The Average Velocity Calculator finds the mean velocity over an interval of constant acceleration, using the initial and final velocity values. Enter u and v, and the tool returns the average with the arithmetic shown, ready to feed directly into a displacement calculation if time is also known.
Average velocity is a summary of an entire interval of motion, not a reading at any single instant. Under constant acceleration, that summary works out to a simple arithmetic mean of the start and end speeds, which is one of the cleanest relationships in introductory mechanics.
Calculate average velocity from initial and final velocity
Under constant acceleration, average velocity is the arithmetic mean of the initial and final velocities.
v̄ = (u + v) / 2Worked example: u = 5 m/s, v = 11 m/s.
1. Add the two velocities. 5 + 11 = 16.
2. Divide by two. 16 / 2 = 8 m/s.
Use average velocity to find displacement
Once average velocity is known, multiplying by the elapsed time gives displacement directly, without needing a separate acceleration-based formula.
s = v̄ × tContinuing the example, with t = 3 s:
s = 8 × 3 = 24 m.
This matches the result from the more familiar s = ½(u + v)t exactly, since that formula is just this same average-velocity idea written with u and v spelled out inside the equation rather than pre-averaged.
Understand why the mean works here
Under constant acceleration, velocity increases (or decreases) at a steady rate from u to v, tracing a straight line on a velocity-time graph. The average height of that straight line, over the whole interval, is exactly the midpoint between its starting and ending values, which is why the simple arithmetic mean gives the correct average velocity.
This shortcut only holds because the rate of change is constant; if acceleration varied during the interval, the true time-weighted average velocity could differ from the plain mean of the endpoints.
Compare average velocity to average speed
Average velocity uses signed values, so a trip that reverses direction can have an average velocity much smaller in magnitude than the average speed, or even a different sign entirely. Average speed is total path length divided by total time, a purely scalar calculation that ignores direction changes.
A runner who jogs to +40 m and back to +10 m has covered 70 m of path, and average speed reflects that full distance. But displacement is only +10 m from the start, so average velocity over the same time is a much smaller number tied to the net position change, not the distance covered.
Check the special case of starting from rest
When an object starts from rest, u = 0, and the average velocity formula simplifies neatly.
v̄ = v / 2 (when u = 0)This shortcut only applies when the object genuinely starts from rest; using v/2 when u is not actually zero will give the wrong average and, by extension, the wrong displacement if that average feeds into a further calculation.
Work through a second worked example
An object starts at u = 3 m/s and reaches v = 15 m/s under constant acceleration. 1. Add the two velocities. 3 + 15 = 18. 2. Divide by two. 18 / 2 = 9 m/s.
If this interval lasted t = 4 s, the resulting displacement would be s = 9 × 4 = 36 m, found by chaining the average-velocity result directly into the displacement formula shown earlier on this page.
Confirm the result with the midpoint reading
Because velocity rises in a straight line under constant acceleration, the instantaneous velocity at the halfway point in time equals the average velocity found from the endpoints.
For the u = 5, v = 11 example above, if the interval takes 3 seconds, the velocity at t = 1.5 s should read 8 m/s, the same value found from (5 + 11) / 2.
Checking this midpoint reading is a useful way to confirm a constant-acceleration assumption before relying on the plain average for a displacement calculation.
Frequently asked questions
What is the formula for average velocity?
Under constant acceleration, average velocity is the mean of initial and final velocity: v̄ = (u + v) / 2. For u = 5 m/s and v = 11 m/s, v̄ = 8 m/s.
Does average velocity equal half the final velocity?
Only when the object starts from rest (u = 0). In that special case, v̄ = v/2. Otherwise, use the full formula with both u and v.
How is average velocity different from average speed?
Average velocity uses signed displacement over time and can be smaller than, or even opposite in sign to, average speed, which uses total path length over time and ignores direction entirely.
Can average velocity be used to find displacement?
Yes. Multiply average velocity by the elapsed time: s = v̄ × t. This gives the exact same result as the full s = ½(u + v)t formula.
Does this formula work if acceleration is not constant?
No. The simple arithmetic mean of u and v only equals the true average velocity when acceleration is constant throughout the interval. Varying acceleration requires more advanced methods to find the true average.
Can average velocity be negative?
Yes. If both u and v are negative, or if their sum is negative, the resulting average velocity will also be negative, indicating net motion in the negative direction over the interval.
Is average velocity the same as instantaneous velocity at the midpoint of the time interval?
Under constant acceleration, yes: the instantaneous velocity at the exact midpoint in time equals the average velocity over the whole interval, since velocity increases linearly with time in that case.
Summary
Average velocity under constant acceleration is the arithmetic mean of initial and final velocity, v̄ = (u + v)/2, giving 8 m/s for u = 5 m/s and v = 11 m/s. Multiplying that average by elapsed time gives displacement directly, matching the result from the fuller s = ½(u + v)t equation.
The shortcut works only because velocity changes at a steady rate; it does not apply when acceleration varies during the interval.