Projectile Range Calculator
This Projectile Range Calculator works out how far a projectile travels across level ground, along with its maximum height and total time in the air, from the launch speed, launch angle and gravity. You enter the initial speed in metres per second, the launch angle in degrees measured from the horizontal, and the acceleration due to gravity, which is about 9.81 metres per second squared at the Earth's surface. The tool then applies the standard projectile motion equations, assuming launch and landing at the same height and ignoring air resistance. Range is largest at a 45 degree launch angle for a given speed, while a steeper angle gives more height and a longer flight time but less horizontal distance, and a shallower angle does the opposite. Physics students, teachers, sports coaches and anyone curious about throwing, kicking or launching objects use this to predict and compare trajectories quickly. A few tips improve your results. First, measure the angle from the horizontal ground, not from the vertical, since the formulae assume the horizontal reference. Second, remember the model ignores drag, so real ranges for light or fast objects fall short of the ideal value, especially at high speeds. Third, use the local value of gravity if you need precision, as it varies slightly with latitude and altitude, though 9.81 is fine for most work. Fourth, keep your speed in metres per second, converting from kilometres per hour by dividing by 3.6 first. Used this way the calculator gives a clear, dependable picture of an ideal trajectory for study and comparison.
Range = v squared times sin(2 theta) / g. Max height = v squared times sin squared(theta) / (2 g). Flight time = 2 v sin(theta) / g.
How it works
The calculator converts the angle to radians, then finds range as speed squared times the sine of twice the angle divided by gravity. Maximum height uses speed squared times the square of the sine of the angle, divided by twice gravity. Time of flight is twice the speed times the sine of the angle, divided by gravity.
Worked example
With a speed of 20 m/s, an angle of 45 degrees and gravity of 9.81, range is 400 times sin(90) over 9.81, which is 40.77 m. Maximum height is 10.19 m and the time of flight is 2.88 s.
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