β‘ Kinematics Calculator
Solve kinematic equations for v, a, t, d given any 3 variables.
Solved values are marked *
How to Use This Calculator
This calculator solves constant-acceleration motion problems. Enter the values you know among initial velocity, final velocity, acceleration, time, and displacement, and it finds the rest.
Decide your sign convention first. Usually forward and up are positive. Be consistent through the whole problem.
Enter the quantities you know: initial velocity v0, final velocity v, acceleration a, time t, or displacement d.
Click Calculate. The calculator picks the right SUVAT equation automatically and solves for the missing values.
Sanity-check the answer: velocities should have sensible magnitudes and displacement should point the way you expect.
The SUVAT Equations
These three equations describe all straight-line motion with constant acceleration, and each one omits exactly one variable. The first has no displacement, the second has no final velocity, and the third has no time. That structure is deliberate: with any three knowns you can always find an equation containing your unknown.
Constant acceleration is the key restriction. Gravity near Earth qualifies, a car braking smoothly qualifies, but a rocket burning fuel with changing mass does not. Within that restriction the equations are exact, not approximations, which is why they anchor the first month of every physics course.
Worked Example
Where This Comes Up
Kinematics is the grammar of motion, so it appears everywhere: braking distances for cars (a car at 30 m/s braking at 6 m/s^2 stops in 75 m), sprint analysis in sports science, elevator design, and every projectile problem, which is just horizontal and vertical kinematics running at the same time.
The number one error is sign inconsistency: treating gravity as positive in one equation and negative in another. Pick a convention and write it down. The second classic mistake is using these equations when acceleration is not constant, like a skydiver whose air resistance grows with speed. If the problem mentions drag, springs, or changing mass, SUVAT does not apply.
Frequently Asked Questions
What do the letters u, v, a, t, s stand for?
In the SUVAT equations, u is initial velocity, v is final velocity, a is constant acceleration, t is time, and s is displacement. This calculator labels initial velocity v0 and displacement d.
When can I use these equations?
Only when acceleration is constant. That covers free fall, cars braking steadily, and objects on frictionless inclines. If acceleration changes during the motion, you need calculus instead.
Is displacement the same as distance?
Only for straight-line motion in one direction. If the object turns around, displacement is the net change in position while distance is the total path length.
What does negative acceleration mean?
It means acceleration opposite to the chosen positive direction, often called deceleration. The equations handle it fine as long as you keep the sign consistent.
Which equation should I use?
Pick the one that includes your three knowns and your unknown: v = u + at (no s), s = ut + 1/2at^2 (no v), v^2 = u^2 + 2as (no t).