Maximum Height Calculator for Projectile Motion

Projectile motion describes an object moving under gravity after launch. In the standard ideal model, horizontal velocity remains constant while vertical velocity decreases steadily because of gravitational acceleration. Maximum height occurs at the instant the upward vertical velocity reaches zero. The calculator resolves the initial velocity into its vertical component and then applies a constant-acceleration equation to find the vertical rise above the launch point. The vertical component is initial speed multiplied by the sine of the launch angle. Squaring that component and dividing by twice the gravitational acceleration gives maximum height. The horizontal component does not directly affect peak height, although it determines how far the object travels while rising. The calculator also divides vertical launch speed by gravity to obtain time to peak. Both results assume that launch and measurement use the same inertial reference frame. Angle is measured upward from the horizontal. A zero-degree launch has no upward component and therefore no rise above its starting elevation in this model. A ninety-degree launch sends all initial speed vertically and produces the greatest height for a fixed speed. Intermediate angles divide velocity between horizontal and vertical motion. Because the sine term is squared, peak height changes nonlinearly with angle and grows with the square of initial speed. Earth's standard gravitational acceleration near sea level is approximately 9.81 m/s², which is supplied as the default. Gravity varies slightly with latitude and altitude, and other worlds have substantially different values. You can replace the default to model the Moon, Mars, or a laboratory approximation. Keep velocity in metres per second and gravity in metres per second squared to receive height in metres and time in seconds. Real trajectories may reach a different height because aerodynamic drag, wind, lift, spin, changing gravity, or propulsion violates the ideal assumptions. Drag generally lowers peak height and makes numerical simulation necessary. The formula also returns rise relative to the launch point, not elevation above ground or sea level. Add the initial elevation if an absolute peak elevation is needed. This maximum height calculator is useful for physics exercises, sports estimates, ballistics introductions, and checking trajectory calculations. It exposes both the equation and time result so the arithmetic can be audited. For safety-critical or high-speed applications, use a validated trajectory model that includes atmospheric and object-specific effects.