Calculate Ideal Throwing Range from Velocity
Calculator for the range, which a diagonally thrown, compact object can reach at maximum. Air resistance is neglected in this calculation. This noticeably reduces the achievable distance. At typical throwing speeds and with compact, heavy objects, air resistance reduces the actual throwing distance by approximately 10 to 20 percent.
The item is thrown with an angle of 45 degrees and lands on start height. The trajectory is an upside down parabola.
Enter one value at velocity and range, the other value will be calculated.
Example: a stone thrown with 60 km/h can fly up to 28 meters.
The formula is a=v²/g.
When the object is thrown from the hand and the throwing direction is towards a flat surface, the release point is higher than the landing point, and a slightly shallower angle will result in a longer throw. The best angle is usually between 40 and 44 degrees, which allows to throw about 1 to 3 meters further. This almost compensates for the reduced distance caused by air resistance.
The calculation of the throwing range with air resistance would be described by nonlinear differential equations that cannot be easily solved analytically.
The maximum range of a thrown object depends on its initial velocity, launch angle, and acceleration due to gravity, which is approximately 9.81 m/s² on Earth. The optimal launch angle for the greatest distance is 45 degrees, as the horizontal and vertical velocity components are equal at this angle, resulting in a symmetrical parabola. Theoretically, the range can be calculated precisely without considering air resistance. In practice, however, air resistance reduces the distance and deforms the trajectory, resulting in a shorter actual range. Furthermore, factors such as the shape of the object, the launch height, and environmental influences like wind also play a role. Incidentally, the acceleration due to gravity is not uniform. On the Moon, it is only about 1.62 m/s², which would result in a significantly greater range for the same launch velocity than on Earth, approximately six times greater.
Last updated on 01/16/2026. Author: Jürgen Kummer
German: g-Beschleunigung
Retrieved on 2026-09-17 from https://rechneronline.de/g-acceleration/range.php