Projectile Motion Calculator

Projectile Motion Calculator

Initial Velocity (u)

m/s

Angle of Projection (θ)

°

Acceleration due to Gravity (g)

m/s²

What is Projectile Motion?

Projectile motion is a type of motion in which an object is thrown into the air and moves under the influence of gravity alone. Common real-life examples include a football kick, a stone thrown at an angle, a javelin throw, or a cannonball fired from a cannon. In projectile motion, the object follows a curved path called a parabolic trajectory.

The motion of a projectile can be divided into two independent components: horizontal motion (constant velocity) and vertical motion (uniformly accelerated motion due to gravity). These two motions occur simultaneously but do not affect each other.

Key Formulas Used

Time of Flight (T):
T = (2u sinθ) / g

Maximum Height (H):
H = (u² sin²θ) / (2g)

Horizontal Range (R):
R = (u² sin2θ) / g

Where:
u = initial velocity (m/s)
θ = angle of projection (degrees)
g = acceleration due to gravity (≈ 9.81 m/s²)

How to Use This Calculator

1. Enter the initial velocity of the projectile in meters per second (m/s).
2. Enter the angle of projection in degrees.
3. Keep gravity as 9.81 m/s² (default) or modify if required.
4. Click Calculate to instantly get time of flight, maximum height, and horizontal range.

Worked Example

Suppose a ball is thrown with an initial velocity of 20 m/s at an angle of 45°.

Using the formulas:
Time of flight ≈ 2.88 s
Maximum height ≈ 10.2 m
Horizontal range ≈ 40.8 m

This calculator is extremely useful for physics students, engineering students, competitive exam aspirants, and anyone studying motion in mechanics. It eliminates manual calculations and reduces mistakes, helping you understand projectile behavior quickly and accurately.