About this tool
Kinematics / SUVAT Calculator is a free, in-browser tool that solves problems of straight-line motion under constant acceleration. Enter any three of the five variables — displacement s, initial velocity u, final velocity v, acceleration a and time t — and it works out the missing two instantly. Nothing is uploaded; every calculation runs locally as you type.
It uses the four standard SUVAT equations: v = u + a·t, s = u·t + ½a·t², v² = u² + 2·a·s, and s = ½(u + v)·t. From your three known values the tool picks the equation that isolates each unknown. When the time step is quadratic (s, u and a known) it solves ½a·t² + u·t − s = 0 with t = (−u ± √(u² + 2·a·s)) / a and keeps the physical, non-negative root.
Use it for projectile drops, braking distances or ramp problems: for free fall set the acceleration to g = 9.81 m/s². All five inputs use SI units — metres, metres per second, metres per second squared and seconds.
Frequently asked questions
How many values do I need to enter?
Exactly three of the five (s, u, v, a, t). With three knowns the constant-acceleration equations fully determine the remaining two. Fewer than three is under-determined; the tool asks for three before it solves.
Which equations does it use?
The four SUVAT equations: v = u + at, s = ut + ½at², v² = u² + 2as, and s = ½(u+v)t. It automatically chooses the one that isolates each unknown from the three values you supplied.
How does it handle the quadratic case for time?
When s, u and a are known, time comes from ½at² + ut − s = 0, so t = (−u ± √(u² + 2as))/a. The tool takes the smallest non-negative root, which is the physically meaningful first time the displacement is reached.
How do I model free fall?
Set acceleration a to g = 9.81 m/s² (downward). Enter a positive value if you treat downward as positive, or −9.81 if upward is positive; keep your sign convention consistent for u, v and s. Everything runs in your browser.
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