Displacement Calculator
Calculate displacement three ways. Use constant velocity (d = vt), the average of an initial and final velocity (s = ½(u+v)t), or a constant acceleration (s = ut + ½at²). The acceleration mode also reports the final velocity, the average velocity, and the total distance travelled, in either metric or imperial units.
Formula
Worked example
Acceleration mode: an object starts at 5 m/s and accelerates at 2 m/s² for 4 s. s = (5 × 4) + (½ × 2 × 4²) = 20 + 16 = 36 m, and the final velocity is v = 5 + 2 × 4 = 13 m/s.
What displacement measures
Displacement is the change in position of an object, the straight-line vector pointing from its starting point to its finishing point. It differs from distance, which is the total length of the path actually travelled. An athlete who runs one lap of a 400 metre track covers 400 metres of distance but has zero displacement, because they end up exactly where they began. This calculator reports both: the displacement (a signed vector) and the distance (always positive path length), which only differ when the object reverses direction during the interval. The result carries a sign: a positive displacement lies in your chosen positive direction, and a negative one lies opposite to it.
Three ways to find displacement
Pick the mode that matches the values you have. With a constant velocity and a time, displacement is simply d = vt. When you know the initial and final velocities and the time, displacement is the average velocity times the time, s = ½(u + v)t, which holds whenever the acceleration is constant. When you instead know the initial velocity, a constant acceleration and the time, use s = ut + ½at². That third equation adds two contributions: the first term, ut, is the displacement from drifting at the initial velocity, and the second, ½at², is the extra displacement from the acceleration, which grows with the square of time and so dominates over long intervals. The acceleration mode also returns the final velocity from v = u + at and the average velocity.
Units, reverse motion, and where this applies
You can work in metric or imperial, and switch the velocity unit between metres per second, kilometres per hour, miles per hour or feet per second; every value is converted to SI internally and the answer is converted back. These equations assume a constant acceleration acting along a single straight line, the foundation of the standard equations of motion. They model a car braking steadily, a ball thrown straight up, or an object sliding down a frictionless ramp. When the initial velocity and acceleration have opposite signs the object can slow, stop and reverse: the calculator detects that turning point and reports the longer path-length distance separately from the net displacement. The equations do not apply when the acceleration changes during the interval, such as speed-dependent air resistance, or to curved two-dimensional motion, which must be resolved into separate components.
Kinematic equations for constant acceleration
| Equation | Solves for | Quantity missing |
|---|---|---|
| s = ut + ½at² | Displacement | Final velocity |
| s = ½(u + v)t | Displacement | Acceleration |
| v = u + at | Final velocity | Displacement |
| v² = u² + 2as | Final velocity | Time |
The four standard equations relating displacement (s), velocities (u, v), acceleration (a), and time (t).
Frequently asked questions
What is the difference between displacement and distance?
Distance is the total length of the path travelled and is always positive. Displacement is the straight-line change in position from start to finish, including direction, so it can be positive, negative, or zero. They are equal only when the motion never reverses; if the object slows, stops and turns around, this calculator shows the larger distance separately from the net displacement.
Which mode should I use?
Use the constant-velocity mode (d = vt) when speed does not change. Use the average-velocity mode (s = ½(u+v)t) when you know the starting and ending velocities and the time. Use the acceleration mode (s = ut + ½at²) when you know the starting velocity, a constant acceleration and the time; it also returns the final and average velocities.
What if there is no acceleration?
Set the acceleration to 0 in the acceleration mode and s = ut + ½at² collapses to s = ut, the constant-velocity result, or just use the constant-velocity mode directly. The displacement is then simply the initial velocity multiplied by the time.
Can displacement be negative?
Yes. Displacement is a vector, so its sign shows direction relative to your chosen positive axis. A negative result means the object finishes behind its starting point, for example if a strong negative acceleration reverses an object moving in the positive direction and carries it back past the start.