Projectile Max Height Calculator
The maximum height of a projectile is the peak altitude it reaches before gravity pulls it back down. Using the kinematic equation H = v² sin²(θ) / (2g), you can determine this height from the initial speed and launch angle. The vertical component of velocity at the peak is exactly zero, making this a straightforward application of energy or kinematics principles. This calculator also shows the time to reach peak height. Enter the initial speed in m/s, the launch angle in degrees, and gravitational acceleration (9.81 m/s² at Earth's surface) to find the answers.
Projectile max height formula
H = v² × sin²(θ) / (2g)
Where v is the initial speed (m/s), θ is the launch angle in degrees, and g is gravitational acceleration. The time to reach peak height is t = v sin(θ) / g.
Understanding maximum projectile height
- At 90° (straight up), all of the initial kinetic energy converts to potential energy at the peak, giving the maximum possible height for a given speed.
- At 0° the height is zero: the object travels horizontally without rising.
- Doubling the initial speed quadruples the maximum height, because H is proportional to v².
- On the Moon (g = 1.62 m/s²) a projectile rises about six times higher than on Earth for the same launch conditions.
- The formula assumes launch and landing are at the same height. For elevated launches you would need to add the launch height.
Projectile max height: frequently asked questions
What is the maximum height of a projectile?
The maximum height is the highest point a projectile reaches during its flight. At this point the vertical component of velocity is zero. It depends on the vertical component of initial speed and gravitational acceleration.
Which angle gives maximum height?
A launch angle of 90 degrees (straight up) gives the maximum possible height for a given speed. At 45 degrees you get the maximum range, but the height is only half of what you would achieve by launching straight up.
How is the formula H = v² sin²(θ)/(2g) derived?
Using kinematics: the vertical velocity at the peak is zero. Starting from v_y = v sin(θ) and using v_y² = v_y0² - 2g H, setting v_y = 0 gives H = v_y0²/(2g) = v² sin²(θ)/(2g).
Does air resistance affect the maximum height?
Yes, in reality air drag reduces both height and range. This formula assumes a vacuum. For dense, slow-moving objects the difference is small; for light or high-speed projectiles, actual height will be noticeably less than the calculated value.
Can I use feet per second instead of meters per second?
Yes. Use g = 32.174 ft/s² and enter speed in ft/s; the result will be in feet. Ensure all inputs use the same unit system.
Official sources
- NIST Reference on Constants, Units, and Uncertainty: Standard acceleration of gravity.
- OpenStax University Physics Volume 1: Projectile Motion.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.