$, then it's the case of free fall, which we detailed at the free fall calculator. Also, you may want to have a look at our even more accurate equivalent – the free fall with air resistance calculator.
 If $\alpha = 45\degree$, then the equation may be written as:
And in that case, the range is maximal if launching from the ground ($h = 0$).
 If $\alpha = 0\degree$, then vertical velocity is equal to $0$ ($v_y = 0$). In this case, we can calculate the horizontal projectile motion. As the sine of $0\degree$ is $0$, then the second part of the equation disappears, and we obtain:
The initial height from which we're launching the object is the maximum height in projectile motion.
Other tools related to projectiles' motion
The motion of a projectile is a classic problem in physics, and it has been analyzed in every possible aspect. The fact that we can easily reproduce it and observe it was a contributing factor. We decided to create a suit of tools related to the motion of a projectile:

The projectile motion calculator for a comprehensive analysis of the problem;

The trajectory calculator to analyze the problem as a geometric function; and

A set of specific tools:
 The projectile range calculator;
 The time of flight calculator; and
 The horizontal projectile motion calculator (for $\alpha=0$).
Maximum height calculator helps you find the answer
Just relax and look how easytouse this maximum height calculator is:

Choose the velocity of the projectile. Let's type $30\ \mathrm{ft/s}$.

Enter the angle. Assume we're kicking a ball ⚽ at an angle of $70\degree$.

Optionally, type the initial height. In our case, our starting position is the ground, so type in $0$. Can the ball fly over a $13\ \mathrm{ft}$ fence?

Here it is – maximum height calculator displayed the answer! It's $12.35\ \mathrm{ft}$. So it will not fly over the mentioned barrier – throw it harder or increase the angle to reach your goal.
Just remember that we don't take air resistance into account!