# Velocity Calculator

Calculate resultant velocity magnitude and direction angle from horizontal and vertical components. Uses v = sqrt(vx² + vy²) and atan2.

## What this calculates

Velocity is a vector quantity that describes both the speed and direction of an object's motion. When motion occurs in two dimensions, you can decompose velocity into horizontal (vx) and vertical (vy) components. This calculator finds the resultant velocity magnitude and direction from those components using the Pythagorean theorem and inverse tangent.

## Inputs

- **Horizontal Velocity (vx)** (m/s) — Velocity component along the x-axis.
- **Vertical Velocity (vy)** (m/s) — Velocity component along the y-axis.

## Outputs

- **Resultant Velocity** (m/s) — v = sqrt(vx² + vy²)
- **Direction Angle** (°) — Angle measured from the positive x-axis
- **Horizontal Component** (m/s) — vx component of the velocity vector
- **Vertical Component** (m/s) — vy component of the velocity vector

## Details

The resultant velocity is found using v = √(vx² + vy²), which is the Pythagorean theorem applied to the velocity vector. The direction angle is calculated with θ = atan2(vy, vx), giving the angle measured counterclockwise from the positive x-axis.

Understanding velocity components is essential for analyzing projectile motion, navigation, and any two-dimensional motion problem. For example, a ball thrown at an angle has a constant horizontal velocity (ignoring air resistance) and a changing vertical velocity due to gravity. By resolving these components, you can predict the trajectory of the ball.

Unlike speed, which is a scalar and always positive, velocity can have negative components indicating direction. A negative vx means motion to the left, while a negative vy means downward motion. The direction angle fully captures this directional information in a single value between -180° and 180°.

## Frequently Asked Questions

**Q: What is the difference between speed and velocity?**

A: Speed is a scalar quantity that measures how fast an object is moving, while velocity is a vector that includes both speed and direction. An object moving at 5 m/s north has a velocity, but its speed is simply 5 m/s.

**Q: How do you find velocity from components?**

A: Use the Pythagorean theorem: v = sqrt(vx² + vy²) for magnitude, and θ = atan2(vy, vx) for the direction angle. The atan2 function correctly handles all four quadrants.

**Q: What does a negative direction angle mean?**

A: A negative direction angle means the velocity vector points below the horizontal (positive x-axis). For example, -30° indicates the object is moving to the right and downward at 30° below horizontal.

**Q: Why use atan2 instead of atan?**

A: The atan function only returns angles between -90° and 90°, which covers only two quadrants. The atan2(vy, vx) function correctly determines the angle in all four quadrants by considering the signs of both components.

**Q: Can velocity components be negative?**

A: Yes. Negative vx means the object is moving in the negative x-direction (left), and negative vy means it is moving in the negative y-direction (downward). The resultant magnitude is always non-negative.

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Source: https://vastcalc.com/calculators/physics/velocity
Category: Physics
Last updated: 2026-04-21