Enter motion data
Formula used
| Motion model | Formula | Best use |
|---|---|---|
| Constant speed | d = vt | Speed remains unchanged. |
| Uniform acceleration | d = ut + ½at² | Acceleration stays constant. |
| Two velocities | d = ((u + v) ÷ 2)t | Initial and final velocities are known. |
| No time value | d = (v² − u²) ÷ 2a | Time is unknown. |
| Velocity-time graph | d = area under |v-t graph| | Velocity changes across intervals. |
How to use this calculator
- Select the motion model matching your known values.
- Enter measurements and choose their correct units.
- Choose output units and rounding preferences.
- Add journey segments when speeds or directions change.
- Submit the form and review every calculation step.
- Export, copy, or print the completed result.
Distance and displacement
Distance measures the entire path travelled. Displacement measures positional change. They are not always equal.
Distance is never negative. Displacement can be signed. Round trips can produce zero displacement.
| Journey | Distance | Displacement |
|---|---|---|
| Walk 100 m forward | 100 m | 100 m |
| Walk 100 m forward, then 40 m backward | 140 m | 60 m |
| Complete one full 400 m lap | 400 m | 0 m |
Example data
| Example | Inputs | Expected distance |
|---|---|---|
| Constant-speed car | 20 m/s for 15 s | 300 m |
| Acceleration from rest | u = 0, a = 3 m/s², t = 6 s | 54 m |
| Free fall on Earth | u = 0, t = 2 s | 19.6133 m |
| Out-and-back walk | 80 m forward, 30 m backward | 110 m |
Frequently asked questions
What is distance travelled?
It is the complete length of an object’s path.
Can distance be negative?
No. Distance uses path magnitude and remains non-negative.
Why can displacement be negative?
Its sign represents direction relative to the chosen axis.
Which formula should I select?
Choose the formula containing your known motion quantities.
Does rest time affect distance?
No, but rest time lowers the overall average speed.
Can the calculator handle direction changes?
Yes. Use journey segments or velocity-time data.
How is graph distance calculated?
Absolute trapezoidal areas are added across every interval.
What happens when velocity crosses zero?
The interval splits at zero before calculating distance.
Can I use Moon gravity?
Yes. Earth, Moon, Mars, and custom gravity are supported.
Are mixed units supported?
Yes. Every input converts internally into SI units.