Projectile Motion Calculator

The Projectile Motion Calculator is provided in support of our Physics Tutorials on Dynamics which explore Motion, the meaning of force, types of forces including gravitational force and weight, resistive forces, terminal velocity, elastic force and tension, inertia and explain Newtons Laws of Motion in clear detail with practical working examples and formula. A list of the supporting Dynamics Physics Tutorials is available at the bottom of this page. This calculator will calculate:

  1. The resultant of all forces acting on an object
  2. The acceleration caused by these forces on the object
  1. The position (x, y) of a projectile at any instant t during its motion when the initial velocity v0 and the initial angle θ to the horizontal direction are given
  2. The components of the initial velocity (v0x, v0y) of a projectile when the magnitude of initial velocity |v0| and the initial angle θ to the horizontal direction are given
  3. The components of instantaneous velocity (vx, vy) of a projectile at any instant t during its motion when the magnitude of initial velocity |v0| and the initial angle θ to the horizontal direction are given
  4. The magnitude of the instantaneous velocity |v| at a given instant t
  5. The acute angle α formed by the projectile and the horizontal direction at any instant t during its motion when the initial velocity v0 and the initial angle θ to the horizontal direction are given
  6. The maximum height hmax the projectile can reach during its flight when the initial velocity v0 and the initial angle θ to the horizontal direction are given

Projectile Motion Calculator
Projectile Motion Calculator Results (detailed calculations and formula below)
Horizontal Component of the Initial Velocity (v0x) m/s
Vertical Component of the Initial Velocity (v0y) m/s
Horizontal Position of the Object at a Certain Instant (x(t)) m
Vertical Position of the Object at a Certain Instant (y(t)) m
Vertical Component of the Instantaneous Velocity at a Given Instant (vy) m/s
Magnitude of the Velocity at a Given Instant (|v|) m/s
Angle formed by the Instantaneous Velocity Vector and the Horizontal Direction (α) °
Maximum Height (hmax) m

Please note that the formula for each calculation along with detailed calculations is shown further below this page. As you enter the specific factors of each projectile motion calcualtion, the Projectile Motion Calculator will automatically calculate the results and update the formula elements with each element of the projectile motion calculation. You can then email or print this motion calculation as required for later use.

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Horizontal Component of the Initial Velocity Formula and Calculation

v0x = |v0| × cos θ
v0x = ×
v0x = m/s (metre per second)

Vertical Component of the Initial Velocity Formula and Calculation

v0y = |v0| × sin θ
v0y = ×
v0y = m/s (metre per second)

Horizontal Position of the Object at a Certain Instant Formula and Calculation

x(t) = x0 + |v0| × cos θ × t
x(t) = + × ×
x(t) = m (metre)

Vertical Position of the Object at a Certain Instant Formula and Calculation

y(t) = y0 + |v0| × sin θ × t + g × t2/2
y(t) = + × × + × 2/2
y(t) = m (metre)

Vertical Component of the Instantaneous Velocity at a Given Instant Formula and Calculation

vy(t) = |v0| × sin θ + g × t
vy(t) = × + ×
vy(t) = m/s (metre per second)

Magnitude of the Velocity at a Given Instant Formula and Calculation

|v| = √(|v0| × cos θ)2 + (|v0| × sin θ + g × t)2
|v| = √( × )2 + ( × + × )2
|v| = m/s (metre per second)

Angle formed by the Instantaneous Velocity Vector and the Horizontal Direction Formula and Calculation

α = tan-1|v0| × sin θ + g × t/|v0| × cos θ
α = tan-1 × + × / ×
α = ° (degree)

Maximum Height Formula and Calculation

hmax = - (|v0| × sin θ)2/2 × g
hmax = - ( × )2/2 ×
hmax = m (metre)

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