Projectile Motion Calculator
Calculate the range, max height and time of flight of a launched projectile.
Assumptions used in this calculation
- No air resistance, level ground: Assumes no air resistance and that launch and landing heights are equal (level ground).
About this calculator
Predicting where a launched object will land, a thrown ball, a fired projectile, water from a hose, means tracking two independent motions at once: constant horizontal velocity and gravity-driven vertical acceleration, then combining them algebraically, a step that trips up most people doing it by hand. This calculator takes an initial launch velocity and angle and decomposes them into horizontal and vertical velocity components, then applies the standard kinematic equations to compute horizontal range (v²sin(2θ)/g), maximum height (v²sin²(θ)/2g), and total time of flight (2v·sin(θ)/g) in one pass. Because these three outputs share the same underlying trigonometric decomposition, solving for all of them by hand means correctly applying sine and cosine to the same angle three separate times without a slip. The model assumes idealized projectile motion under gravity alone, with no air resistance, so it's most accurate for dense, compact objects over moderate ranges, real-world drag will reduce actual range below the calculated value.
Worked example
20 m/s at 45°
Result: 40.8 m range, 10.2 m max height, 2.88s flight
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