Example data table
| Segment | Δx (m) | Δt (s) | Segment velocity (m/s) |
|---|---|---|---|
| 1 | 120 | 10 | 12.0 |
| 2 | 80 | 8 | 10.0 |
| 3 | -30 | 6 | -5.0 |
| Totals | 170 | 24 | 7.0833 |
Formula used
How to use this calculator
- Choose a method: Intervals for many segments, or Two points for start/end.
- Select distance and time units, then choose an output velocity unit.
- For intervals, fill each row with Δx and Δt. Use negative Δx to show reverse direction.
- For two points, enter x1, x2, t1, and t2. Make sure t2 differs from t1.
- Press Calculate to see results above the form.
Average velocity across intervals
1) What average velocity measures
Average velocity is net displacement divided by total time. It keeps direction, so it can be negative. The calculator also reports average speed, which ignores direction and stays nonnegative. It summarizes motion over any chosen time window. Use it for labs, fitness logs, and trips.
2) Why intervals matter
Motion is rarely one smooth segment. Intervals let you model cruise, stops, and reversals with (Δx, Δt) rows. A stop is Δx = 0 with a positive duration, lowering the overall average even if moving segments are fast. Use up to 12 intervals for detailed routes.
3) Quick numeric example
Travel (120 m, 10 s), wait (0 m, 20 s), then travel (80 m, 8 s). Totals are ΣΔx = 200 m and ΣΔt = 38 s, so v̄ ≈ 5.263 m/s. Removing the stop row gives 200 m over 18 s, so v̄ ≈ 11.11 m/s.
4) Displacement versus distance
Displacement uses signs. Distance uses absolute values. If you go (100 m, 10 s) then (−100 m, 10 s), net displacement is 0 m so average velocity is 0, but average speed is (200 m)/(20 s) = 10 m/s. This pattern appears in loops and out-and-back trips.
5) Typical ranges to test
Walking is often 1.2–1.6 m/s (≈ 4.3–5.8 km/h). Jogging may be 2–4 m/s, while sprint bursts can exceed 7 m/s. City driving can average 8–15 m/s (≈ 29–54 km/h) when stops are included.
6) Units and conversions
Values convert to meters and seconds internally, then convert back to your selected output. References: 1 km = 1000 m, 1 mile = 1609.344 m, 1 ft = 0.3048 m, 1 hour = 3600 s, and 1 min = 60 s. Velocity references: 1 m/s = 3.6 km/h and ≈ 2.2369 mph.
7) Two-point method
When you only know start and end position/time, use v̄ = (x2 − x1) / (t2 − t1). This is common for GPS summaries or lab timing gates. It cannot reveal internal stops, but it matches the interval method over the same span.
8) Practical accuracy checks
Keep every Δt greater than zero, and use negative Δx only for direction changes. If results look too large, confirm you did not mix seconds with minutes or miles with kilometers. Increase decimals for close comparisons, then round for reporting. For sensor data, average several intervals to reduce noise.
FAQs
1) What is the difference between velocity and speed?
Velocity includes direction and can be negative. Speed ignores direction and is always nonnegative. This calculator shows both so you can compare net motion versus total travel.
2) Can I enter a stop or waiting time?
Yes. Add an interval with Δx = 0 and a positive Δt. This lowers the overall average while leaving other segment velocities unchanged.
3) Why does average velocity become zero after going out and back?
If your final position equals your start position, net displacement is zero. Since v̄ = ΣΔx / ΣΔt, the result is zero even though you travelled distance.
4) Do I need equal time intervals?
No. Each row can have a different duration. The calculator correctly sums all time and displacement, then computes the overall average from totals.
5) What happens if I enter a negative time?
Negative or zero time is rejected because it is not physically meaningful for elapsed duration. Use a positive Δt and represent direction with the sign of Δx.
6) Which method should I choose?
Use intervals when you have segment data, stops, or reversals. Use two points when you only know start/end position and time. Both give the same overall average when covering the same span.
7) Why is my CSV/PDF velocity not rounded like the screen?
Exports store the underlying computed values for accuracy. The displayed values are rounded to your chosen decimals. Increase decimals if you want closer matching.