# Projectile Motion Calculator (Range, Height, Time) Compute range, max height, flight time, and the full trajectory of a projectile given speed, angle, and optional initial height > Canonical page: https://elysiatools.com/en/tools/projectile-motion-calculator - **Category:** Math & Numbers - **Keywords:** projectile motion, trajectory, range, maximum height, flight time, launch angle, ballistics, kinematics, physics, mechanics, parabola ## Overview Projectile motion is motion under gravity alone (no air resistance, uniform gravity). Inputs: initial velocity v₀, launch angle θ, gravity g (default 9.80665), initial height h₀ (default 0). - Horizontal velocity: vx = v₀·cos(θ) (constant) - Vertical velocity: vy₀ = v₀·sin(θ) - Max height: H = h₀ + vy₀²/(2g) - Flight time: t = (vy₀ + √(vy₀² + 2g·h₀))/g - Range: R = vx · t When h₀ = 0, max range occurs at 45°. ## Inputs - **Initial Velocity (v₀, m/s)** (number): e.g. 20 - **Launch Angle (θ, °)** (number): 0–90, e.g. 45 - **Gravity (g, m/s²)** (number): 9.80665 (Earth). Moon ≈ 1.62, Mars ≈ 3.71 - **Initial Height (h₀, m)** (number): height of the launch point above the landing level (default 0) ## When to use - When solving physics and kinematics homework problems involving parabolic trajectories. - When modeling ballistics or sports science scenarios, such as calculating the flight path of an arrow or ball. - When designing game mechanics that require realistic projectile paths under custom gravity settings. ## How it works - Enter the initial velocity (v₀) in meters per second and the launch angle (θ) in degrees. - Optionally adjust the gravity constant (g) for different planetary bodies and set the initial launch height (h₀). - The calculator computes the horizontal and vertical velocity components to determine the flight time, maximum height, and total horizontal range. ## Use cases - Physics students verifying kinematics equations for parabolic motion. - Game developers tuning projectile trajectories for arrows, stones, or rockets. - Sports coaches analyzing the optimal launch angle and speed for throwing or kicking a ball. ## Frequently asked questions ### Does this calculator account for air resistance? No, it calculates ideal projectile motion under uniform gravity without air resistance. ### What launch angle yields the maximum range? When launching from ground level (initial height is zero), a 45-degree angle yields the maximum range. ### Can I calculate projectile motion on other planets? Yes, you can customize the gravity field, such as entering 1.62 m/s² for the Moon or 3.71 m/s² for Mars. ### How does initial height affect the flight time and range? A higher initial height increases both the flight time and the horizontal range because the projectile takes longer to fall to the ground. ### What units are used for the inputs and outputs? 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