Calculadora de Altura Máxima (Projétil)
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
h = v²·sin²θ/(2g)
About this calculator
This calculator determines the maximum height reached by a projectile when launched with an initial velocity and launch angle. The calculation uses the kinematic formula that considers initial velocity, launch angle, and gravitational acceleration. It is a useful tool for physics students, engineers, and enthusiasts wishing to analyze projectile motion in ideal situations without air resistance.
How it works: you enter the initial velocity (in m/s), launch angle (in degrees), and gravitational acceleration (default 9.81 m/s²). The calculator applies the formula h = v²·sin²θ/(2g) to obtain the maximum height. The sine of the angle is squared, multiplied by the velocity squared, and divided by twice the gravity. The result is given in meters, with configurable precision.
When to use? In physics problems involving oblique launch, such as calculating the highest point of a kicked ball, a fired projectile, or any object launched at an angle. It is also useful in ballistics, sports (e.g., height of a basketball shot), and simulations. Remember that the formula assumes no air resistance and constant gravity.
Cautions: the formula is valid only for launches in vacuum or with negligible air resistance. The angle must be between 0° and 90° (upward launch). For complementary angles (e.g., 30° and 60°), the maximum height is the same if the velocity is equal. Ensure units are consistent: velocity in m/s, angle in degrees, gravity in m/s². Do not use for horizontal launches (angle 0°) as the maximum height will be zero.
Frequently asked questions
What is the difference between maximum height and range?
Maximum height is the highest point the projectile reaches, while range is the horizontal distance traveled until it returns to the ground. They are calculated with different formulas.
Can I use this calculator for vertical launch (angle 90°)?
Yes, for 90° the formula simplifies to h = v²/(2g), which is the maximum height of a vertical upward launch.
What happens if I enter an angle greater than 90°?
Angles above 90° represent downward launch, and the maximum height will be zero or negative. The calculator may not work correctly; use only angles between 0° and 90°.
Does the calculator consider air resistance?
No, the formula ignores air resistance. For real situations with resistance, the result will be an approximation, usually overestimating the height.
Why is the maximum height the same for complementary angles (e.g., 30° and 60°)?
Because the sine of complementary angles is equal, and the formula depends on sin²θ. So for the same velocity, the maximum height is identical.