Projectile Motion Calculator — Range, Time of Flight & Maximum HeightR = v₀²sin(2θ)/g · H = v₀²sin²(θ)/2g · T = 2v₀sin(θ)/g
Use this free Projectile Motion Calculator to instantly compute all key projectile motion parameters for any object launched at an angle under constant gravitational acceleration (g = 9.81 m/s²) — using the standard projectile motion equations of classical kinematics: Horizontal Range (R) = v₀² × sin(2θ) / g · Maximum Height (H) = v₀² × sin²(θ) / 2g · Time of Flight (T) = 2v₀ × sin(θ) / g · Horizontal Velocity (vₓ) = v₀ × cos(θ) · Vertical Velocity (vᵧ) = v₀ × sin(θ) — where v₀ is the initial launch velocity (m/s) and θ is the launch angle in degrees.
This online projectile motion solver is trusted across a wide range of physics and engineering applications: A-Level, AP Physics, IB Physics, and JEE/NEET exam preparation, university kinematics and mechanics coursework, ballistics and trajectory analysis, sports science — ball launch angle optimization, aerospace and rocket trajectory simulation, and real-world motion analysis. Enter your initial velocity, launch angle, and optional initial height to instantly calculate maximum range, peak height, total flight time, and the complete trajectory path of the projectile — with results in both metric (m, m/s) and imperial (ft, ft/s) units. No air resistance is assumed, consistent with standard Newtonian mechanics and classical physics models.
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Projectile Motion Calculator — Range, Height, and Time of Flight From Launch Conditions
Projectile motion decomposes into two independent components: horizontal motion at constant velocity and vertical motion under constant gravitational acceleration. A ball launched at 20 m/s at 45° travels 40.8 m horizontally and reaches a maximum height of 10.2 m before returning to the same elevation in 2.89 seconds — and all three outcomes are determined entirely by the initial speed and angle. The projectile motion calculator computes all trajectory parameters from any two known inputs, covering sports physics, ballistics, and engineering launch problems.
The 45° launch angle maximizes range only when the launch and landing heights are equal and air resistance is neglected. In real applications both assumptions often fail. Javelin throwers aim at roughly 30-35° because the javelin is launched above head height; artillery shells are fired at angles varying with target distance; water from a garden hose optimizes differently depending on whether you are watering nearby or distant plants. The calculator handles launches from elevated positions and targets at different heights, producing realistic trajectory solutions.
Air resistance transforms projectile motion from a clean parabola into a complex drag-dependent curve that cannot be solved analytically. At low speeds (below ~10 m/s), neglecting air resistance produces acceptable engineering estimates. At high speeds — a golf ball at 70 m/s, a bullet at 900 m/s — drag forces are comparable to or exceed gravity, and the simple calculator significantly overpredicts range. The calculator provides the idealized solution and flags the speed regime where drag corrections become non-negligible.