Displacement
Find net position change from velocity-time relationships. Free online calculator with formulas and step-by-step solutions.
Key formula
s = vt, s = ut + (1/2)at^2, s = ((u + v)/2)t
How do you calculate displacement?
For constant velocity along a line, s = v t. Under constant acceleration, use s = u t + ½ a t² or s = ((u + v)/2) t. Displacement is net position change; distance traveled can be larger if the path turns back.
About this tool
Displacement is the net change in position — a vector from start to finish, not the total path length. This page keeps the constant-velocity and constant-acceleration relations visible so you pick the right expression for s.
How to use this calculator
- Choose the variable you want to solve for and confirm which values are already known.
- Enter inputs in consistent units before calculating so the formula is applied correctly.
- Check whether the result is physically reasonable by comparing it with the size of the inputs.
- Use the step-by-step breakdown to see how the equation was rearranged and evaluated.
Worked examples
Example 1: constant velocity
v = 12 m/s for t = 4.0 s in a straight line. s = v t = 48 m in the direction of v.
Example 2: from rest with a
u = 0, a = 2.0 m/s², t = 5.0 s. s = ut + ½at² = 0 + ½(2)(25) = 25 m.
Example 3: average of u and v
u = 10 m/s, v = 20 m/s, t = 6.0 s (constant a). s = ((10+20)/2)(6) = 90 m.
Frequently asked questions
What is the displacement formula?
Common forms: s = vt (constant v), s = ut + ½at², and s = ((u+v)/2)t under constant acceleration. Pick the form that matches your knowns.
Is displacement the same as distance?
No. Displacement is net position change (vector or signed). Distance is path length (always ≥ 0). They match only for straight one-way motion.
When do I use SUVAT instead?
When you have mixed knowns among s, u, v, a, t under constant acceleration, use the kinematics calculator and choose the matching equation.
Can displacement be negative?
Yes, if your positive axis points the other way. Negative s means net motion opposite the positive direction.
What units does displacement use?
Metres (m) in SI. Convert cm or km before substituting into s = vt or the SUVAT forms.