Work out an object's displacement four ways: from a constant velocity and time, from initial and final velocity, from initial velocity, acceleration and time (s = ut + ½at²), or from start and end coordinates. It also shows the distance actually travelled when the object turns around.
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Calculate displacement from
Constant or average velocity; negative = opposite direction
Negative if slowing down (or for gravity when up is positive)
Compares the distance actually travelled with the displacement
Enter your values to see the result.
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How to use the Displacement Calculator
Choose the method that matches the values you have.
Enter the values with their units; use negative numbers for the opposite direction.
Pick the distance unit for the result.
Read the displacement and the distance travelled, final and average velocity.
Check the steps, chart and table to follow the motion over time.
Graphically, displacement is the signed area under a velocity-time graph. For constant acceleration that area is a trapezium, which is where ½(u + v)t comes from; splitting it into a rectangle (ut) and a triangle (½at²) gives the other form.
When distance and displacement differ
If the velocity changes sign during the time interval, the object stops and turns around at t = −u / a. The calculator finds that moment and adds the two legs separately:
Displacement s = ut + ½at² at the end time, which can be smaller than the path, zero or negative.
Distance travelled = |s at turnaround| + |s at end − s at turnaround|.
Example: a car moving at 30 m/s brakes at −6 m/s². After 4 s its displacement is 30 × 4 − 3 × 16 = 72 m and it is still moving forward at 6 m/s, so distance and displacement are equal. A ball thrown up at 20 m/s is different: after 3 s its displacement is 15.87 m, but it has travelled 24.92 m because it went up 20.39 m and came back down 4.52 m.
Tips
Pick a positive direction first (forward, up, east) and give opposite velocities and accelerations a minus sign.
Convert units before multiplying. 60 mph for 2.5 hours is 150 miles; 60 mph for 2.5 seconds is 67.06 m, not 150 m. The calculator converts everything to SI internally.
Average velocity is displacement ÷ time, while average speed is distance ÷ time. They are only equal when the object never turns around.
For two unknowns (for example time and final velocity from a known displacement), use the Kinematics Calculator.
Frequently asked questions
What is displacement in physics?
Displacement is the change in an object's position: a vector from where it started to where it ended, with both size and direction. It is measured in length units such as meters, and it can be negative (in one dimension) or zero if the object returns to its starting point.
What is the formula for displacement?
At constant velocity, s = v × t. With constant acceleration, s = ut + ½at², or s = ½(u + v)t if you know both velocities. From positions, Δx = x₂ − x₁, and in 2D the magnitude is √(Δx² + Δy²).
What is the difference between distance and displacement?
Distance is the total length of the path travelled and is always positive. Displacement only depends on the start and end points. A runner who completes one 400 m lap has run 400 m of distance but has zero displacement.
How do you calculate displacement with acceleration?
Use s = ut + ½at². For a ball thrown up at 20 m/s with a = −9.80665 m/s², after 3 s: s = 20 × 3 − ½ × 9.80665 × 9 = 60 − 44.13 = 15.87 m above the start. It reached the top at 2.04 s, so it actually travelled 20.39 m up and 4.52 m back down, a distance of 24.92 m.
Can displacement be negative?
Yes. In one-dimensional motion the sign shows direction relative to the positive direction you chose. A negative displacement means the object ended up on the negative side of its starting point.
How do I find displacement from coordinates?
Subtract the start coordinates from the end coordinates to get the components (Δx, Δy, Δz), then use the Pythagorean theorem for the magnitude and atan2(Δy, Δx) for the direction. Walking 30 m east and 40 m north gives a displacement of 50 m at 53.13° from east (bearing 36.87°).
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