Resultant Velocity Calculator

Ever tried to walk across an escalator that’s moving? You’re walking in one direction, while the escalator pulls you in another. The combined effect is your resultant velocity. In physics, resultant velocity shows the final speed and direction when two or more velocities act on a body.

To make this simple, we’ve built a Resultant Velocity Calculator. It helps you solve tricky vector problems without endless math. You’ll see clear steps, quick results, and accurate angles in seconds.

What is Resultant Velocity in Physics?

Resultant velocity is the single velocity that results from adding two or more velocity vectors. Think of it as the “net effect” of all motions acting on an object.

If a boat moves north while a river flows east, the boat’s actual path is diagonal. That diagonal speed is the resultant velocity.

Resultant Velocity Formula

The formula depends on the method you use. Here are the most common ones:

1. From Components (x, y, z)

If you know the velocity parts in each direction:

Resultant velocity:

Vr = √(vx² + vy² + vz²)

Direction angle:

θ = tan⁻¹(vy / vx)

2. Two Vectors with Angle θ Between Them

If two velocities v1 and v2 act with an angle θ:

Vr = √(v1² + v2² + 2v1v2cosθ)

Direction:

θr = tan⁻¹( (v2 sinθ) / (v1 + v2 cosθ) )

3. Projectile Motion Case

When an object is launched with horizontal and vertical velocities:

Vr = √(vx² + vy²)

Here, vx is horizontal speed and vy is vertical speed at that instant.

How to Use the Resultant Velocity Calculator

Our tool is simple. Here’s how you can use it:

Step 1: Choose Input Method

Select whether you want to use components, magnitudes with angles, or two vectors with an angle.

Step 2: Enter Values

Type the known speeds and angles. The calculator accepts m/s, km/h, mph, ft/s, or knots.

Step 3: Hit Calculate

Press the calculate button. The tool shows the resultant velocity, its direction, and component values.

Step 4: Interpret the Result

You’ll see the magnitude of the final velocity and the angle of motion. This makes it easy to understand the object’s true path.

Example for Better Understanding

Let’s say a plane flies at 200 km/h east. A wind blows at 50 km/h north.

Convert to components:

vx = 200 km/h → 55.56 m/s

vy = 50 km/h → 13.89 m/s

Resultant velocity:

Vr = √(55.56² + 13.89²) ≈ 57.27 m/s

Direction:

θ = tan⁻¹(13.89 / 55.56) ≈ 14° north of east

So, the plane’s actual path is slightly tilted north while moving east.

How to Draw Resultant Velocity

1. Draw the first velocity vector in its direction.
2. Place the second vector tail at the head of the first (tip-to-tail method).
3. Draw a line from the start of the first vector to the end of the second. That line is the resultant velocity vector.

Final Verdict

The Resultant Velocity Calculator makes physics simple. You don’t need to struggle with long equations or trigonometry tables. Just enter values, and you’ll get clear results fast. Whether you’re a student, teacher, or just curious, this tool helps you master vector problems with ease.

FAQs

What is resultant velocity in physics?

It’s the net velocity when two or more velocities act on an object.

How to find resultant velocity of two vectors?

Use the law of cosines: Vr = √(v1² + v2² + 2v1v2cosθ).

Can I calculate resultant velocity with angle?

Yes, the calculator gives both the magnitude and the angle.

How do you calculate resultant change in velocity?

Subtract the initial velocity vector from the final velocity vector, then find the magnitude.

Is resultant velocity used in projectile motion?

Yes, it helps calculate the combined horizontal and vertical speeds of a projectile.