CalcLibrary

Kinematics Calculator

Solve one-dimensional constant-acceleration motion when one of displacement, time, acceleration, initial velocity, or final velocity is missing. This is the generic 1D SUVAT-style tool: not constant-speed travel, not gravity-only free fall, and not 2D projectile motion.

Active equation
m/s²
km/h
km/h
Examples

A car slows from 72 km/h to 0 km/h at -6 m/s². The solver returns about 33.33 m of stopping displacement and keeps the negative acceleration visible instead of pretending this is a constant-speed trip.

Displacement / distance (s)
33.3333 m
Average velocity
36 km/h
Derived time
3.3333 s
Equation used
v^2 = u^2 + 2as, s = \frac{v^2-u^2}{2a}
Knowns used
u, v, a
Constant-acceleration estimate only. This page does not model changing acceleration, drag, friction details, 2D motion, or gravity-only shortcuts.

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Examples

How It Works

Formula

v=u+a⋅tv = u + a \cdot t

s=ut+12at2s = ut + \frac{1}{2}at^2

v2=u2+2asv^2 = u^2 + 2as

s=u+v2ts = \frac{u+v}{2}t

Variables

ss

Signed displacement / distance(m or ft)

tt

Time interval(s)

aa

Constant acceleration(m/s² or ft/s²)

uu

Initial velocity(m/s, km/h, ft/s, or mph)

vv

Final velocity(m/s, km/h, ft/s, or mph)

Pick the quantity you want to solve, then choose the set of three known motion values you already have. The page reveals only the relevant inputs for that branch, converts the entered units into one internal basis, and solves the missing quantity with the constant-acceleration equations that match those knowns.

The calculator is built around the standard constant-acceleration relationships v=u+atv = u + at, s=ut+12at2s = ut + \frac{1}{2}at^2, v2=u2+2asv^2 = u^2 + 2as, and s=u+v2ts = \frac{u+v}{2}t. Some branches use a direct rearrangement, while others solve a quadratic honestly when time or a signed velocity can have more than one valid answer. The result surface then shows the missing quantity first, plus average velocity, one derived cross-check, and the equation trail used for that branch.

The scope stays strict: one dimension, one constant acceleration over the whole interval, and only the values you entered. There is no drag model, no changing acceleration, no launch-angle decomposition, and no gravity shortcut hidden behind the scenes.

Frequently Asked Questions

01What does this kinematics calculator solve?
It solves one missing 1D constant-acceleration quantity at a time: displacement, time, acceleration, initial velocity, or final velocity. You choose the unknown first, then the calculator only shows known-value sets that can legitimately determine that target.
02Why does the page talk about displacement instead of only distance?
Because direction can matter in kinematics. If your chosen positive direction is forward or upward, negative displacement means the motion finishes in the opposite direction. If direction does not matter for your case, just enter a positive distance.
03Why can time sometimes have two answers?
Quadratic kinematics cases can describe the same signed displacement at two different times under constant acceleration. The calculator surfaces both non-negative solutions instead of silently hiding one, so you can tell the difference between the earlier and later event.
04How is this different from speed-distance-time, free-fall, and projectile motion?
Speed-distance-time assumes zero acceleration, so it fits constant or average-speed travel only. Free-fall is a gravity-only vertical motion shortcut. Projectile motion is a 2D launch model. This page is the generic 1D constant-acceleration solver when direction and changing velocity matter.
05When should I not use this calculator?
Do not use it when acceleration changes over the interval, drag matters, forces vary enough that constant acceleration is a poor approximation, or the motion needs 2D or vector-component handling. This tool stays intentionally narrow and honest about that scope.

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