Average velocity answers a simple question: taking the trip as a whole, how fast did your position change, and in which direction? It is net displacement divided by elapsed time. Detours, stops and backtracking all disappear into one number. This calculator works it out three ways. It can combine a trip entered leg by leg, divide a total displacement by a total time, or take the midpoint of two velocities under constant acceleration. Alongside the answer it reports the average speed, which is often the number people actually meant.
How to use the average velocity calculator
- In What do you know? pick one of three modes.
- A trip in several legs (the default): under Each leg is given as, choose “Displacement, time” or “Velocity, time”. Type one leg per line in Legs, two numbers separated by a comma or space, using a minus sign for legs in the opposite direction. Set the displacement or velocity unit, the Time unit and Show the average in. For velocity legs, Show displacement in sets the unit of the displacement totals; Auto uses m or km (ft or mi for mph and ft/s).
- Total displacement and total time: choose what to solve for (average velocity, displacement or time) and enter the other two. The answer comes with conversions to other units.
- Initial and final velocity (constant acceleration): solve for the average, the initial or the final velocity from the other two.
- In leg mode the result also lists average speed, total displacement, total distance, total time, the plain mean of the leg velocities and a table of the legs.
Average velocity formulas
Pick one direction as positive. Displacements and velocities are signed, and every leg’s time must be greater than zero. In total mode, solving for time requires the displacement and average velocity to have the same sign.
Worked example: a three-leg drive
Legs: 60 km east in 1 h, then 40 km east in 0.5 h, then 20 km back west in 0.5 h (entered as −20).
Net displacement: 60 + 40 − 20 = 80 km. Total time: 2 h.
Average velocity: 80 ÷ 2 = 40 km/h east
Total distance: 60 + 40 + 20 = 120 km, so average speed = 120 ÷ 2 = 60 km/h
The table shows each leg’s own velocity: 60, 80 and −40 km/h. Their plain mean is (60 + 80 − 40) ÷ 3 = 33.3 km/h, which matches neither real answer. The calculator lists it on purpose, labeled as not the true average, because it is such a common mistake.
Why you must weight by time
An average velocity is a time-weighted average: each leg counts in proportion to how long it lasts. The plain mean treats a half-hour leg the same as a one-hour leg, which is why it misses. A classic textbook trap makes the point. You drive the first 60 km of a trip at 30 km/h and the second 60 km at 60 km/h. The answer is not 45 km/h. The first half takes 2 h and the second only 1 h, so you spend most of the trip going slowly: 120 km ÷ 3 h = 40 km/h. Enter the legs as “Velocity, time” (30, 2 and 60, 1) and the calculator shows 40 km/h next to the misleading 45 km/h mean. For equal distances, the correct average is the harmonic mean of the speeds, not the arithmetic mean.
Round trips have zero average velocity
Drive 12 km to a store in 15 minutes and come home by the same road in 21 minutes. Enter the legs as 12, 15 and −12, 21 with the time unit set to minutes. The net displacement is 0 km, so the average velocity is 0 km/h, while the average speed over the 36 minutes is 40 km/h. Zero average velocity does not mean nothing happened. It means the trip ended where it began. A negative average velocity simply means the net motion was in the direction you called negative.
The other two modes
Total displacement and total time is the plain definition, v̄ = Δx ÷ Δt, with each quantity in its own units. At an average of 60 km/h, a net displacement of 150 km takes 2.5 h. A walker averaging 1.4 m/s for 20 minutes ends up 1,680 m from the start. Δx is always final position minus initial position, not the odometer reading.
Initial and final velocity uses the midpoint rule, which is valid only for uniform acceleration. A cart that speeds up steadily from 4 m/s to 16 m/s averages 10 m/s. Working backward is just as easy: an average of 15 m/s from a start of 5 m/s means a final velocity of 25 m/s. To turn an average into a displacement, multiply by the time with the s = ½(u + v)t calculator. For a single constant-velocity stretch, the s = vt displacement calculator is the simplest tool.
Frequently asked questions
What is the difference between average velocity and average speed?
Average velocity is net displacement divided by elapsed time, so backtracking cancels out and the result can be negative or zero. Average speed is total distance divided by elapsed time and is never negative. They are equal only when the motion never reverses direction.
Why isn't my average velocity just the average of the leg velocities?
A plain mean gives every leg the same weight, but a leg that lasts longer contributes more to the trip. Driving 60 km at 30 km/h and then 60 km at 60 km/h averages 40 km/h, not 45 km/h, because the slow leg takes twice as long.
Can average velocity be zero even though the object moved?
Yes. Any trip that ends where it started has zero net displacement, so its average velocity is zero no matter how far or how fast it went. Its average speed is still positive.
When can I use (u + v) ÷ 2 for average velocity?
Only when the acceleration is constant, so velocity changes linearly with time. For stop-and-go motion or any irregular speed changes, divide total displacement by total time instead.