Kinematics Equation Solver
Solve constant-acceleration motion problems from any three of displacement, initial and final velocity, acceleration and time, showing which equation was used and why.
Last reviewed by the Radiatus Cloud team
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Five variables, four equations, three knowns
Constant acceleration relates displacement, initial velocity, final velocity, acceleration and time. Each of the four standard equations omits exactly one of the five, which is what makes choosing between them mechanical: identify the variable you neither know nor want, and use the equation without it. Knowing any three determines the other two, and the difficulty in these problems is almost always identifying the three rather than doing the algebra.
The equations require constant acceleration
Every one of them assumes acceleration does not change during the interval. Free fall near the ground satisfies this closely when air resistance is negligible, and a car accelerating does not, since the acceleration varies with gear and speed. Where acceleration changes, the interval has to be split into pieces over which it is roughly constant, or calculus is needed. Applying the equations across a change in acceleration is the most common source of wrong answers.
Signs cause more errors than the algebra
Displacement, velocity and acceleration are all directional, and mixing conventions produces answers that are wrong in a way that looks plausible. Choosing one positive direction at the start and applying it consistently, including to gravity, resolves nearly all of it. An object thrown upwards has positive initial velocity and negative acceleration under the usual convention, and a negative final displacement simply means it ended below where it started.
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Frequently Asked Questions
How do I choose which equation to use?
Identify the variable you neither know nor need. Each of the four equations omits exactly one of the five quantities, so the one omitting your unwanted variable is the one to use.
What if acceleration is not constant?
These equations do not apply. Split the motion into intervals over which acceleration is roughly constant and solve each separately, or use calculus. Applying them across a change in acceleration is the most common source of wrong answers.
Why do I get two answers for time?
Because the displacement equation is quadratic, so an object can be at the same height twice, once going up and once coming down. Both are usually physically meaningful, and a negative time is not, since it refers to before the motion started.
Which direction is positive?
Whichever you choose, applied consistently. Upwards positive means gravity is negative; downwards positive means it is positive. Mixing the two within one problem produces answers that are wrong in a way that looks plausible.
Does mass affect these calculations?
No. Mass appears nowhere in the kinematic equations, which describe motion rather than its causes. It matters for the forces producing the acceleration and not for the relationship between the motion quantities themselves.
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How to Use
Enter any three of the five values to solve for the rest.
Disclaimer: This tool is provided "as is" without warranty of any kind. Results are for educational and utility purposes.