Displacement Calculator
Find the straight-line displacement, the total distance travelled and the direction, from coordinates, a multi-leg path or constant acceleration.
📍 What is Displacement?
Displacement is the change in position of an object, written as a vector from where it started to where it ended. It has a size, the straight-line gap between the two points, and a direction. It does not care about the route in between. If you walk around a block and return to your front door, your displacement is zero even though your feet covered hundreds of metres. That total length of the path is called the distance, and unlike displacement it has no direction and can never be smaller than the size of the displacement.
The idea is the foundation of mechanics. Velocity is displacement divided by time, acceleration is the change of velocity, and work is a force dotted with a displacement. Pilots and sailors describe displacement as a bearing and a range, surveyors work with coordinates, and robots and game characters track position changes in two or three dimensions. Students meet it in kinematics problems with a ball thrown upwards, where the final position can be below the start, giving a negative displacement even though the ball travelled up and then down.
This calculator has three modes, each aimed at a different way displacement shows up. In Two points mode you give a start and an end coordinate and get the components, the size, the direction angle and a compass bearing, with a diagram. In Multi-leg path mode you list up to five legs, each with a distance and an angle, and the tool adds the components, shows a table of running totals, and compares the net displacement with the total distance. In Motion mode you give an initial velocity, an acceleration and a time along a line, and the tool gives the displacement, detects any reversal, and computes the distance travelled, with position and velocity charts.
It is different from a general kinematic equation solver. The kinematic equations calculator takes three known SUVAT quantities and finds the missing ones, while this page is about the vector nature of displacement, the contrast with distance, two-dimensional paths and the direction of the result. Remember that vector quantities add by components, and that the size of the sum is not the sum of the sizes unless the legs point the same way.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Displacement Between Two Points
Start (2, 3) m, end (8, 11) m
Example 2 — Walk East, North, then West
40 m at 0°, 30 m at 90°, 20 m at 180°
Example 3 — Out and Back, Zero Displacement
5 m at 30°, then 5 m at 210°
Example 4 — Ball Thrown Upward for Six Seconds
v₀ = 20 m/s upward, a = −9.80665 m/s², t = 6 s
Example 5 — A Car Speeding Up
v₀ = 10 m/s, a = 2 m/s², t = 5 s
❓ Frequently Asked Questions
🔗 Related Calculators
What is the difference between displacement and distance?
Distance is the total length of the path travelled and has no direction. Displacement is the straight line vector from the start to the end, with a size and a direction. Walking 40 m east, 30 m north and 20 m west covers 90 m but gives a displacement of only 36.06 m.
What is the formula for displacement?
For positions, displacement is the final position minus the initial position: delta r = r_f minus r_i. For constant acceleration along a line, delta x = v0 t + 0.5 a t squared. In two dimensions, add the x and y components separately.
How do you calculate displacement from coordinates?
Subtract the start from the end for each axis to get dx and dy, then the size is sqrt(dx squared + dy squared). From (2, 3) to (8, 11), dx = 6, dy = 8 and the displacement is 10 at 53.13 degrees from the x axis.
Can displacement be zero while distance is not?
Yes. If an object returns to its starting point, displacement is zero but the distance is the full length of the trip. A lap around a track, or 5 m out and 5 m back, are examples. The average velocity for such a trip is also zero.
Can displacement be negative?
In one dimension the sign shows the direction relative to the chosen positive axis, so a displacement of minus 56.52 m means 56.52 m in the negative direction. The size of a displacement is never negative.
How do you find displacement from velocity and time?
With constant velocity, displacement is v t. With constant acceleration it is v0 t + 0.5 a t squared. A car starting at 10 m/s and accelerating at 2 m/s2 for 5 s has a displacement of 75 m. Check the final velocity too: it is 20 m/s.
How is the direction angle of a displacement found?
The angle from the positive x axis is atan2(dy, dx), reported here from 0 to 360 degrees counterclockwise. The compass bearing is measured clockwise from north, atan2(dx, dy). A displacement of 8 east and 6 south has an angle of 323.13 degrees and a bearing of 126.87 degrees.
How do I add several displacements?
Add them as vectors: sum the x components and sum the y components separately, then combine. Each leg of length d at angle theta contributes d cos(theta) to x and d sin(theta) to y. The multi-leg mode does this and lists every running total.
How do I find the distance when the object turns around?
Find the turning time t = minus v0 / a, the position there, then add the distance out and the distance back separately. A ball thrown up at 20 m/s for 6 s has a displacement of minus 56.52 m but travels 97.31 m in total.
Is displacement the same as the net change in position?
Yes. Displacement depends only on where the object starts and ends, not on the route. Two different routes with the same endpoints have the same displacement but may have very different distances.
What are the units of displacement?
Displacement is a length, so the SI unit is the metre. The calculator labels results in metres, but if you type all lengths in kilometres or feet the results are in those units, as long as you stay consistent. The motion mode needs seconds and metres per second.