Particle Velocity Calculator

Calculator Form

Calculation Mode

Distance Unit

Time Unit

Velocity Unit

Displacement

Elapsed Time

Direction Angle (degrees, optional)

Initial Position

Travel Time for Displacement (optional)

Speed

Direction Angle (degrees)

Travel Time for Displacement (optional)

Particle Speeds

Enter values separated by commas, spaces, semicolons, or new lines.

Swarm vx List

Swarm vy List

Example Data Table

Mode	Sample Inputs	Key Output	Meaning
Displacement ÷ Time	Δs = 24 m, Δt = 3 s	v = 8 m/s	Average velocity from motion over time.
Components to Resultant	vx = 6 m/s, vy = 8 m/s	\|v\| = 10 m/s	Resultant speed from orthogonal components.
Speed and Angle	v = 15 m/s, θ = 30°	vx = 12.99 m/s, vy = 7.5 m/s	Component breakdown of a vector.
Gas Average Speed	4, 5, 6, 7, 8, 9	vavg = 6.5 m/s	Mean particle speed for a gas sample.
Particle Swarm	vx: 3,4,5,2 \| vy: 2,1,0,3	Mean swarm speed ≈ 3.64 m/s	Net movement of the whole swarm.

Formula Used

Average Velocity

v = Δs / Δt

Use this when displacement and elapsed time are known.

x Component

vx = v cos θ

This gives the horizontal part of the velocity vector.

y Component

vy = v sin θ

This gives the vertical part of the velocity vector.

Resultant Speed

|v| = √(vx² + vy²)

Use this when the two orthogonal components are known.

Direction Angle

θ = tan^-1(vy / vx)

Use atan2(vy, vx) in code to preserve the correct quadrant.

Gas and Swarm Averages

vavg = Σv / n and v̄ = Σv⃗ / n

Average scalar speeds for gas lists, or average vectors for swarm motion.

How to Use This Calculator

Select the calculation mode that matches your data.
Enter the working units for distance, time, and velocity.
Fill in the required inputs for the selected mode.
Click Calculate Particle Velocity to show the result above the form.
Review the result table and the Plotly graph.
Use the CSV or PDF buttons to export the computed summary.
Use the example table below to compare your values with sample cases.

FAQs

How do I calculate the x component of the velocity of the particle?

Use vx = v cos θ when speed and angle are known. If horizontal displacement and time are given, use vx = Δx / Δt. Keep your angle measured from the positive x-axis and use consistent units.

How do I calculate the y component of the velocity of the particle?

Use vy = v sin θ when speed and direction are known. If vertical displacement and time are known, use vy = Δy / Δt. The sign shows whether motion is upward or downward.

How do I calculate vx, the x component of the velocity of the particle?

vx is the horizontal component of the velocity vector. Multiply total speed by cos θ, or divide horizontal displacement by elapsed time. This calculator returns vx automatically in the speed-angle and displacement modes.

How do I calculate velocity particle swarm?

Average each component first: v̄x = Σvx / N and v̄y = Σvy / N. Then compute swarm speed with √(v̄x² + v̄y²). This shows the group’s net motion rather than the average of individual speed magnitudes.

The molecules in a six particle gas have velocities. How do I calculate vavg?

Add the six speeds and divide by six: vavg = (v1 + v2 + v3 + v4 + v5 + v6) / 6. If direction matters, average the x and y components separately instead of averaging magnitudes alone.

What is the difference between speed and velocity?

Speed is only magnitude. Velocity includes both magnitude and direction. A particle moving 10 m/s east has a speed of 10 m/s, but its velocity is 10 m/s east.

Why can average velocity be zero even when a particle moves?

Average velocity depends on net displacement, not total path length. If a particle returns to its starting point, displacement becomes zero, so average velocity is zero even though distance traveled is not zero.

Can a velocity component be negative?

Yes. A negative component means the particle moves opposite the positive axis direction. For example, negative vx indicates motion toward the left if the positive x-axis points right.