SUVAT Equations Calculator (Kinematics)
By Santaji GadepatilinUpdated October 27, 2026
The SUVAT equations describe motion with constant acceleration using five quantities: displacement, initial velocity, final velocity, acceleration and time. Knowing any three lets you find the other two.
Displacement (s) (m) vs Time (t) (s) — other inputs held at your current values.
How to use the SUVAT equations calculator
Enter any three of u, v, a, t and s. The other two are solved automatically — press × on a field to choose which values are calculated.
The equations
v = u + at
s = ½(u + v)t
s = ut + ½at²
v² = u² + 2as
s = vt − ½at²
Worked example
u = 5 m/s, a = 2 m/s², t = 10 s:
- v = 5 + 2 × 10 = 25 m/s
- s = 5 × 10 + ½ × 2 × 10² = 150 m
Braking distance example
A car at 20 m/s (72 km/h) brakes at −8 m/s². Set u = 20, v = 0, a = −8: it stops in 2.5 s over 25 m. Doubling the speed to 40 m/s quadruples the distance to 100 m.
Which equation to use
Each SUVAT equation leaves out one of the five quantities:
| Equation | Missing |
|---|---|
| v = u + at | s |
| s = ½(u + v)t | a |
| s = ut + ½at² | v |
| s = vt − ½at² | u |
| v² = u² + 2as | t |
Pick the one that omits the quantity you neither know nor need. The calculator handles this automatically.
Stopping distance table
Reaction time 1.5 s, deceleration 7 m/s² (dry road):
| Speed | Thinking distance | Braking distance | Total |
|---|---|---|---|
| 30 km/h | 12.5 m | 5.0 m | 17.5 m |
| 50 km/h | 20.8 m | 13.8 m | 34.6 m |
| 70 km/h | 29.2 m | 27.0 m | 56.2 m |
| 100 km/h | 41.7 m | 55.1 m | 96.8 m |
| 120 km/h | 50.0 m | 79.4 m | 129.4 m |
On wet roads deceleration may drop to about 4–5 m/s², increasing braking distance by 40–75%.
Vertical motion
For objects thrown upward, use a = −9.81 m/s² (taking up as positive). A ball thrown up at 15 m/s reaches a maximum height of v² ÷ 2g = 11.5 m after 1.53 s.
Limits
SUVAT applies only when acceleration is constant. For changing acceleration, such as a car with varying throttle or an object with significant air resistance, use calculus or a numerical method.
Sign convention
Pick one direction as positive. Velocities and accelerations in the opposite direction are negative — for example, a = −9.81 m/s² for an object thrown upwards.
Frequently asked questions
What are the SUVAT equations?
Five equations linking displacement (s), initial velocity (u), final velocity (v), acceleration (a) and time (t) for constant acceleration.
How many values do I need?
Any three. The other two can then be calculated.
When do they not apply?
When acceleration changes, for example with air resistance at high speed. Then calculus or numerical methods are needed.
What does SUVAT stand for?
s (displacement), u (initial velocity), v (final velocity), a (acceleration) and t (time).
How do I find acceleration from distance and time?
If starting from rest, a = 2s ÷ t². A car covering 100 m in 10 s from rest accelerates at 2 m/s².