Average Velocity Calculator
Choose a method to compute velocity: distance & time, acceleration over time, or weighted average of segment velocities. Units accepted.
Equation Preview
Helping Notes
- Distance & Time: v = distance / time
- With acceleration: v = u + a·t (constant acceleration)
- Weighted average: v̄ = (v₁t₁ + v₂t₂) / (t₁ + t₂)
- Type values with units (m, km, mi, s, minute, hour, m/s, km/h, mi/h). We normalize common aliases.
Results
Velocity
Conversions
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Error
What is Average Velocity Calculator?
An Average Velocity Calculator determines the net change in position per unit time over a specified interval. In one dimension, average velocity equals total displacement divided by total time. In multiple dimensions, it is a vector from the starting position to the ending position, divided by elapsed time. The concept differs from average speed, which uses total distance traveled (always nonnegative) rather than displacement (which can cancel when reversing direction). Key definitions are:
About the Average Velocity Calculator
This tool accepts positions at two times, a table of time-stamped positions, or piecewise constant velocities with durations. It returns average velocity (scalar in 1D or vector in 2D/3D), average speed, elapsed time, and displacement. It highlights sign and direction, shows intermediate steps, and supports common unit conversions. For multi-axis data, it reports components as well as magnitude. Formulas are displayed in clear, responsive blocks for study and documentation.
How to Use this Average Velocity Calculator
- Select input type: two positions, a time–position table, or velocity segments with durations.
- Enter values carefully with consistent units (e.g., meters and seconds, or miles and hours).
- Press calculate to compute displacement, elapsed time, average velocity, and average speed.
- Review the step-by-step breakdown and verify signs/directions match your scenario.
- Optionally convert units and copy the results for homework, labs, or reports.
Examples
Example 1: 1D displacement
From \(x_1=12\,\text{m}\) to \(x_2=92\,\text{m}\) in \(\Delta t=4\,\text{s}\):
Example 2: Out-and-back trip
From 0 to 100 m in 10 s, then back to 0 in 10 s (total 20 s):
Example 3: Time-weighted velocities
\(v_1=10\,\text{m/s}\) for 3 s, \(v_2=-2\,\text{m/s}\) for 4 s:
Example 4: 2D vectors
\(\mathbf r_1=(1,2)\,\text{m},\; \mathbf r_2=(5,-1)\,\text{m}\) over \(\Delta t=2\,\text{s}\):
FAQs
What is the difference between average velocity and average speed?
Average velocity uses displacement (can be negative); average speed uses total distance (nonnegative). They are equal only on monotonic paths.
Can average velocity be zero?
Yes—if starting and ending positions are the same, displacement is zero even if distance traveled is large.
Can average velocity be negative?
Yes. The sign encodes direction along the chosen axis; negative indicates motion opposite the positive direction.
Is the average of speeds equal to average speed?
Not necessarily. Average speed is time‑weighted by each segment’s duration, not the simple arithmetic mean of speeds.
How do I convert between m/s and km/h?
Multiply m/s by 3.6 to get km/h; divide km/h by 3.6 to get m/s.
Does acceleration affect average velocity?
No. Average velocity depends only on net displacement and total time, regardless of how speed varied in between.
What if the time interval is zero?
It is undefined because division by zero occurs; choose distinct times to compute an average.
Can this handle 2D or 3D motion?
Yes. Enter vector positions; the calculator returns component-wise average velocity and its magnitude.
Why is my average speed larger than |average velocity|?
Because distance \(\ge\) |displacement|, especially on paths with turns or reversals.
Are units important?
Yes. Keep position and time units consistent; the output’s units follow directly (e.g., meters per second).
How do I combine multiple segments?
Use the time‑weighted formula \(v_{\text{avg}}=\sum v_i\Delta t_i/\sum\Delta t_i\) or accumulate displacement then divide by total time.