Projectile Motion Calculator
Work out the range, height and flight time of a projectile from its launch speed and angle.
The path of a thrown object
A projectile — a ball, a jet of water, anything launched and left to gravity — follows a curved path determined by its launch speed and angle. This works out how far it travels, how high it rises, and how long it stays in the air, the classic physics of thrown and launched objects.
Enter the launch speed and angle to see the range, height and time.
The forty-five-degree sweet spot
A neat result falls out of the physics: ignoring air resistance, a launch angle of forty-five degrees gives the maximum range for a given speed, because it balances how fast the object moves forward against how long it stays airborne. Steeper and it goes high but not far; shallower and it stays low. This is why throwing or hitting for distance instinctively uses a mid-height arc.
Questions & answers
What launch angle gives the greatest distance?
Forty-five degrees, ignoring air resistance — it balances forward speed against time in the air for maximum range.
Does it account for air resistance?
It uses the classic model without air resistance, exact for the ideal case and a good approximation for many everyday projectiles.
Is anything uploaded?
No. The calculation happens in your browser.