Motion analysis
What is displacement?
Displacement is the change in position between an initial point and a final point. It includes direction and can be positive, negative, or zero.
Formula
Displacement formula
DisplacementΔx = x₂ − x₁
- Δx is displacement.
- x₁ is initial position.
- x₂ is final position.
Worked example
Calculate displacement from two positions
- Initial position is 10 metres.
- Final position is 35 metres.
- Apply Δx = 35 − 10.
- Displacement is 25 metres.
Important distinction
Displacement versus distance
Distance measures the total path travelled, while displacement compares only the starting and ending positions. A complete round trip can have a positive distance but zero displacement.
Direction
Why displacement can be negative
A negative value means the final position lies in the selected negative direction relative to the initial position.
Applications
Where displacement is used
- Linear motion experiments.
- Position-time graph analysis.
- Average velocity calculations.
- Projectile and free-fall problems.
- Introductory kinematics exercises.
Related tools
Continue your motion analysis
Use the Average Velocity Calculator to calculate displacement per unit time.
Use the Average Speed Calculator when total distance rather than displacement is required.
Interpretation limits
Assumptions and limitations
Displacement represents the straight-line change from an initial position to a final position. It does not describe the full path travelled or the total distance covered during the motion.
Position values must use the same reference frame, coordinate direction, and compatible units. A positive or negative result indicates direction according to the selected sign convention.
Questions and answers
Displacement FAQ
What formula does the displacement calculator use?
It uses displacement equals final position minus initial position: Δx = x₂ − x₁.
Can displacement be negative?
Yes. Negative displacement means the final position is in the negative direction relative to the initial position.
Can displacement be zero?
Yes. Displacement is zero when the final position is the same as the initial position.
What is the difference between distance and displacement?
Distance measures total path length, while displacement measures the straight-line change in position and includes direction.