Solve any SUVAT kinematics equation — enter 3 of 5 variables (s, u, v, a, t) and calculate the remaining two. Includes velocity profile and motion table.
The five SUVAT equations describe motion under constant acceleration: s (displacement), u (initial velocity), v (final velocity), a (acceleration), and t (time). Each equation relates four of the five variables, so knowing any three lets you solve for the other two. These equations are the foundation of classical kinematics and apply to everything from falling objects to braking cars.
The five equations are: v = u + at, s = ut + ½at², s = vt − ½at², v² = u² + 2as, and s = ½(u+v)t. In practice, you rarely need to memorize all five — they're derived from the first two plus the definition of acceleration. However, choosing the right equation matters because each omits one variable, and you should pick the equation that omits the variable you neither know nor need.
This calculator automatically selects the correct equation based on which three variables you provide. It shows the time-resolved velocity and displacement profile and overlays a reference table of all five SUVAT equations so you can verify the approach.
Use this calculator when a motion problem has constant acceleration and you want the missing displacement, velocity, acceleration, or time without juggling the equation choice yourself. It is useful for homework checks, quick engineering estimates, and sanity-checking worked solutions.
v = u + at. s = ut + ½at². s = vt − ½at². v² = u² + 2as. s = ½(u+v)t.
Result: v = 29.43 m/s, s = 44.15 m
An object in free fall from rest for 3 seconds: v = 0 + 9.81×3 = 29.43 m/s, s = 0 + ½(9.81)(9) = 44.15 m. It falls about 44 meters and reaches ~106 km/h.
Start with the three values you know, then pick the SUVAT form that excludes the unknown you do not want. That keeps the algebra short and reduces sign mistakes.
Negative acceleration is not automatically wrong; it usually means the object is slowing down or moving opposite to the chosen positive direction.
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It is a compact label for displacement, initial velocity, final velocity, acceleration, and time in constant-acceleration motion.
Each equation leaves out one variable, so you can choose the form that matches the values you already know.
Yes, if you split the motion into horizontal and vertical components and treat each one as a separate constant-acceleration problem.
Then the SUVAT equations are not valid. You need a calculus-based model for velocity and position.
No. Displacement has direction and can be negative; distance is the total path length and is always positive.
Because the equations are often quadratic in time. One solution is usually the physically meaningful time you want.