Free SUVAT Calculator

What Is the SUVAT Calculator?

The SUVAT Calculator is a free online kinematics tool purpose‑built for motion with constant (uniform) acceleration. It works with the five classic SUVAT variables—displacement ($s$), initial velocity ($u$), final velocity ($v$), acceleration ($a$), and time ($t$)—and can instantly compute the two unknown values whenever three are provided. Instead of memorising which formula to apply or solving algebraic steps by hand, users simply enter their known data; the calculator selects the appropriate SUVAT equations and returns the results along with clear reasoning.

This Constant Acceleration Calculator is especially valuable for students studying GCSE A‑level physics, for anyone preparing for exams that include linear motion, or for professionals needing quick displacement or velocity calculations. With built‑in unit converters for length, speed, and time, the tool eliminates conversion errors and allows you to work in whatever units are most comfortable.

SUVAT Variables and the Five Equations

The acronym SUVAT stands for the five quantities that uniquely describe a uniformly accelerated straight‑line motion:

Variable	Meaning	Typical unit
$s$	Displacement (distance from start position)	metre (m)
$u$	Initial velocity (velocity at $t=0$)	m/s
$v$	Final velocity (velocity after time $t$)	m/s
$a$	Acceleration (constant rate of velocity change)	m/s²
$t$	Time elapsed since the start of observation	second (s)

These five quantities are linked by five standard formulas, each useful for a different combination of known variables:

Formula	Best used when you know…
$v = u + a t$	$u$, $a$, $t$
$s = \dfrac{1}{2}(u+v)t$	$u$, $v$, $t$
$s = u t + \dfrac{1}{2} a t^{2}$	$u$, $a$, $t$
$s = v t - \dfrac{1}{2} a t^{2}$	$v$, $a$, $t$
$v^{2} = u^{2} + 2 a s$	$u$, $a$, $s$ (no time needed)

No matter which three variables you start with, at least one of these equations can be used, and by combining them the remaining two unknowns become solvable.

Deriving the SUVAT Equations from a Velocity‑Time Graph

Under uniform acceleration a graph of velocity against time is a straight line. The slope of that line defines acceleration:

$$a = \dfrac{\Delta v}{\Delta t} = \dfrac{v - u}{t} \quad\Rightarrow\quad v = u + a t .$$

The displacement is the area under the graph. Because the shape is a trapezoid, its area equals the average velocity multiplied by the time:

$$s = \dfrac{u + v}{2} \times t .$$

Substituting $v = u + a t$ into this area formula gives $s = u t + \frac{1}{2} a t^{2}$. Substituting $u = v - a t$ yields $s = v t - \frac{1}{2} a t^{2}$. Finally, eliminating $t$ from the first two relations produces the time‑independent equation $v^{2} = u^{2} + 2 a s$. These five equations are not independent; any one can be obtained from the others, but having all five on hand makes problem solving more flexible.

Worked Example: Putting the Formulas into Practice

Consider a student who leaves a classroom and runs toward an exit.

Step 1 – From rest to the classroom door
Starting from rest ($u = 0$), she covers $7\ \text{m}$ in $4\ \text{s}$. Using $s = \frac{1}{2}(u+v)t$:

$$7 = \frac{1}{2}(0+v)\times 4 \quad\Rightarrow\quad v = 3.5\ \text{m/s}.$$

Her acceleration during this segment can be found with $v = u + a t$:

$$3.5 = 0 + a \times 4 \quad\Rightarrow\quad a = 0.875\ \text{m/s}^{2}.$$

Step 2 – Accelerating down the corridor
She now continues with a constant acceleration of $0.75\ \text{m/s}^{2}$ (initial velocity $3.5\ \text{m/s}$) and must cover $50\ \text{m}$. The final velocity at the exit is obtained from $v^{2} = u^{2} + 2 a s$:

$$v^{2} = (3.5)^{2} + 2 \times 0.75 \times 50 = 12.25 + 75 = 87.25 \quad\Rightarrow\quad v \approx 9.34\ \text{m/s}.$$

The time needed for this leg comes from $v = u + a t$:

$$9.34 = 3.5 + 0.75\,t \quad\Rightarrow\quad t \approx 7.79\ \text{s}.$$

Step 3 – Will the teacher catch her?
Two seconds after the student starts the corridor segment, a teacher bursts from the classroom door (same starting point) and accelerates from rest at $2\ \text{m/s}^{2}$. The question: does the teacher reach the student before she passes the exit?
The student’s total time to the exit is $7.79\ \text{s}$. In that time the teacher has been moving for $7.79 - 2 = 5.79\ \text{s}$. The teacher’s displacement is:

$$s_{\text{teacher}} = \frac{1}{2} \times 2 \times (5.79)^{2} \approx 33.5\ \text{m}.$$

Since $33.5\ \text{m} < 50\ \text{m}$, the teacher cannot catch the student before she reaches the exit. The SUVAT equations make this comparison quick and exact.

How to Use the SUVAT Calculator

1. Choose which three variables you know (any combination of $s$, $u$, $v$, $a$, $t$).
2. Enter the values in the calculator’s input fields. Use the built‑in unit converters if you need to switch between metric and imperial, or between different sub‑units.
3. The tool immediately computes the two missing variables, applying the correct SUVAT formula(s) and displaying intermediate steps.
4. Review the results and compare with your own analysis if desired.

Whether you are checking homework, preparing for a test, or designing a simple motion scenario, this kinematics calculator handles the algebra so you can focus on the physics.

Why This Constant Acceleration Calculator Stands Out

• Comprehensive – handles all five SUVAT equations automatically.
• User‑centred – clear interface with labelled inputs and real‑time updates.
• Educational – shows which formula was used and how the answer was derived.
• Flexible – supports any combination of known values, including cases where time is unknown.
• Free and online – no downloads, works on any device with a browser.

Whether you are a GCSE student, an A‑level candidate, or a curious learner, the SUVAT Equations Calculator gives you instant, reliable answers for straight‑line motion under constant acceleration.