📐 SUVAT Calculator
Kinematics equations calculator
How to Use This Calculator
Enter Known Values
Input at least 3 of the 5 SUVAT variables (s, u, v, a, t). Leave the fields you want to calculate blank. The calculator will automatically determine which values to compute based on what you provide.
Understanding the Variables
s = Displacement (m) - change in position; u = Initial velocity (m/s) - starting speed; v = Final velocity (m/s) - ending speed; a = Acceleration (m/s²) - rate of change of velocity; t = Time (s) - duration of motion.
Click Calculate
Press the "Calculate" button. The calculator uses the appropriate SUVAT equations to find the missing values. You need at least 3 known values to calculate the others.
Review Results
The calculated values are displayed in the results section. Use these for solving kinematics problems, analyzing motion, or completing physics homework.
Formula
v = u + at
s = ut + ½at²
v² = u² + 2as
s = ½(u + v)t
Where:
s = Displacement (m)
u = Initial velocity (m/s)
v = Final velocity (m/s)
a = Acceleration (m/s²)
t = Time (s)
These equations apply to motion with constant acceleration.
Example 1: Car accelerating from rest
Given: u = 0 m/s, a = 5 m/s², t = 10 s
Step 1: Calculate final velocity
v = u + at = 0 + 5 × 10 = 50 m/s
Step 2: Calculate displacement
s = ut + ½at² = 0 + ½ × 5 × 10² = 250 m
The car reaches 50 m/s and travels 250 m in 10 seconds.
Example 2: Object with initial and final velocity
Given: u = 10 m/s, v = 30 m/s, s = 200 m
Step 1: Calculate acceleration
v² = u² + 2as
30² = 10² + 2a(200)
900 = 100 + 400a
a = 800 / 400 = 2 m/s²
Step 2: Calculate time
t = (v - u) / a = (30 - 10) / 2 = 10 s
Understanding SUVAT Equations
• All SUVAT equations assume constant acceleration
• You need at least 3 known variables to solve for the others
• v = u + at: Relates velocity to time and acceleration
• s = ut + ½at²: Displacement in terms of time
• v² = u² + 2as: Relates velocities to displacement (no time)
• s = ½(u + v)t: Average velocity formula
About SUVAT Calculator
The SUVAT Calculator is an essential physics tool for solving kinematics problems involving motion with constant acceleration. SUVAT stands for the five key variables in kinematics: Displacement (s), Initial velocity (u), Final velocity (v), Acceleration (a), and Time (t). These variables are related by four fundamental equations of motion that describe how objects move when acceleration is constant. This calculator automatically selects and applies the appropriate SUVAT equations to calculate missing values when you provide at least three known variables. It's an invaluable tool for students, engineers, and anyone working with motion analysis.
When to Use This Calculator
- Physics Homework: Solve kinematics problems involving constant acceleration motion
- Motion Analysis: Calculate missing motion parameters when you know some of the SUVAT variables
- Engineering Calculations: Analyze motion in mechanical systems, vehicles, or projectiles
- Sports Physics: Calculate velocities, distances, and times for accelerating objects in sports
- Educational Purposes: Learn how SUVAT equations work and practice solving kinematics problems
- Problem Solving: Quickly find missing values in motion problems without manual equation manipulation
Why Use Our Calculator?
- ✅ Automatic Equation Selection: Chooses the right SUVAT equation based on your inputs
- ✅ Flexible Input: Enter any 3+ variables and calculate the rest
- ✅ All Four Equations: Uses all standard kinematics equations for comprehensive solutions
- ✅ Educational Value: Shows which equations are used and how they're applied
- ✅ Time-Saving: Solves complex kinematics problems instantly
- ✅ Physics Standard: Uses the standard SUVAT notation recognized worldwide
Common Applications
Physics Education: Help students understand kinematics and solve motion problems. The SUVAT equations are fundamental to physics education and this calculator makes them accessible.
Vehicle Analysis: Calculate acceleration, velocities, and distances for vehicles. Useful for analyzing car performance, braking distances, and acceleration times.
Projectile Motion: Analyze motion of projectiles (though full projectile motion requires 2D SUVAT). Calculate vertical motion components using SUVAT equations.
Mechanical Systems: Analyze motion in machines, robotics, and mechanical devices where objects move with constant acceleration.
Tips for Best Results
- Constant Acceleration: SUVAT equations only work for constant acceleration; variable acceleration requires calculus
- Minimum 3 Variables: You need at least 3 known values to calculate the others; 4 known values verify the solution
- Sign Convention: Use consistent signs: positive for forward/upward, negative for backward/downward
- Units Matter: Ensure all inputs use consistent units (meters, seconds, m/s, m/s²)
- One-Dimensional: SUVAT applies to 1D motion; for 2D motion, apply SUVAT separately to x and y components
Frequently Asked Questions
What does SUVAT stand for?
SUVAT is an acronym for the five key variables in kinematics: s = Displacement, u = Initial velocity, v = Final velocity, a = Acceleration, t = Time. These variables are used in the four fundamental equations of motion for constant acceleration.
Why do I need at least 3 variables?
Each SUVAT equation relates 4 variables. If you know 3 variables, you can solve for the 4th using one equation. With only 2 known variables, you have multiple unknowns and can't get a unique solution. Having 4 known variables allows you to verify calculations.
What if acceleration is not constant?
SUVAT equations only work for constant acceleration. If acceleration varies, you need calculus (integration) to solve motion problems. For variable acceleration, use v = ∫a dt and s = ∫v dt.
Can I use SUVAT for 2D motion?
SUVAT applies to one-dimensional motion. For 2D motion (like projectiles), apply SUVAT separately to the x-component (horizontal) and y-component (vertical) of motion. Each component has its own SUVAT variables.
What's the difference between displacement and distance?
Displacement (s) is the change in position (vector), while distance is the total path length (scalar). For straight-line motion, they're the same. SUVAT uses displacement, which can be negative if motion is in the opposite direction.
Which equation should I use?
The calculator automatically selects the appropriate equation based on your inputs. Generally: use v = u + at when you have u, v, a, t; use v² = u² + 2as when time is unknown; use s = ut + ½at² for displacement with time; use s = ½(u + v)t when acceleration is unknown.