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PROJECTILE MOTION (HORIZONTAL TRAJECTORY) CALCULATOR

Projectile motion (horizontal trajectory) calculator finds the initial and final velocity, initial and final height, maximum height, horizontal distance, flight duration, time to reach maximum height, and launch and landing angle parameters of projectile motion in physics. Moreover, following plots are drawn for the projectile motion.

  - Height (or Vertical Position) vs. Time

  - Vertical Velocity vs. Time

  - Horizontal Position vs. Height (or Vertical Position)

  - Horizontal Velocity vs. Time

  - Horizontal Position vs. Angle

The effect of air resistance is ignored in calculations. Projectile motion formulas used for calculations are given in the "List of Equations" section.

Projectile Motion Calculator

Projectile Motion Calculator:

 KNOWN PARAMETERS
UNIT SYSTEM SELECTION

(m, m/s, m/s2 )
(ft, ft/s, ft/s2 )
 INPUT PARAMETERS
Parameter Value Unit
Initial Velocity (V0) m/s
Launch Angle (α) deg
Initial Height (y0) m
Final Height (yf) m
Gravity* m/s^2

Note: Use dot "." as decimal separator.

Note*: Gravity vector is negative in downward direction.

 



RESULTS
Parameter 1st Solution 2nd Solution
(If exists)		 Unit
Initial Velocity (V0) [m/s]
Initial Horizontal Velocity (V0x)
Initial Vertical Velocity (V0y)
Final Velocity (Vf)
Final Horizontal Velocity (Vfx)
Final Vertical Velocity (Vfy)
Initial Height (y0) [m]
Final Height (yf)
Maximum Height (h)
Horizontal Distance (l)
Flight Duration (t) [s]
Time to Reach Max. Height (th)
Launch Angle (α0) [deg]
Landing Angle (αf)

 

Note: Default rounding is 5 decimal places.

Definitions:

Projectile Motion: Projectile motion is a form of motion which takes place in two dimensions. The shape of the motion is a parabola.


Inputs explained

  • V0: initial speed at launch.
  • α0: launch angle (degrees) measured from the horizontal.
  • y0: initial height at launch.
  • yf: final height (landing height). If yf = y0, the flight time often has a simpler form.
  • g: gravitational acceleration (use a negative value if upward is positive y, e.g. -9.80665 m/s²).

Worked example

Example: V0 = 20 m/s, α0 = 45°, y0 = 0 m, yf = 0 m, g = -9.81 m/s². Then V0x = V0·cosα0 ≈ 14.14 m/s and V0y = V0·sinα0 ≈ 14.14 m/s.

  • Time of flight (same launch/landing height): t ≈ 2·V0y/|g| ≈ 2.88 s
  • Range: l ≈ V0x·t ≈ 40.7 m
  • Maximum height: hmax ≈ V0y²/(2|g|) ≈ 10.2 m

Tip: If your calculator outputs differ, check the sign of gravity and the angle unit.

Common mistakes

  • Wrong gravity sign: this page expects gravity negative downward (e.g. -9.81 m/s²).
  • Degrees vs radians: the angle input is in degrees unless you switch units.
  • Mixed units: keep units consistent (m/s with m and m/s², or ft/s with ft and ft/s²).
  • Landing height: yf must match your real target height (ground is not always 0).

List of Projectile Motion Equations

Position formula
(in x-direction)		 xt=x0+v0xt
Position formula
(in y-direction)		 yt=y0+V0yt+1/2gt2
Velocity formula
(in x-direction)		 Vx = V0x
Velocity formula
(in y-direction)		 Vyt = V0y+gt

FAQ

Does this calculator include air resistance?

No. It assumes ideal projectile motion with constant gravity and no drag.

Why is gravity negative in the input?

This page uses a sign convention where upward is positive y. Therefore gravity is negative downward (for SI units, enter -9.80665 m/s²).

Need a simpler range-only tool?

For a quick calculation of range, maximum height and flight time, use the Trajectory Calculator.

Supplements:

Reference: