Solve the five SUVAT equations of motion. Enter any 3 of s, u, v, a, t and find the missing one, with full working shown.
Each equation leaves out exactly one variable. The solver picks the equation whose missing variable is the one you did not enter:
| If you don't know | Equation used |
|---|---|
| s (and solving for v, u, a or t) | v = u + a·t |
| v (and solving for s, u, a or t) | s = u·t + ½·a·t² |
| t (and solving for s, u, v or a) | v² = u² + 2·a·s |
| u (and solving for s, v, a or t) | s = v·t − ½·a·t² |
| a (and solving for s, u, v or t) | s = ½·(u + v)·t |
Enter exactly 3 known values; the variable you are solving for and one more stay blank. Signs follow one consistent direction: negative means backwards along your axis.
v = u + a·t = 0 + 3×6 = 18 m/s
s = u·t + ½·a·t² = 0 + ½×3×6² = 54 m
Try it above: solve for v with u = 0, a = 3, t = 6 — then solve for s with the same inputs.
SUVAT is a memory aid for the five quantities in the constant-acceleration equations of motion: s = displacement (m), u = initial velocity (m/s), v = final velocity (m/s), a = acceleration (m/s²), t = time (s). If you know any three, the equations let you solve for a fourth.
The five SUVAT equations are: (1) v = u + at, (2) s = ut + ½at², (3) v² = u² + 2as, (4) s = vt − ½at², and (5) s = ½(u + v)t. Each equation leaves out exactly one variable, which is how you choose between them.
Use the equation that does NOT contain the variable you neither know nor want. For example, if you do not know t and do not need it, use v² = u² + 2as. This calculator picks the right equation automatically from the three values you enter.
Equations (2) and (4) give a quadratic in t with up to two positive roots. The smaller root is the first time the object reaches that displacement; the larger root means it passes the same point again on the way back (for example a ball thrown upward). This calculator reports both.
When a = 0 the motion is uniform (constant velocity): v = u and s = u·t. The calculator handles this automatically instead of dividing by zero, and tells you when the inputs become indeterminate or inconsistent.
Yes. The sign indicates direction along your chosen axis: negative velocity means moving backwards, negative acceleration means slowing down (or speeding up backwards). Keep one consistent sign convention for the whole problem.
From v² = u² + 2as you get v = ±√(u² + 2as). Both roots are physical: the object can pass the same displacement moving in either direction with the same speed. The calculator shows the direction matching your initial velocity first.
It means the quadratic's discriminant is negative, so your inputs describe something physically impossible — for example asking when a ball reaches a height above its maximum. Check your numbers and sign convention rather than forcing an answer.
Displacement: m, km, ft, mile. Velocity: m/s, km/h, mph. Acceleration: m/s², km/h², ft/s², mph/s. Time: s, min, h. Everything is converted to SI units before solving, and the answer is converted back to the unit you select.
The physics is the same: GLBB (Gerak Lurus Berubah Beraturan) is the Indonesian curriculum name for uniformly accelerated linear motion. This page is written in English for the UK GCSE and A-level “suvat” syllabus. For the Indonesian GLBB displacement calculator, see our Kalkulator Perpindahan.
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