THE NUMORIX GUIDE
How to use the Projectile Motion Calculator
Last reviewed September 14, 2026
What this calculator does
The engine resolves launch speed into v0x = v0*cos(theta) and v0y = v0*sin(theta), with theta converted from degrees to radians.
Formula and method
The engine resolves launch speed into v0x = v0*cos(theta) and v0y = v0*sin(theta), with theta converted from degrees to radians. For launch height h it solves t = (v0y + sqrt(v0y^2 + 2*g*h))/g, then calculates range = v0x*t, maximum height = h + v0y^2/(2*g), and impact speed from the horizontal and final vertical components.
Variables and inputs
The UI accepts launch speed in m/s, launch angle in degrees, launch height in meters, and gravity in m/s^2. Speed, angle, and height must be nonnegative with angle at most 90 degrees; gravity must be positive. The page displays range, flight time, maximum height, and impact speed to three decimals.
Worked example
With v0 = 20 m/s, theta = 45 degrees, h = 0 m, and g = 9.80665 m/s^2, v0x and v0y are each about 14.1421 m/s. Flight time is 2.884 s, range is 40.789 m, maximum height is 10.197 m, and impact speed returns to 20.000 m/s.
How to interpret the result
The result is the ideal two-dimensional trajectory of an object launched from the entered height and landing at ground level. With no drag, a level launch and landing preserve impact speed, while the angle and height determine how long the horizontal component acts.
Common mistakes to avoid
Enter the launch angle in degrees, not radians, and use gravitational acceleration rather than a velocity in the gravity field. Do not interpret range as a safe travel distance when wind, obstacles, terrain, or air resistance matter.
Assumptions and limitations
The engine assumes constant gravity, a point object, a flat landing level at y = 0, and no air resistance, wind, spin, lift, or rolling after impact. It accepts a nonzero launch height, but it does not model a different landing height or uncertainty in the measured inputs.