Kinematics Calculator (SUVAT equations)

Understanding the kinematics (SUVAT) calculator — concept and principle

Kinematics describes motion without asking what causes it. For motion in a straight line with constant acceleration, five quantities are linked: displacement s, initial velocity u, final velocity v, acceleration a and time t, often remembered as SUVAT. These equations are used in physics classes, for braking and acceleration estimates and for objects falling under gravity. Enter u, a and t to get the final velocity, displacement and average velocity.

Each second adds 9.81 m/s; distance grows with t², reaching 44.145 m at 3 s.

How it is calculated

Final velocity: v = u + at.
Displacement: s = ut + ½at².
Average velocity: v_avg = u + ½at, which equals (u + v) ÷ 2 and also s ÷ t.
A further relation, v² = u² + 2as, links the same quantities without time.

Units: velocity in m/s, acceleration in m/s², time in s, displacement in m. Signs matter: choose one direction as positive, and a negative a means acceleration in the opposite direction.

The principle

Constant acceleration means velocity changes by the same amount every second, so after t seconds it has changed by at; that is v = u + at. On a velocity–time graph this is a straight line, and displacement is the area under it: a rectangle u × t plus a triangle ½ × t × at, giving s = ut + ½at². Because velocity changes linearly, the average velocity is simply the midpoint of the start and end values. Eliminating t between the first two equations gives v² = u² + 2as.

Worked example

Inputs: u = 0 m/s, a = 9.81 m/s² (roughly free fall near Earth's surface), t = 3 s.
v = 0 + 9.81 × 3 = 29.43 m/s.
s = 0 × 3 + ½ × 9.81 × 3² = 44.145 m.
Average velocity = 0 + ½ × 9.81 × 3 = 14.715 m/s; check: 44.145 ÷ 3 = 14.715.
Check with v² = u² + 2as: 2 × 9.81 × 44.145 = 866.12 = 29.43².

Each point is the calculator re-run with only “Acceleration a (m/s²)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Acceleration a (m/s²)	Final velocity v (m/s)
2.45	7.3575
4.91	14.715
7.36	22.0725
9.81	29.43
12.3	36.7875
14.7	44.145
19.6	58.86

How to read the result

A positive v means the object is moving in the positive direction at time t; a negative v means it has reversed. Displacement is the net change in position, not the total distance travelled: if an object goes up and comes back, s can be zero even though it moved. For scale, 29.43 m/s is about 106 km/h, reached after only 3 s of free fall without air resistance.

Common mistakes

Mixing units such as km/h with m/s; divide km/h by 3.6 to get m/s.
Using inconsistent signs, for example a positive g for an object thrown upward that is defined as moving positive.
Applying the equations when acceleration is not constant.

Keep in mind: SUVAT equations assume constant acceleration along a straight line. Real vehicles, drag and changing forces break that assumption, so treat results as idealised estimates; safety-critical calculations such as stopping distances need validated methods and qualified professionals.

Frequently asked questions

How do I find the time if I know u, v and a?

Rearrange v = u + at to t = (v − u) ÷ a.

Why is it called SUVAT?

From the symbols s, u, v, a, t. Each of the standard equations leaves out one of the five quantities.

Can I use it for deceleration?

Yes. Enter a negative acceleration when the object slows down in the positive direction.

Sources: Halliday, D., Resnick, R. & Walker, J. Fundamentals of Physics (Wiley). · OpenStax, University Physics Volume 1, chapter 3 (Motion Along a Straight Line).

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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