Calculate the (average) velocity of an object along a straight line. Enter the displacement (change in position) and time elapsed to determine the velocity. If you know the initial and final positions, the displacement is (final position − initial position).
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Velocity Formula, Units, and Calculator Guide
Velocity measures how quickly position changes in a chosen direction. This calculator is designed for average velocity, which means it compares net displacement over the full elapsed time. It can also be used in reverse to solve for displacement or time when the other two values are known.
Core Formulas
v = \frac{\Delta x}{\Delta t}\Delta x = x_2 - x_1
\Delta x = v \cdot \Delta t
\Delta t = \frac{\Delta x}{v}A positive velocity means motion in the positive chosen direction. A negative velocity means motion in the opposite direction. If the starting and ending positions are the same, average velocity is zero even if distance was traveled in between.
What Each Input Means
| Value | Meaning | Common Units |
|---|---|---|
| Displacement (Δx) | Change in position from start to finish. This is directional, so it can be positive or negative. | m, km, mi |
| Time (Δt) | Total elapsed time for the motion interval. Time must be greater than zero. | s, min, hr |
| Velocity (v) | Signed rate of positional change. | m/s, km/h, mph |
What the Calculator Can Solve
| Known Values | Find | Relationship Used |
|---|---|---|
| Displacement and time | Velocity | v = \frac{\Delta x}{\Delta t} |
| Velocity and time | Displacement | \Delta x = v \cdot \Delta t |
| Displacement and velocity | Time | \Delta t = \frac{\Delta x}{v} |
How to Use the Velocity Calculator
- Choose a direction convention so the sign of displacement is meaningful.
- Enter any two known values.
- Make sure the units are consistent or select the correct unit options before calculating.
- Interpret the sign of the answer as direction, not just magnitude.
Velocity vs. Speed
| Quantity | Uses | Direction Included? |
|---|---|---|
| Velocity | Displacement over time | Yes |
| Speed | Distance over time | No |
If an object moves away from its starting point and then returns, its distance traveled can be large while its average velocity over the full trip can still be zero.
Common Unit Conversions
| Conversion | Formula |
|---|---|
| Meters per second to kilometers per hour | \text{km/h} = \text{m/s} \times 3.6 |
| Kilometers per hour to meters per second | \text{m/s} = \frac{\text{km/h}}{3.6} |
| Miles per hour to meters per second | \text{m/s} = \text{mph} \times 0.44704 |
| Meters per second to miles per hour | \text{mph} = \text{m/s} \times 2.23694 |
Quick Examples
Example 1: An object changes position by 240 meters in 30 seconds.
v = \frac{240}{30} = 8 \text{ m/s}Example 2: An elevator moves 36 meters downward in 12 seconds. If upward is positive, the displacement is negative.
v = \frac{-36}{12} = -3 \text{ m/s}Example 3: A vehicle travels at 72 kilometers per hour for 1.5 hours.
\Delta x = 72 \times 1.5 = 108 \text{ km}Example 4: A runner covers 400 meters at 5 meters per second.
\Delta t = \frac{400}{5} = 80 \text{ s}Common Mistakes
- Using total distance instead of displacement.
- Mixing units, such as kilometers with seconds.
- Ignoring direction when assigning positive or negative values.
- Trying to calculate with zero elapsed time.
- Assuming this result is instantaneous velocity when it is actually an average over an interval.
When This Calculator Is Most Useful
- Basic physics and kinematics problems
- Travel and motion estimates
- Lab measurements and classroom exercises
- Checking displacement, time, or velocity from two known values
