X and Y Velocity Calculator

Calculator

Input mode From speed and angle From x and y components

Initial speed

Launch angle (degrees)

Initial x velocity

Initial y velocity

Time

Gravity

Apply gravity to vertical motion

Calculate Reset

Example Data Table

Formula Used

Horizontal velocity: v_x = v × cos(θ)

Vertical velocity: v_y = v × sin(θ)

Resultant speed from components: v = √(v_x² + v_y²)

Launch angle from components: θ = atan2(v_y, v_x)

Horizontal displacement: x = v_x × t

Vertical velocity at time t: v_y(t) = v_y - g × t

Vertical displacement at time t: y = v_y × t - 0.5 × g × t²

These equations work well for projectile motion when air resistance is ignored.

How to Use This Calculator

1. Choose an input mode.
2. Enter either speed and angle, or the x and y components.
3. Enter time if you want displacement and later velocity values.
4. Enter gravity and enable it for projectile motion.
5. Press calculate to show the result block above the form.
6. Review the graph for horizontal and vertical velocity behavior.
7. Use the export buttons to save result data or example data.

FAQs

1. What are x and y velocity components?

X velocity is motion along the horizontal direction. Y velocity is motion along the vertical direction. Together, they describe the full velocity vector of an object moving at an angle.

2. How does the calculator find x and y velocity?

It uses trigonometry. The horizontal component equals speed multiplied by cosine of the angle. The vertical component equals speed multiplied by sine of the angle.

3. What angle reference should I use?

Use the launch angle measured from the positive horizontal axis. Positive angles point upward. Negative angles point downward.

4. Why does x velocity stay constant here?

This model ignores air resistance. Without horizontal force, horizontal velocity remains constant. Only vertical velocity changes when gravity is applied.

5. When does vertical velocity become zero?

During upward projectile motion, vertical velocity becomes zero at the highest point. The calculator also estimates that time when gravity is enabled.

6. Can I enter negative values?

Yes. Negative component values are allowed in component mode. A negative angle is also valid when using speed and angle mode.

7. Which units should I use?

Use any consistent unit system. For example, meters, seconds, and meters per second work well. Keep all inputs in matching units.

8. When should I disable gravity?

Disable gravity when you only want pure vector decomposition or constant vertical motion. Enable it for basic projectile motion analysis.