Projectile Max Height Calculator
Enter a launch speed and angle to get the peak height of a projectile in metres — and see why the height climbs to its maximum when you fire straight up.
What is the maximum height of a projectile?
The peak of the trajectory
The projectile max height is how high a launched object rises before gravity pulls it back down — the very top of its arc. The projectile max height calculator turns two measurements, the initial velocity in metres per second and the launch angle in degrees, into the peak height in metres. It uses the classic projectile-motion result for flat ground with no air resistance: only the vertical part of the launch speed lifts the object, and the steeper you aim, the higher it goes. It is the number behind how high a kicked ball, a fired arrow, or a water jet will reach.
Enter a launch speed in metres per second and an angle between 0° and 90° to get the peak height in metres instantly.
The maximum height depends on the vertical component of the launch velocity, which is the speed multiplied by the sine of the angle. Squaring it and dividing by twice the gravitational acceleration gives the peak height.
h = (v² × sin²θ) / (2g)Here v is the launch speed, θ is the launch angle measured from the horizontal, and g is the standard gravitational acceleration, 9.80665 m/s². Because the angle enters through sin²θ, the height grows fastest as you tilt toward the vertical — sin 90° = 1, so a vertical launch puts every bit of speed into rising.
Suppose an object is launched at 20 m/s at an angle of 45°.
Find the vertical speed factor
sin 45° ≈ 0.7071, so sin²45° = 0.5 — half of the launch energy goes upward.
Square the velocity and combine
20² × 0.5 = 200 — the vertical term of the launch.
Divide by twice gravity
200 / (2 × 9.80665) = 200 / 19.6133 ≈ 10.197 m — the maximum height.
The peak height answers one question: how far above the launch point the object climbs before falling back. The key insight is that height is driven entirely by the vertical part of the velocity, so the angle matters enormously. A launch straight up (90°) gives the greatest possible height for a given speed, because sin²90° = 1 puts all the speed into rising — at 20 m/s that is 20.39 m, double the 45° result. As you flatten the angle, the height drops off with sin²θ: at 45° you are at half the maximum, and at 0° (a perfectly horizontal launch) the height is zero, since none of the speed points upward. This is why range and height pull in opposite directions — the 45° angle that maximises horizontal distance is well short of the height a steeper shot reaches.
The formula is exact for an idealised projectile, but a couple of practical points are worth keeping in mind.
No air resistance and a launch height of zero
This calculator assumes no air resistance and a launch from ground level, so the height is measured above the point of release. Real projectiles lose energy to drag and rise a little less than the formula predicts, and the effect grows with speed and surface area. Keep your units consistent — metres per second for the speed and degrees for the angle — and the peak height comes back in metres using standard gravity of 9.80665 m/s².