Calculate displacement (s) using the kinematic equation s = ut + ½at². Enter your initial velocity (u), acceleration (a), and time (t) — or solve for any one of those variables instead. Choose what you want to find, pick your preferred units, and get the result along with a breakdown of each component of the motion.
Result
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Velocity Term (ut)
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Acceleration Term (½at²)
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Solving For
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Displacement is a vector quantity that measures the shortest straight-line change in position of an object from its starting point to its ending point, including direction. Distance, on the other hand, is the total path length traveled regardless of direction. An object can travel a long distance but have zero displacement if it returns to its starting point.
This calculator uses the kinematic equation s = ut + ½at², where s is displacement, u is initial velocity, a is acceleration, and t is time. The equation is algebraically rearranged to solve for whichever variable you choose as the unknown.
The standard acceleration due to Earth's gravity is 9.80665 m/s² (or approximately 32.174 ft/s²). Use this value when an object is in free fall or moving under gravitational influence. For upward motion against gravity, use a negative value.
Yes. Select 'Find u | Given s, t and a' from the dropdown, then enter the known values for displacement (s), time (t), and acceleration (a). The calculator rearranges the formula to u = (s - ½at²) / t and returns the initial velocity.
Choose 'Find t | Given a, u and s' and enter values for acceleration, initial velocity, and displacement. The calculator solves the quadratic equation ½at² + ut - s = 0 using the quadratic formula and returns the positive time value.
This calculator supports multiple unit systems. Displacement can be in meters, centimeters, feet, inches, or miles. Velocity can be in m/s, cm/s, ft/s, in/s, or mi/h. Acceleration supports m/s², cm/s², ft/s², in/s², and mi/s². Time can be entered in seconds, minutes, or hours. All values are converted internally to a consistent unit for calculation.
If acceleration is zero, the object moves at a constant velocity and the displacement formula simplifies to s = ut. The calculator handles this case correctly — just enter 0 for acceleration and it will compute the result using only the velocity and time terms.
Yes. A negative displacement value means the object has moved in the opposite direction to the defined positive direction. This can occur when initial velocity and acceleration act in opposing directions, or when the object moves backward from its starting position.