Resultant Velocity Calculator

Calculate the resultant of multiple velocity vectors

Add up to 5 velocities together to find the resultant magnitude and direction

Last updated: December 20, 2025

CreatorFrank Zhao

Velocity 1

More info

m/s

Angle 1

More info

deg

Velocity 2

More info

m/s

Angle 2

More info

deg

Do you want to add up to 5 velocities together?

Resultant velocity

Enjoy the absolute value of the resultant velocity, its direction, and the x and y components.

Resultant velocity

More info

m/s

Angle

More info

deg

x component of the resultant velocity

m/s

y component of the resultant velocity

m/s

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What is velocity?

Velocity tells you how fast something is moving and which way it’s moving. That second part matters: speed is just a number, while velocity is a vector.

Average velocity

\bar{v} = \frac{\Delta r}{\Delta t}

Here $\Delta r$ is the displacement (how your position changed) and $\Delta t$ is the time interval.

✅ Quick intuition: going 10 m east in 2 s is 5 m/s east. If you go 10 m east and then 10 m west, your speed was non‑zero, but your average velocity might be close to zero.

In SI units, velocity is usually measured in m/s, but real life often uses km/h or mph. This calculator lets you switch units per field. If you want a dedicated converter, theconversion toolspage is handy.

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What is resultant velocity? Velocity in 2D

In 2D, a velocity vector has an x (left/right) component and a y (up/down) component. The resultant velocity is what you get when multiple velocities act together — for example, an aircraft’s airspeed plus wind, or a swimmer’s speed plus current.

Think in components first:

Convert each vector from “magnitude + angle” into components: $v_x = v\cos(\theta)$ and $v_y = v\sin(\theta)$ .
Add components across all vectors: $\sum v_x$ and $\sum v_y$ .
Convert back to magnitude and direction: $v_{\mathrm{res}} = \sqrt{(\sum v_x)^2 + (\sum v_y)^2}$ , $\theta_{\mathrm{res}} = \operatorname{atan2}(\sum v_y, \sum v_x)$ .

Resultant velocity (core idea)

\vec{v}_{\mathrm{res}} = \vec{v}_1 + \vec{v}_2 + \cdots + \vec{v}_n

This calculator supports up to 5 vectors. The angle is measured counterclockwise from the +x axis.

💡Related: If your situation is a projectile (launch speed + launch angle), try ourProjectile Motion Calculator →

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How to find the resultant velocity: Example

Quick start (3 steps)

Enter the first velocity

Type a magnitude in Velocity 1 and set Angle 1. Angle is measured from the +x axis (counterclockwise).

Enter the second velocity

Fill Velocity 2 and Angle 2. The result updates instantly.

Read the resultant

Check Resultant velocity, Angle, and the x/y components. The components are great for sanity checks.

Worked example: boat + river current

You’re watching a boat cross a river. The boat moves at 15 km/h relative to the water in the +x direction. The river current is 7 km/h in the +y direction (perpendicular).

Inputs

Velocity 1: 15 km/h, Angle 1: 0°
Velocity 2: 7 km/h, Angle 2: 90°

Results (what you should see)

x component: 15 km/h
y component: 7 km/h
Resultant magnitude: ≈ 16.55 km/h
Resultant direction: ≈ 25° above +x

Sanity-check math

v_{\mathrm{res}} = \sqrt{15^2 + 7^2} \approx 16.55,\quad \theta_{\mathrm{res}} = \arctan\!\left(\frac{7}{15}\right) \approx 25^{\circ}

The calculator uses atan2 internally so the angle stays correct in all quadrants.

Real-world use cases

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Boats & currents

Combine boat speed (relative to water) with river current to get the observed motion from shore.

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Airspeed + wind

Add aircraft airspeed to wind velocity to estimate ground speed and drift direction.

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Robotics / drones

Combine commanded velocity with a disturbance vector (wind, conveyor belt motion, etc.).

🏃‍♂️

Running in wind

Model how a crosswind changes your effective velocity relative to the air.

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Projectile components

Convert a launch speed and angle into x/y components. For full trajectories, use the projectile calculator.

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Momentum Calculator

Connect velocity to momentum (p = mv).

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Free Fall Calculator

Velocity over time under gravity.

Tips & best practices

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Angle conventions:

This calculator assumes angles are measured counterclockwise from the +x axis. If your “north/east” reference differs, convert it first (or treat north as +y and east as +x).

Common mistakes to avoid

Mixing degrees and radians (double‑check the angle unit dropdown).
Entering a negative “speed”. If a vector points opposite, keep the speed positive and rotate the angle by 180°.
Forgetting the checkbox for Velocity 3–5. Turn it on to include extra vectors.

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FAQs

What is the difference between velocity and resultant velocity?

Velocity describes motion in one frame for one vector. Resultant velocity is the single vector you get after adding multiple velocity vectors together (for example: your walking velocity plus a moving walkway).

How do I calculate the resultant velocity by hand?

Convert each vector to components, add components, then convert back: $v_x = v\cos(\theta)$ , $v_y = v\sin(\theta)$ , $v_{\mathrm{res}} = \sqrt{(\sum v_x)^2 + (\sum v_y)^2}$ .If you only have two vectors and they’re at right angles, it becomes the Pythagorean theorem.

Can the resultant velocity be zero?

Yes. If vectors cancel perfectly, both component sums are zero. Example: 2 m/s at 30° and 2 m/s at 210° are opposite directions, so the resultant is 0.

Why does the direction sometimes look “weird” (like negative degrees)?

Angles can be represented in multiple equivalent ways. For example, −10° is the same direction as 350°. If you prefer a 0–360° convention, mentally add 360° when the calculator shows a negative angle.

When should I use Velocity 3–5?

Any time your motion comes from more than two effects — for example, a conveyor belt + a robot arm + a drift term. Turn on the checkbox and enter the extra vectors.

Note: This tool is for 2D vector addition. It doesn’t model acceleration, forces, drag, or changing currents. For time‑dependent motion, use a dedicated kinematics model.

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