Projectile Motion Calculator
Calculate the range, max height and flight time of a projectile launched at any speed and angle, ignoring air resistance.
Range
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Maximum height —
Time of flight —
Idealized model: no air resistance, level launch and landing height, constant gravity g = 9.81 m/s².
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How it works
Range = v²sin(2θ)/g; max height = v²sin²(θ)/(2g); time = 2v·sin(θ)/gFrequently Asked Questions
How do I calculate the range of a projectile?
Range = v² × sin(2θ) ÷ g, where v is launch speed, θ is the launch angle, and g ≈ 9.81 m/s². A ball launched at 20 m/s at 45° travels about 40.8 m — and 45° gives the maximum range for a given speed.
What launch angle gives the maximum range?
45°, assuming launch and landing are at the same height — sin(2×45°) = sin(90°) = 1, the largest possible value, which is why 45° is the classic 'longest throw' angle in physics problems.
Does this account for air resistance?
No — this uses the standard idealized model (no air resistance), which is accurate for dense, compact objects over short distances but overestimates range for light or fast-spinning objects like a thrown ball in real conditions.