Kinematics Solver — SUVAT Equations
Solve all four SUVAT kinematic equations simultaneously. Enter any 3 of the 5 variables (displacement, initial velocity, final velocity, acceleration, time) and the solver finds the remaining values instantly. No signup, runs entirely in your browser.
Enter any 3 known values. Leave unknowns blank.
How to Use the Kinematics Solver
- 1Identify which 3 of the 5 SUVAT variables you know: displacement (s), initial velocity (u), final velocity (v), acceleration (a), time (t).
- 2Enter them in SI units — meters, m/s, m/s², seconds. Leave the two unknowns blank.
- 3Use negative values for anything opposing your chosen positive direction — deceleration is a negative a.
- 4The solver applies whichever SUVAT equations fit and fills in the remaining two variables.
Worked Example: Emergency Stop from 100 km/h
A car travels at 100 km/h — first convert to SI: 100 / 3.6 ≈ 27.8 m/s. The driver brakes hard on dry asphalt, decelerating at 7 m/s² (about 0.7 g, a realistic maximum for road tires). The knowns are u = 27.8, v = 0, a = −7. The solver applies v² = u² + 2as to get the stopping distance: s = u² / (2 × 7) = 772.8 / 14 ≈ 55.2 m, and v = u + at for the stopping time: t = 27.8 / 7 ≈ 4.0 s.
The quadratic term is what surprises people: because s grows with u², a car at 50 km/h (13.9 m/s) needs only 13.8 m to stop — one quarter of the distance at double the speed, not half. And this is pure braking distance; add roughly one second of driver reaction time (another 27.8 m at highway speed) for the true stopping gap. Change u in the solver and watch how steeply the distance climbs.
Kinematics Tips
Free fall
For free fall, set a = 9.81 m/s² (downward), u = 0, and enter either the height (s) or time (t). The solver finds the impact velocity and time of fall.
Braking distance
For a car braking to rest, set v = 0 and enter initial speed and deceleration (negative a). The solver gives stopping distance (s) and time to stop.
Sign convention
Choose a positive direction (usually the direction of initial motion). Displacement, velocity, and acceleration opposing that direction should be entered as negative values.
Multiple phases
For motion in multiple phases (e.g. accelerating then coasting), solve each phase separately. The final velocity of one phase becomes the initial velocity of the next.
Frequently Asked Questions
What are the SUVAT equations?
SUVAT equations describe motion under constant acceleration. The four equations are: (1) v = u + at, (2) s = ut + ½at², (3) v² = u² + 2as, (4) s = ½(u+v)t. These relate displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t).
How many known values do I need?
You need exactly 3 of the 5 variables to solve for the other 2. The calculator automatically identifies which equations can be applied and solves sequentially until all variables are found.
What does SUVAT stand for?
SUVAT is a mnemonic: S = displacement, U = initial velocity, V = final velocity, A = acceleration, T = time. These are the five variables governed by the equations of uniform (constant) acceleration.
Can this handle deceleration?
Yes. Enter acceleration as a negative value for deceleration. For example, a car braking from 30 m/s with a = −5 m/s² will come to rest (v = 0) in 6 seconds over 90 meters.
What if I get a contradictory result?
If the values are physically inconsistent (e.g. final velocity greater than initial with negative acceleration), the solver may not find a valid solution. Check that your values are physically realistic and consistent with constant acceleration.
Is my data stored?
No. All calculations run locally in your browser. No data is sent to any server.