Displacement CalculatorSUVAT · s = ut + ½at²
Displacement is an object’s change in position: how far it ends up from where it started, and in which direction. With constant acceleration, s = ut + ½at². This calculator solves the three SUVAT forms of displacement and finds the size and angle of a 2D displacement vector from its x and y components.
Formula verified against OpenStax — University Physics, Volume 1 · OpenStax — University Physics, Volume 1
By Manzoor Ahmad · Pharmacist & calculator developerReviewed & updated
Find the displacement
Pick the SUVAT form that matches your known values.
Step-by-step working
What is displacement?
Displacement is the straight-line change in an object’s position, from its starting point to its final point, including direction. It is measured in metres.
Unlike distance, displacement ignores the route taken. A runner who completes a full lap has run 400 m but has zero displacement. In kinematics it is the “s” in the SUVAT equations.
Quick answers
How do I find displacement with initial velocity, acceleration and time?
Plug the values into s = ut + ½at². A sprinter leaving the blocks from rest at 4 m/s² covers ½ × 4 × 2² = 8 m in the first two seconds. Keep acceleration negative if the object is slowing down.
What is a SUVAT calculator?
It solves the five constant-acceleration equations linking s, u, v, a and t. This page handles the three that return s; the final velocity calculator and the acceleration calculator cover the rest of the set.
How do you calculate resultant displacement?
Add the components first, then use Pythagoras: |s| = √(Δx² + Δy²). Walk 6 km east and 2.5 km south and you are 6.5 km from your start, on a bearing of about 112.6°.
Why is my displacement smaller than the distance I travelled?
Displacement only counts where you ended up relative to where you began. Any detour, U-turn or zig-zag adds distance but not displacement, which is why the calculator flags direction reversals.
Displacement formulas (SUVAT)
The first three need constant acceleration. The vector form applies to any two perpendicular components.
| Symbol | Meaning | SI unit |
|---|---|---|
| s | Displacement | m |
| u | Initial velocity | m/s |
| v | Final velocity | m/s |
| a | Constant acceleration | m/s² |
| t | Time | s |
| Δx, Δy | Perpendicular components | m |
How to find displacement
- List the SUVAT values you know (s, u, v, a, t) and the one you need.
- Choose the equation that contains your known values and s, but not the missing one.
- Substitute in SI units, keeping the signs that show direction.
- For 2D motion, combine perpendicular components with Pythagoras and find the angle with tan⁻¹(Δy/Δx).
Worked example: three routes to the same answer
A cyclist moving at 5 m/s accelerates at 2 m/s² for 4 s, reaching 13 m/s. How far has she moved?
s = ½(u + v)t = ½(5 + 13)×4 = 36 m
s = (v² − u²) ÷ 2a = (169 − 25) ÷ 4 = 36 m
All three equations give 36 m, a useful way to check your work. In 2D mode, walking 3 km east then 4 km north gives a displacement of 5 km at a compass bearing of 36.87°.
Displacement vs distance
Distance is the length of the path you actually travelled; displacement is the straight-line arrow from start to finish. They are equal only for straight-line motion that never reverses.
| Distance | Displacement | |
|---|---|---|
| Quantity type | Scalar | Vector |
| Depends on path? | Yes | No: only start and end |
| Can be zero after moving? | No | Yes, if you return to the start |
| Can be negative? | No | Yes (direction) |
Common mistakes to avoid
- Dropping the sign of acceleration when an object slows down. Deceleration must enter the equation as a negative a.
- Using SUVAT when acceleration changes. These equations are only valid for constant acceleration.
- Reporting distance when displacement is asked for, or the reverse, after an object turns around.
Manzoor Ahmad
Pharmacist turned Web Developer & Calculator Engineer · 13+ years in web developmentI’m a pharmacist by training who turned into a full-time tech geek, and for 13+ years I’ve designed and coded web tools. My pharmacy degree included physical pharmacy and pharmaceutics — states of matter, heat, flow and reaction kinetics — so the physics behind these tools is familiar ground, not a new hobby.
I’m not a physicist, so I don’t ask you to take my word for it: every formula on this page is traced to an open university textbook or NIST reference data, and the calculator is tested against published worked examples before it goes live. Spot an error? Tell me and it will be fixed and dated on the next update.
Displacement Calculator: frequently asked questions
With constant acceleration, s = ut + ½at². Equivalent forms are s = ½(u + v)t and s = (v² − u²) ÷ 2a. For constant velocity, s = vt.
Displacement is a vector: it has both magnitude and direction. Distance is the corresponding scalar.
Yes. If an object returns to its starting point, its displacement is zero even though it has travelled some distance.
Calculate the area between the graph line and the time axis. Areas below the axis count as negative displacement.
Use Pythagoras: |s| = √(Δx² + Δy²). The direction is θ = tan⁻¹(Δy ÷ Δx), adjusted for the correct quadrant.
SUVAT stands for the five variables of uniformly accelerated motion: s (displacement), u (initial velocity), v (final velocity), a (acceleration) and t (time).
The metre (m), the same unit as distance.
References & sources
- OpenStax — University Physics, Volume 1 — Ch. 3.4, Motion with Constant Acceleration
- OpenStax — University Physics, Volume 1 — Ch. 2, Vectors
- HyperPhysics, Georgia State University
Disclaimer: This calculator is an educational tool built on idealised textbook models. It is not a substitute for professional engineering or safety calculations.