SUVAT Calculator

Calculate kinematic variables for uniformly accelerated motion

Input any three SUVAT variables to solve for the remaining two.

Last updated: December 24, 2025

Solver Tip

Input exactly three values to solve for the remaining two. If no results appear or you see Infinity, the scenario is physically impossible.

SUVAT Variables

Displacement (s)

More info

Initial Velocity (u)

More info

m/s

Final Velocity (v)

More info

m/s

Acceleration (a)

More info

m/s²

Time (t)

More info

sec

1Velocity Change

v = u + at

2Average Velocity

s = \frac{(u + v)t}{2}

3Main Equation

s = ut + \frac{1}{2}at^2

4From Final Velocity

s = vt - \frac{1}{2}at^2

5Without Time

v^2 = u^2 + 2as

sDisplacement

uInitial Velocity

vFinal Velocity

aAcceleration

tTime

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Introduction / Overview

This SUVAT calculator helps you solve 1D motion problems with constant acceleration. You enter any three of the five kinematics variables, and the calculator solves for the remaining two.

✅ SUVAT works best when acceleration is constant (or approximately constant) — like a car accelerating steadily, a ball under gravity (ignoring air resistance), or a trolley rolling down a gentle ramp.

Who typically uses SUVAT?

GCSE / A-level / AP Physics students practicing constant-acceleration questions
Teachers building quick classroom examples or checking answers
Engineers and hobbyists doing back-of-the-envelope motion estimates

Need full 2D motion (angles, trajectories, range)? Check our Projectile Motion Calculator. If you’re reviewing how you performed on a past paper, our Test Grade Calculator can help.

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How to Use / Quick Start Guide

The calculator is designed for the classic “three knowns, two unknowns” workflow. Use the unit selectors next to each input if you need to switch between meters/feet or seconds/minutes.

Pick a sign convention

Decide what counts as the positive direction (e.g., “up” or “to the right”). Keep that choice consistent.

Enter exactly three values

Input any three of $s,\,u,\,v,\,a,\,t$ . The other two fields will become results.

Sanity-check the output

Watch out for negative time or impossible combinations. If your scenario is inconsistent, the calculator will show a warning under the relevant field.

Example A: find final velocity

Inputs: $u=0\ \text{m/s}$ , $a=2\ \text{m/s}^2$ , $t=5\ \text{s}$

v = u + at

⟹

v = 0 + (2)(5)

⟹

v = 10\ \text{m/s}

Interpretation: after 5 seconds of steady acceleration, the object is moving at $10\ \text{m/s}$ .

Example B: find displacement

Inputs: $u=4\ \text{m/s}$ , $v=12\ \text{m/s}$ , $t=3\ \text{s}$

s = \frac{(u+v)t}{2}

⟹

s = \frac{(4+12) \times 3}{2}

⟹

s = 24\ \text{m}

Interpretation: the average velocity is $(u+v)/2 = 8\ \text{m/s}$ , so over 3 seconds you travel 24 m.

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The SUVAT formulas - velocities

Start with a simple velocity–time picture. With uniform acceleration, velocity changes in a straight line, so the acceleration is the slope.

Acceleration as a rate of change

a = \frac{\Delta v}{\Delta t}

If velocity changes from $u$ to $v$ over time $t$ (starting at $t=0$ ), then:

a = \frac{v-u}{t}

→

v = u + at

This is the velocity update formula: initial velocity plus “acceleration × time”.

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The SUVAT formulas — displacement

Displacement $s$ is “where you end up relative to where you started”. It can be zero even if you moved around and came back.

With constant acceleration, the velocity–time graph is a straight line. Displacement is the area under that line:

\text{area} = (\text{average velocity})\times (\text{time})

s = \frac{(u+v)t}{2}

If you substitute $v=u+at$ into the average-velocity formula, you get a version that uses $u, a, t$ :

s = ut + \frac{1}{2}at^2

And if you instead substitute $u=v-at$ , you get the “final-velocity” form:

s = vt - \frac{1}{2}at^2

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The SUVAT formulas — skipping time

Sometimes you want an equation that doesn’t involve time. A common trick is to eliminate $t$ by combining the velocity and displacement formulas.

One clean route (shown as a chain):

t = \frac{v-u}{a}

→

s = \frac{(u+v)t}{2}

→

2as = (u+v)(v-u)

v^2 = u^2 + 2as

This is the “no time” equation — great when you know displacement but not how long it took.

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What does SUVAT stand for?

SUVAT is just an acronym for the five variables in constant-acceleration motion:

The letters

s

— displacement

u

— initial velocity

v

— final velocity

a

— acceleration

t

— time

Fun fact: the order is basically a mnemonic choice. It could have been “TUAVS”… but we’re glad it wasn’t.

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Some simple SUVAT questions

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Study tip:

The calculator is great for checking your work — but you’ll learn faster if you try the algebra first, then use the calculator as a backstop. In an exam, you can’t rely on a website.

Q1. From rest to the doorway

Starting from rest, you cover $s=7\ \text{m}$ in $t=4\ \text{s}$ . What speed are you moving at when you reach the door?

Step 1: Find acceleration from displacement

s = ut + \frac{1}{2}at^2

⟹

7 = 0 + \frac{1}{2}a(4^2) = 8a

⟹

a = 0.875\ \text{m/s}^2

Step 2: Find final velocity

v = u + at

⟹

v = 0 + (0.875)(4)

⟹

v = 3.5\ \text{m/s}

Answer: $v=3.5\ \text{m/s}$ .

Q2. The corridor sprint

You start from rest and accelerate at $a=0.75\ \text{m/s}^2$ for $s=50\ \text{m}$ . What is your final speed?

v^2 = u^2 + 2as

⟹

v^2 = 0 + 2(0.75)(50) = 75

⟹

v = \sqrt{75} \approx 8.66\ \text{m/s}

Answer: $v\approx 8.66\ \text{m/s}$ .

Q3. Can the chaser catch you?

Two seconds after you start, someone begins from rest at the door and accelerates at $2\ \text{m/s}^2$ . Using your Q2 motion, will they catch you before you reach the end?

Use the calculator twice: once for you (to find the time to reach 50 m), and once for the chaser. The “who arrives first” answer is the one with the smaller $t$ .

Q4. What if you keep your speed?

Suppose you already have a nonzero speed when you enter the corridor. How does that change your chance of getting caught?

Hint: treat your starting speed as $u$ and solve for the required $t$ to cover 50 m.

“But Sir… why learn SUVAT if I can just use a calculator?”
The best answer is: learning SUVAT teaches you how to pick the right model, spot impossible inputs, and explain your reasoning. A tool can compute — but you still want to understand.

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FAQs

How can I calculate acceleration without time?

If you know $u$ , $v$ , and $s$ , you can use the no-time equation:

a = \frac{v^2 - u^2}{2s}

Example: $u=10$ , $v=20$ , $s=7.5$

a = \frac{v^2 - u^2}{2s}

⟹

a = \frac{20^2 - 10^2}{2 \times 7.5} = \frac{300}{15} = 20\ \text{m/s}^2

How many SUVAT equations are there?

There are five standard SUVAT equations for constant acceleration. They connect the five variables $s,\,u,\,v,\,a,\,t$ .

What are the SUVAT formulas?

v = u + at

s = \frac{(u+v)t}{2}

v^2 = u^2 + 2as

s = ut + \frac{1}{2}at^2

s = vt - \frac{1}{2}at^2

You can rearrange these to solve for different unknowns — the calculator does that rearrangement for you.

What is the acceleration of a car reaching 25 m/s in 5 s from rest?

Use:

a = \frac{v-u}{t}

With $u=0$ , $v=25$ , $t=5$ :

a = \frac{25-0}{5} = 5\ \text{m/s}^2

Why does the calculator sometimes warn that the scenario is impossible?

Most often, it’s because the inputs contradict constant-acceleration motion — for example, asking for a change in velocity with $t=0$ , or an unreachable displacement that would require taking the square root of a negative number.

Can SUVAT handle negative values?

Yes — negative values are often necessary. For instance, if you choose “up” as positive, gravity is $a\approx -9.81\ \text{m/s}^2$ . The key is consistent sign convention.

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Limitations / Disclaimers

SUVAT assumes a 1D model with constant acceleration. If acceleration changes with time, or motion is truly 2D/3D, results may be misleading.

Units: the calculator includes unit selectors, but you’re responsible for choosing the correct unit.
Interpretation: if the calculator shows a warning, treat it as a prompt to re-check your sign convention and given values.
Education: this tool is for learning and estimation; it does not replace your course notes or professional judgement.
Exams: we don’t recommend trying to bring an online calculator into an exam.

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