Resultant Velocity Calculator
Calculate resultant velocity magnitude and direction from multiple velocity vectors in 2D with step-by-step vector math.
What Is Resultant Velocity?
Resultant velocity is the single velocity vector that has the same effect as two or more velocity vectors acting together. In two dimensions, each velocity is split into horizontal and vertical components, then the components are added separately.
Vector Addition of Velocities
$$V_x = \sum v_i \cos\theta_i, \quad V_y = \sum v_i \sin\theta_i$$ $$V = \sqrt{V_x^2 + V_y^2}, \quad \theta = \mathrm{atan2}(V_y, V_x)$$Angles are measured from the positive x axis. The magnitude \(V\) is the speed of the combined motion. The direction \(\theta\) tells where the object moves relative to the reference axis.
Common Applications
Resultant velocity appears when a boat crosses a river with current, when wind affects an aircraft ground speed, or when multiple forces produce motion in different directions. Adding velocity vectors gives the true path and speed an observer would measure.
Related tools: Resultant Force Calculator, Projectile Motion Calculator, and Velocity Calculator.
Frequently Asked Questions
How do I add velocities at right angles?
Split each vector into x and y parts. For perpendicular vectors, use the Pythagorean theorem: if one part is 3 m/s and the other is 4 m/s, the resultant is 5 m/s.
What angle convention does this calculator use?
Angles are measured counterclockwise from the positive x axis in degrees. A velocity aimed straight up uses 90 degrees.
Can I add more than two velocity vectors?
Yes. Select three vectors in the tool. Each contributes its own cosine and sine terms to the total horizontal and vertical components.
Is resultant velocity the same as average velocity?
No. Resultant velocity is the vector sum at one instant. Average velocity is displacement divided by total time over an interval.
What if one velocity opposes another?
Vectors pointing in opposite directions subtract. A 5 m/s east vector and a 3 m/s west vector give a 2 m/s east resultant when aligned on the same axis.
Related Tools
Full Red Screen
Effective Gear Ratio Calculator
DNA Concentration Calculator
SHA3-512 Hash Generator
IQ Percentile Calculator
Logic Gate Calculator
Split Unicode into Fragments
Line Length Checker
YAML to JavaScript POJO Generator
TypeScript To TypeScript Declaration
Cloud Base Calculator
Hex Binary Converter
GDP Gap Calculator
Google Fonts Pair Finder
Currency Appreciation Depreciation Calculator
Lung Nodule Growth Rate Calculator
Fixed Charge Coverage Ratio Calculator
Stone to Kg Converter
Plist to JSON Converter
Wood Beam Span Calculator