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Calculate the initial vertical velocity easily using our tool. Step-by-step physics formulas for projectiles, angles, and displacement included.
Do you want to calculate the vertical speed of a moving object? Our Initial Vertical Velocity Calculator helps you find it quickly. You don’t need to struggle with formulas. This tool works for physics students, hobbyists, and engineers. It gives step-by-step solutions and works with different input types.
The initial vertical velocity is the speed at which an object moves up or down when it starts. In simple words, it’s the first vertical push or fall speed of an object. For example, when you throw a ball at an angle, it goes up before coming down. The speed going up is the initial vertical velocity.
The general formula depends on what you know:
If you know speed and angle:
v₀y = v₀ × sin(θ)
Where v₀y is the vertical speed, v₀ is total speed, and θ is the angle.
If you know displacement and time:
v₀y = (y − y₀)/t + ½ g t
Where y − y₀ is vertical displacement, t is time, and g is gravity.
If you know final velocity and time:
v₀y = vy + g t
Where vy is final vertical speed.
If you know displacement and final velocity:
v₀y = √(vy² + 2 g (y − y₀))
These formulas work without air resistance.
Using our tool is easy. First, select your scenario: angle, final velocity, or displacement. Then, enter the values like speed, angle, time, or displacement. Choose the units. The calculator converts them to standard units automatically. Finally, click Calculate. You’ll get the initial vertical velocity instantly.
It also shows steps so you can learn the method. Each step explains the formula, conversion, substitution, and final result. For example, if you throw a ball at 20 meters per second at 30 degrees, the calculator finds the vertical speed as 10 m/s.
When you know the speed and angle:
v₀y = v₀ × sin(θ)
This formula splits the total speed into vertical and horizontal parts.
If you know final velocity and time:
v₀y = vy + g t
It helps find the initial push when you know where the object ended.
If you only know height and time:
v₀y = (y − y₀)/t + ½ g t
This formula comes from basic motion equations.
If you know where it ended and final speed:
v₀y = √(vy² + 2 g (y − y₀))
It calculates the starting speed using energy-like principles.
Imagine tossing a ball at 15 m/s at 45 degrees. The vertical component of speed is:
v₀y = 15 × sin(45°)
v₀y = 15 × 0.707
v₀y ≈ 10.61 m/s
That’s the speed at which the ball moves upward initially.
The Initial Vertical Velocity Calculator is a simple, fast, and accurate tool. It works for all scenarios. You don’t need a physics textbook. Enter your values, and get the speed along with step-by-step calculations. It also converts units like m/s, km/h, mph, or ft/s.
Use it for projectiles, free fall, sports science, or homework.
Yes, you can use displacement and time, or displacement and final velocity formulas.
No, it assumes motion near Earth without air drag.
Yes, you can choose meters, feet, km/h, mph, or m/s.
Horizontal velocity is motion along the ground. Vertical velocity is motion up or down.
Absolutely. It shows step-by-step solutions, so it’s perfect for learning.