Kinematic Velocity Calculator
Calculate final velocity, displacement and average velocity from acceleration and time.
Formula and sources updated · Data sources · 1View algorithm, constants and default inputs (JSON)
About this calculator
The kinematic equations describe motion at constant acceleration, and the three quantities they relate are final velocity, displacement and time. Average velocity is the midpoint between initial and final velocity, which is only true when acceleration is constant.
Worked example
calculated with the default values below
Initial velocity 0 m/s · Acceleration 9.81 m/s² · Time 3 s Final velocity 29.430 m/s · Displacement 44.145 m · Average velocity 14.715 m/s · Final velocity 105.95 km/h · Displacement 0.04415 km · Time to come to rest 0.000 s
Method and assumptions
Formula basis and scope
Final velocity is initial velocity + acceleration × time; displacement is initial velocity × time + acceleration × time² / 2.
Assumes constant signed acceleration in one dimension. Time to stop applies only when velocity and acceleration oppose; the displayed zero otherwise is a sentinel, not a prediction of immediate stopping.
Data sources
Disclaimer
These calculators give general conversion results. Rounding and the precision of the value you enter both affect the output, so treat displayed decimals as indicative rather than exact.
Implementation source
This record describes the implementation used by this page. It is not independent validation. External references, when available, support only the stated formula or definition; estimates and custom rules retain their own assumptions.
Formula and variables
v = u + a × t; d = u × t + ½ × a × t²; t_stop = −u ÷ a when u × a < 0
- v
- Final velocity (m/s)
- u
- Initial velocity (m/s)
- a
- Constant acceleration (m/s²)
- t
- Elapsed time (s)
- d
- Displacement (m)
Average velocity = d ÷ t. Time to rest is shown only when acceleration opposes the initial velocity; km/h = m/s × 3.6.
Frequently asked questions
Why is average velocity exactly half of final velocity here?
The kinematic equations assume constant acceleration, so average velocity is the simple midpoint between initial and final speed. With an initial 0 m/s, 9.81 m/s² acceleration and 3 seconds, final velocity is 29.43 m/s and the average is 14.72 m/s, exactly half. That midpoint rule breaks down the moment acceleration changes, such as in real braking or thrust.