SUVAT Constant-Acceleration Motion Calculator

SUVAT constant-acceleration motion calculator

This SUVAT calculator is designed for one-dimensional motion where acceleration stays constant over the whole interval you are analysing. The five symbols represent displacement s, initial velocity u, final velocity v, acceleration a, and time t. If you know any three values from the same interval, the remaining two can usually be recovered with the classic SUVAT relationships, provided you keep the sign convention and units consistent from start to finish.

How to use this SUVAT calculator for one straight-line interval

• Enter any three SUVAT values from a single motion segment, then leave the other fields blank so the calculator can infer the missing quantities. Mixing values from two stages, such as acceleration followed by braking, tends to produce contradictory results because the equations assume one constant acceleration throughout.
• Choose one positive direction before you type anything. A car moving to the right, a falling object, a lift moving upward, or a ball thrown downward can all be described cleanly once every value is measured against the same axis.
• Keep units consistent across the whole scenario. Metres, seconds, metres per second, and metres per second squared are the usual choice, but any coherent set works if every number belongs to the same unit system. If your inputs come from a worksheet or experiment log, double-check that you have not mixed kilometres with metres or minutes with seconds.
• If the motion changes phase — for example, accelerate, coast, then brake — solve each phase separately instead of forcing several accelerations into one SUVAT interval. The calculator is built to work on a single stretch of constant acceleration, so a phased journey should be broken into separate entries.

SUVAT variable definitions for straight-line motion

s = displacement (m) — straight-line change in position over the interval; positive or negative depending on your chosen direction, not necessarily the total path length travelled.
u = initial velocity (m/s) — velocity at the start of the interval you are modelling, before any acceleration during that interval has acted.
v = final velocity (m/s) — velocity at the end of that interval, which may be greater or smaller than u depending on the sign of a.
a = constant acceleration (m/s²) — the same acceleration throughout the interval; if it changes, the motion is no longer a single SUVAT case.
t = elapsed time (s) — the duration of the interval, usually reported as a non-negative value, even when the displacement or velocity is negative.

Core SUVAT equations for constant-acceleration motion

These SUVAT equations are the backbone of the calculator, and they only apply cleanly when acceleration stays constant for the entire interval. They link the same five variables in different combinations, so the solver can usually work forward from the values you know without requiring you to rearrange the algebra by hand. When more than one equation could be used, the most stable route is often the one that avoids an unnecessary quadratic or a division by a value that is close to zero.

The equations are connected, not independent. In practice, the calculator chooses the route that matches your inputs: velocity pairs are usually handled with v = u + at, displacement with known time fits s = ut + ½at², and the velocity-displacement form v² = u² + 2as is useful when time is unknown, awkward to measure, or hidden inside a later step of the problem. The average-velocity form s = (u + v)t/2 is often the quickest check when you already know both endpoint speeds, because it lets you compare the distance implied by the start and finish velocities with the distance implied by the time.

How to interpret SUVAT results on your chosen axis

• In SUVAT results, signs describe direction, not quality: A negative value of s, u, v, or a means the quantity points opposite your chosen positive axis. That is normal in SUVAT work and is often exactly what you expect for downward motion, reverse motion, or a segment where the object has turned around.
• Acceleration and slowing down are not the same thing: If velocity and acceleration share the same sign, speed increases; if they have opposite signs, speed falls. A negative acceleration can therefore mean either braking or speeding up, depending on direction, so it is the sign relationship that matters rather than the word "negative" by itself.
• Time roots can come in pairs: When the calculator solves s = ut + ½at² for t, the quadratic may produce two answers. One can describe the moment the object passes a position on the way out, and the other can describe a later pass on the way back. Use the root that fits the physical story and the interval you intended to analyse.
• No real solution means the interval is inconsistent: A negative discriminant usually points to mixed units, a sign convention mistake, or a scenario that is not actually one constant-acceleration interval. It can also mean that the values you entered describe different phases of motion, so it is worth rechecking the setup before assuming the equations are wrong.

Worked example: SUVAT car motion from rest

Example: Take forward as positive. A car starts from rest, so u = 0 m/s, and then accelerates uniformly at a = 2.5 m/s² for t = 8 s. Because the acceleration is constant, the calculator can find both the final speed and the displacement from the same SUVAT interval. This is a textbook situation for the equations because no extra forces, stops, or changes of direction need to be modelled separately.

1. Final velocity: v = u + at = 0 + (2.5)(8) = 20 m/s.
2. Displacement: s = ut + ½at² = 0·8 + ½·2.5·8² = 1.25·64 = 80 m.

So this car reaches 20 m/s after 8 s and covers 80 m while the acceleration remains constant. If the road model changed halfway through — for example if the driver lifted off the throttle or began braking — you would treat that as a separate SUVAT problem and solve the later phase on its own. The example also shows why a consistent sign convention matters: the same calculation would still work if the car were moving in the opposite direction, as long as every value used the same axis.

Which SUVAT equation should you use?

The table below matches common SUVAT input combinations to the equations that usually solve them most directly. It is not a rulebook; it is a quick guide for choosing the path that keeps the algebra simplest and the chance of sign mistakes lowest.

SUVAT assumptions and limitations

• One dimension only: This SUVAT calculator treats the motion as a straight line. For projectile motion or any 2D path, split the problem into horizontal and vertical components and solve each axis separately, then combine the results only after both axes are finished.
• Acceleration must stay constant: The equations stop being exact if acceleration changes with time, speed, engine output, drag, or thrust. In those cases, the best approach is to break the motion into simpler intervals so that each one has its own constant acceleration.
• Resistive forces are not modelled on their own: Air resistance, friction that changes with speed, and similar effects usually make the acceleration non-constant unless they have already been folded into a single effective a. If you need those forces explicitly, this calculator is only the first step in the analysis.
• Your sign convention matters: If you switch positive direction partway through a problem, the inputs can look contradictory even when the motion is physically sensible. Decide the axis once, write it down if needed, and keep that convention for every line of the calculation.
• Quadratic time ambiguity is real: Solving s = ut + ½at² can produce two times. The physically meaningful root is the one that lies in the interval you actually care about and matches the direction of travel, so always check whether the earlier or later root is the real answer to your question.
• Inputs should describe one coherent interval: Entering values from different stages of the motion can over-constrain the system. If the numbers do not belong to the same stretch of constant acceleration, the solver cannot make them agree, even if each number is correct on its own.

When the result still looks wrong, read the inputs as a story rather than as isolated numbers. Ask which direction is positive, whether the object is speeding up or slowing down, and whether the interval begins and ends at clearly defined moments. Those checks usually expose the mistake faster than changing equations at random.