SUVAT is a set of five kinematic equations used in physics to describe the motion of an object moving with constant (uniform) acceleration. Each letter stands for a variable: S = displacement, U = initial velocity, V = final velocity, A = acceleration, T = time.

How many SUVAT variables do I need to know?

You need to know exactly 3 of the 5 SUVAT variables to solve for the other 2. With fewer than 3 known values, the equations are under-determined and cannot be solved.

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Section 01

What is SUVAT?

SUVAT is a collection of five physics equations that describe the motion of an object moving with constant (uniform) acceleration in a straight line. The name SUVAT is an acronym formed from the five variables the equations use.

💡 SUVAT meaning: Each letter represents a physical quantity — Sisplacement, Unitial velocity, Velocity (final), Acceleration, and Time. Together, these five variables fully describe any uniformly accelerated motion.

What Does Each Letter in SUVAT Stand For?

Variable	Meaning	SI Unit	Symbol	Can Be Negative?
s	Displacement — the distance travelled in a given direction	metres (m)	m	✓ Yes (direction matters)
u	Initial velocity — speed at the start of the motion	metres per second (m/s)	ms⁻¹	✓ Yes
v	Final velocity — speed at the end of the time period	metres per second (m/s)	ms⁻¹	✓ Yes
a	Acceleration — rate of change of velocity	metres per second squared (m/s²)	ms⁻²	✓ Yes (deceleration is negative)
t	Time — duration of the motion	seconds (s)	s	✗ No (time is always positive)

When Can You Use SUVAT?

The object is moving with constant (uniform) acceleration — acceleration does not change during the motion
Motion is in a straight line (one dimension)
You know at least 3 of the 5 variables
Common examples: free fall, braking vehicles, projectile components, objects on inclined planes

⚠️ SUVAT does NOT apply when: acceleration is changing, the object moves in a curve, or the motion involves variable forces. For those cases, use calculus-based kinematics.

Section 02

The 5 SUVAT Equations

There are five SUVAT equations of motion. Each equation uses four of the five variables, leaving out one. You choose the equation that includes your three known values and the unknown you want to find.

Equation 1

v = u + at

Missing: s

Relates final velocity to initial velocity, acceleration and time. Use when displacement is not needed.

Equation 2

s = ut + ½at²

Missing: v

Finds displacement using initial velocity, acceleration and time. Final velocity not required.

Equation 3

v² = u² + 2as

Missing: t

Relates velocities and displacement without using time. Very useful for distance problems.

Equation 4

s = ½(u + v)t

Missing: a

Calculates displacement using the average velocity. Best when acceleration is unknown.

Equation 5

s = vt − ½at²

Missing: u

Solves for displacement when initial velocity is unknown but final velocity is given.

SUVAT Equations Quick Reference Table

Equation	Formula	Finds	Missing Variable	Common Use
1	v = u + at	v or u or a or t	s	Speed after braking, free fall velocity
2	s = ut + ½at²	s or u or a or t	v	Stopping distance, projectile height
3	v² = u² + 2as	v or u or a or s	t	Distance to reach a speed
4	s = ½(u+v)t	s or u or v or t	a	Distance when acceleration is unknown
5	s = vt − ½at²	s or v or a or t	u	When initial velocity is unknown

Section 03

How to Use the SUVAT Calculator

Our SUVAT solver is designed to be fast and straightforward for GCSE, A-Level, and university physics students. Follow these steps:

1

Identify Your Known Values

Read your question carefully and write down which SUVAT variables are given. You must have exactly 3 known values to solve the problem.
2

Enter the Known Values

Type the known values into the corresponding input fields (s, u, v, a, or t). Leave the unknowns blank — do not enter 0 unless the variable is genuinely zero.
3

Set Direction Convention

Assign positive or negative signs consistently. Choose one direction as positive (usually upward or rightward). Deceleration and downward motion are negative.
4

Select Units

Choose SI units (metres, seconds) or imperial units (feet, seconds) depending on your problem.
5

Click Calculate

Press the Calculate button. The SUVAT calc instantly identifies the correct equation and computes both unknown values.
6

Review the Working

The calculator shows which equation was used and the full step-by-step working — perfect for checking your own solutions or learning the method.

💡 Pro tip: For projectile motion problems, run the SUVAT calculator twice — once for the horizontal component (a = 0) and once for the vertical component (a = −9.81 m/s²). The time value t links both calculations.

Section 04

SUVAT Worked Examples

The following worked examples show exactly how to apply the SUVAT equations calculator to real physics problems step by step.

Example 1 · Free Fall — Find Time to Hit the Ground

A ball is dropped from rest off a building 80 m tall. How long does it take to reach the ground?

s = 80 m u = 0 m/s a = 9.81 m/s² v = ? t = ?

Step 1: Three known values: s, u, a. Missing v and t. Use Equation 2: s = ut + ½at²
Step 2: Substitute: 80 = 0×t + ½ × 9.81 × t²
Step 3: Simplify: 80 = 4.905t²
Step 4: Solve for t: t² = 80 ÷ 4.905 = 16.31
Step 5: t = √16.31 = 4.04 s

✓ Answer: The ball takes 4.04 seconds to hit the ground.

Example 2 · Braking Car — Find Stopping Distance

A car travelling at 30 m/s brakes with a deceleration of 6 m/s². How far does it travel before stopping?

u = 30 m/s v = 0 m/s a = −6 m/s² s = ? t = ?

Step 1: Known: u, v, a. Time not needed. Use Equation 3: v² = u² + 2as
Step 2: Substitute: 0² = 30² + 2 × (−6) × s
Step 3: 0 = 900 − 12s
Step 4: 12s = 900
Step 5: s = 75 m

✓ Answer: The car stops after travelling 75 metres.

Example 3 · Acceleration — Find Final Velocity

A train starts from rest and accelerates at 1.5 m/s² for 20 seconds. What is its final velocity?

u = 0 m/s a = 1.5 m/s² t = 20 s v = ? s = ?

Step 1: Known: u, a, t. Use Equation 1: v = u + at
Step 2: Substitute: v = 0 + 1.5 × 20
Step 3: v = 30 m/s

✓ Answer: The train reaches 30 m/s after 20 seconds.

Section 05

Using SUVAT for Projectile Motion

Projectile motion is one of the most common applications of SUVAT equations at A-Level and university physics. The key is to split motion into two independent components and apply SUVAT to each separately.

Component	Acceleration (a)	Typical Known Values	What You Solve For
Horizontal (x)	a = 0 (no air resistance)	u_x, t	Horizontal displacement (range)
Vertical (y)	a = −9.81 m/s²	u_y, a, t (or s)	Max height, time of flight, final speed

Key Projectile Motion Rules

Horizontal and vertical motions are completely independent
The time of flight t is always the same for both components
At maximum height, vertical velocity = 0 (v_y = 0)
Take upward as positive: gravity gives a = −9.81 m/s²
Horizontal velocity is constant throughout (a_x = 0)

📐 Resolve the initial velocity first: If a projectile is launched at angle θ with speed u, the components are: u_x = u·cos(θ) and u_y = u·sin(θ). Then apply our SUVAT calculator separately to each component.

Section 06

Where Are SUVAT Equations Used?

SUVAT equations appear across physics, engineering, and real-world applications. Understanding where they apply helps you recognise which problems need a SUVAT solver.

🚗

Vehicle Braking

Calculate stopping distances and braking forces in road safety engineering.

⚽

Sports Science

Analyse projectile paths of balls, javelins, and athletes in biomechanics.

🚀

Rocket & Space

Model launch phases and re-entry where acceleration can be treated as roughly constant.

🏗️

Civil Engineering

Design elevators, rollercoasters, and sloped roads using kinematic equations.

📐

GCSE & A-Level Physics

Core topic for AQA, OCR, Edexcel, and WJEC physics curricula.

🔬

University Physics

Foundation for classical mechanics, dynamics, and kinematics modules.

Section 07

Common SUVAT Mistakes to Avoid

Even with a SUVAT calculator, understanding these common errors will help you set up problems correctly and interpret results accurately.

Mistake	What Goes Wrong	How to Fix It
Ignoring signs	Confusing deceleration with acceleration; upward and downward motions	Always define a positive direction first and stick to it throughout
Using wrong units	Mixing km/h with m/s gives wrong answers	Convert all values to SI units (m, s, m/s) before calculating
Entering 0 for unknown	The calculator treats 0 as a known value, not a blank	Leave truly unknown fields empty — only enter 0 if the variable genuinely equals zero
Applying SUVAT to variable acceleration	SUVAT only works for constant acceleration	Check if acceleration is uniform. If not, use calculus methods
Splitting projectile motion incorrectly	Applying gravity horizontally or treating components as linked	Horizontal: a = 0. Vertical: a = −9.81 m/s². They share only t
Forgetting ± in v² = u² + 2as	The square root gives two solutions; the wrong sign is chosen	Check physical context to decide which sign for v makes sense

Section 08

Frequently Asked Questions

Everything you need to know about the SUVAT calculator, SUVAT equations, and how to apply the SUVAT solver to physics problems.

What is SUVAT in physics?

SUVAT refers to the five variables used in classical kinematics equations: S (displacement), U (initial velocity), V (final velocity), A (acceleration), and T (time). The five SUVAT equations describe motion under constant acceleration and are a core topic in GCSE and A-Level physics.

How do you use a SUVAT calculator?

Enter any 3 of the 5 SUVAT values (s, u, v, a, t) into the corresponding fields and leave the unknowns blank. Click Calculate. The SUVAT solver automatically selects the correct equation, solves for both unknowns, and shows the full working — useful for both getting answers quickly and checking your own work.

What are the 5 SUVAT equations?

The five SUVAT equations are: (1) v = u + at — missing s; (2) s = ut + ½at² — missing v; (3) v² = u² + 2as — missing t; (4) s = ½(u+v)t — missing a; (5) s = vt − ½at² — missing u. Each equation contains four of the five variables and is chosen based on which variable is missing from the problem.

Can SUVAT be used for projectile motion?

Yes. For projectile motion, split the motion into horizontal (a = 0) and vertical (a = −9.81 m/s²) components and apply SUVAT equations to each component separately. The time value t is the same for both components and links the two calculations together.

What does s, u, v, a, t stand for?

s = displacement (metres), u = initial velocity (m/s), v = final velocity (m/s), a = acceleration (m/s²), t = time (seconds). Each represents a physical quantity used to describe uniformly accelerated motion in a straight line.

When can you NOT use SUVAT equations?

SUVAT equations require constant (uniform) acceleration. They cannot be used when acceleration is changing over time, in circular motion, when air resistance is significant and variable, or in problems involving varying forces. For those cases, use integration and differentiation (calculus-based kinematics).

Is the SUVAT calculator free to use?

Yes, our SUVAT calculator is completely free with no sign-up, no account, and no limits. It works on all devices — mobile, tablet, and desktop. Results are shown instantly with full working out displayed for every calculation.

How many SUVAT variables do I need to solve a problem?

You need exactly 3 known values to solve for the remaining 2 unknowns. With only 2 known values, the system is under-determined and cannot be solved. With all 5 known, no calculation is needed — you can verify consistency of the values.

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