🏁 Kinematic Equations (SUVAT) Calculator
Enter any three of u, v, a, s and t, and the calculator picks the right kinematic equations and solves for the remaining two.
Enter any three of the five, leave two blank
u (given)
0
m/s
v
29.4
m/s
a (given)
9.8
m/s²
s
44.1
m
t (given)
3
s
Solves the five kinematic (SUVAT) equations: v = u+at · s = ½(u+v)t · v² = u²+2as · s = ut+½at² · s = vt−½at². Constant acceleration. 🔒 In your browser.
How the kinematic equations (suvat) calculator works
For constant acceleration, five variables, initial velocity u, final velocity v, acceleration a, displacement s and time t, are linked by the SUVAT equations: v = u + at, s = ½(u+v)t, v² = u² + 2as, s = ut + ½at², and s = vt − ½at². Given any three, the tool determines which equations apply and solves for the other two exactly.
The square root in v² = u² + 2as is exactly the kind of algebra chatbots get wrong; here the rearrangement is exact. Where a square root allows two signs, the positive root is shown, the other direction is equally valid depending on your sign convention.
Frequently asked questions
What are the SUVAT equations?
The five kinematic equations for constant acceleration: v = u + at, s = ½(u+v)t, v² = u² + 2as, s = ut + ½at², and s = vt − ½at². SUVAT stands for the variables s (displacement), u (initial velocity), v (final velocity), a (acceleration) and t (time).
How many values do I need to enter?
Exactly three. With any three of the five variables known, the other two are fully determined for constant acceleration.
Which equation should I use?
The one that contains your three known variables and the one you want. This tool selects it automatically, pick the missing quantities and it solves them.
Do these work for vertical motion and gravity?
Yes, set a to the acceleration due to gravity (about 9.8 m/s², or −9.8 if you take up as positive). Free fall and projectile vertical motion are SUVAT problems.
Why might there be two answers?
Equations with v² can give a positive or negative root (an object can pass a point moving forwards or backwards). The tool shows the positive root; interpret the sign from your chosen direction.
Do the SUVAT equations assume constant acceleration?
Yes. They are only valid when acceleration is constant. For changing acceleration you need calculus, not SUVAT.