Displacement Calculator (Constant Acceleration)
Displacement calculator (SUVAT): s = v0·t + ½·a·t². Find distance, initial velocity, acceleration or time under constant acceleration.
s = v0 · t + ½ · a · t²
How to use this calculator
- Choose the quantity you want under “Solve for”.
- Type the known values and pick their units: any combination works.
- The result updates as you type. Open “Show the steps” to see the substitution.
Under constant acceleration the displacement is s = v₀·t + ½·a·t², one of the SUVAT equations of kinematics.
Solving for time requires the quadratic formula; the calculator returns the positive root. For free fall, use a = 9.81 m/s² with downward taken as positive.
Formula
s = v0 · t + ½ · a · t²
| Symbol | Quantity | Units |
|---|---|---|
| v0 | Initial velocity | m/s, km/h, mph, kn, ft/s, c |
| a | Acceleration | m/s², ft/s², g, Gal |
| t | Time | s, ms, µs, ns, min, h, d, wk, yr |
| s | Displacement | m, km, cm, mm, µm, nm, pm, Å, in, ft, yd, mi, nmi, au, ly |
Worked example
Given: v0 = 3 m/s · a = 2 m/s² · t = 5 s
s = v0·t + ½·a·t²
Result: s = 40 m
Frequently asked questions
How far does an object fall in 3 s?
From rest, s = ½ · 9.81 · 3² = 44.1 m (ignoring air resistance).
What are the SUVAT equations?
v = u + at, s = ut + ½at², v² = u² + 2as and s = ½(u + v)t, valid for constant acceleration.