Projectile Motion Calculator – Range, Height & Time of Flight

Overview

Projectile motion treats horizontal and vertical movement when the only acceleration is gravity. This calculator translates a launch speed, angle, starting height, and gravity value into actionable metrics: range, peak height, and total flight time. It is ideal for students, simulation writers, or hobbyists who want to see how altering one parameter reshapes the ballistic path without rewriting equations.

Inputs & Usage

Enter the initial speed in meters per second (m/s) to reflect how fast the object leaves the launcher.
Provide the launch angle in degrees, where 0° is horizontal and 90° points straight up.
Supply the initial height to simulate throws from ramps, towers, or trenches.
Choose a gravity profile—Earth, Moon, or Custom—and, if custom, type the acceleration in meters per second squared.
The calculator updates instantly, so you can experiment with different combinations and watch the results panel change in real time.

How it Works

Vertical analysis uses the formula $h (t) = h_{0} + v_{y 0} t - \frac{1}{2} g t^{2}$ , while horizontal distance is $x (t) = v_{x 0} t$ , with $v_{x 0}$ and $v_{y 0}$ derived from the launch speed and angle via cosine and sine. The flight time solves the quadratic equation for when height returns to zero. Peak height occurs at the moment the vertical velocity reaches zero, and the horizontal range is the product of horizontal velocity and total flight time. The calculator runs these deterministic steps in TypeScript and exposes the most meaningful outputs.

Interpretation

The right-side panel highlights the computed values alongside units, helping you check whether the projectile lands far enough or stays aloft long enough for your scenario. The summary sentence restates the range and time, while the inputs section reminds you which parameters were used. Use the error message if something like gravity was misconfigured, or the quadratic discriminant turned negative.

Example

Throw a projectile at 25 m/s with a 45° angle from ground level (0 m) under Earth gravity. The calculator reports about a 64 m horizontal range, a peak height near 11.9 m, and a flight time slightly above 3.6 s. That lets you confirm that your approximations match the analytic solution before building a physical prototype.

Limitations

Air resistance is ignored, so the tool behaves like a vacuum solver. The object is treated as a point mass, and the path stays in a single vertical plane. Spiraling, rotating projectiles, or effects from wind are outside this model, although you can simulate more complex forces by switching to a custom gravity value that mimics an upward or sideways pull.