Fill in any three of displacement (s), initial velocity (u), final velocity (v), acceleration (a) and time (t), and leave the other two empty. The calculator picks the right equations of motion, solves both unknowns with your numbers substituted, and draws the motion over time.
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Enter any 3 values, leave the 2 unknowns empty
Negative for slowing down or for gravity when up is positive
Enter your values to see the result.
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How to use the Kinematics Calculator (SUVAT)
Choose a positive direction (for example up or forward) and use negative values for the opposite way.
Enter exactly three known values and leave the two unknowns empty.
Pick the units for displacement, velocity, acceleration and time.
Press Solve to get both unknowns and the equations used.
Check the chart and table to see how position and velocity change.
The five equations of motion
Equation
Leaves out
Use it when you don't know or need…
v = u + at
s
the displacement
s = ut + ½at²
v
the final velocity
s = vt − ½at²
u
the initial velocity
s = ½(u + v)t
a
the acceleration
v² = u² + 2as
t
the time
All five assume constant acceleration along a straight line. They come from integrating a constant acceleration: velocity grows linearly (v = u + at), and displacement is the area under the velocity-time graph, a trapezium of area ½(u + v)t.
Worked examples
Braking car. A car at 30 m/s stops in 45 m. Known: u = 30, v = 0, s = 45; unknown a and t. Without t: a = (v² − u²) / (2s) = (0 − 900) / 90 = −10 m/s². Without a: t = 2s / (u + v) = 90 / 30 = 3 s.
Ball thrown upward. u = 15 m/s, a = −9.80665 m/s², and at the top v = 0. Then t = (v − u) / a = 1.53 s and s = (v² − u²) / (2a) = 225 / 19.61 = 11.47 m.
Two solutions. The same ball is 10 m above the launch point twice. With s = 10, u = 15, a = −9.80665 and v, t unknown, v² = 225 − 196.13 = 28.87, so v = ±5.37 m/s at t = 0.98 s (going up) and t = 2.08 s (coming down).
Sign conventions and tips
Choose one positive direction and stick to it. Every displacement, velocity and acceleration pointing the other way is negative.
Slowing down means acceleration opposite to velocity, which gives a negative a when the motion is in the positive direction.
Use consistent units. The calculator converts everything to SI internally (m, m/s, m/s², s) and converts the answers back to the units you picked.
Split multi-stage motion. If the acceleration changes (speed up, cruise, brake), solve each stage separately and use the final velocity of one stage as the initial velocity of the next.
Frequently asked questions
What are the SUVAT equations?
They are the five equations of motion for constant acceleration: v = u + at, s = ut + ½at², s = vt − ½at², s = ½(u + v)t and v² = u² + 2as. Here s is displacement, u initial velocity, v final velocity, a acceleration and t time. Each equation leaves out one of the five quantities.
How do I know which kinematic equation to use?
Find the quantity you neither know nor need, and use the equation that does not contain it. For example, if time is not given and not asked for, use v² = u² + 2as. With three known values, any two unknowns can be found this way, which is exactly what the calculator does.
Why are there two answers sometimes?
When you solve for a velocity from v² = u² + 2as, the square root has a positive and a negative root. Both can be physical: a ball thrown upward passes the same height once going up and once coming down. The calculator lists every solution with a time of zero or more.
Do the equations work for falling objects?
Yes. Use a = −9.80665 m/s² (or −32.17 ft/s²) if up is positive, or +9.80665 if you take down as positive, and ignore air resistance. For example, a ball thrown up at 15 m/s reaches its highest point (v = 0) after 1.53 s at 11.47 m.
What is the difference between displacement and distance in kinematics?
Displacement s is the change in position, with a sign for direction. Distance is the total path length. They differ when the object reverses direction during the time interval; the calculator reports both.
When do the SUVAT equations not apply?
Only when acceleration is not constant, for example a car with changing throttle, a falling object with significant air drag, or circular motion. In those cases you need calculus or a numerical method, or you can apply SUVAT to short pieces where acceleration is nearly constant.
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.