SUVAT motion solver

Kinematic Equations Calculator

Solve constant-acceleration motion problems using four standard SUVAT equations.

SUVAT motion solver

Kinematic equations calculator

Select an equation and unknown variable, then enter the remaining known values.

Select a kinematic equation
What do you want to calculate?

Calculator guide

How this calculator works

Kinematic Equations Calculator solves motion problems involving velocity, acceleration, time, and displacement. It helps physics students, engineers, researchers, and laboratory users analyze objects moving with constant acceleration using fundamental equations of motion.

Formula explanation

Kinematic equations describe motion relationships between velocity, acceleration, time, and displacement.

Formula

v = u + at, s = ut + ½at², v² = u² + 2as, s = ½(u + v)t

Worked example

Example: Final velocity can be calculated when acceleration and time are known.

Assumptions

  • The object moves with constant acceleration.
  • Velocity, acceleration, time, and displacement values use compatible units.
  • The equations describe classical mechanics situations.
  • Air resistance and external forces are ignored in the ideal model.

Examples

  • Example: Calculate the final velocity of an accelerating object when initial velocity, acceleration, and time are known.
  • Example: Engineers use kinematic equations to analyze machine movement and controlled motion systems.

Common mistakes

  • Using equations outside valid conditions.
  • Mixing variables.
  • Ignoring constant acceleration requirements.

Variables

  • Initial velocity
  • Final velocity
  • Acceleration
  • Time interval
  • Displacement
  • Motion conditions
  • Reference units
  • Measurement values

Limitations

  • Does not accurately model motion with changing acceleration.
  • Results depend on accurate input measurements.

Scientific references

  • OpenStax University Physics: Kinematics
  • NIST SI Units and Measurement References
  • Classical mechanics principles

Content review

Reviewed by: ScienceCalcHub Physics Review Team | Last reviewed: 2026-08-30

Applications

  • Physics education
  • Projectile and motion analysis
  • Engineering calculations
  • Vehicle motion studies
  • Laboratory motion experiments
  • Scientific research applications

Frequently asked questions

What are kinematic equations used for?

Kinematic equations are used to calculate relationships between displacement, velocity, acceleration, and time for objects moving with constant acceleration.

When can kinematic equations be applied?

They can be applied when acceleration remains constant and the required motion variables are known.

What are the SI units used in kinematic equations?

Common SI units include meters for displacement, meters per second for velocity, meters per second squared for acceleration, and seconds for time.

Why are kinematic equations important in physics?

Kinematic equations help scientists and engineers predict motion behavior, analyze experiments, and design systems involving acceleration and movement.

Accuracy and transparency

Created and maintained by our editorial team

This physics calculator is maintained by the ScienceCalcHub Editorial Team. Its calculation logic is tested with representative inputs, while the supporting guidance is checked for formula clarity, units, assumptions, and common mistakes.

Written by
ScienceCalcHub Editorial Team
Reviewed by
ScienceCalcHub Scientific Review Team
Review standard
Formula accuracy, units, examples, and educational clarity

Learn more about our formula-review and correction process, explore our calculation methodology, or view our scientific references.

  • Calculation logic tested
  • Variables and units explained
  • Assumptions stated clearly
  • Corrections handled transparently

Constant-acceleration motion

What are kinematic equations?

Kinematic equations describe motion when acceleration remains constant. They connect displacement, initial velocity, final velocity, acceleration, and time.

These equations are commonly called SUVAT equations because each letter represents one motion variable.

SUVAT variables

Meaning of each variable

  • s is displacement in metres.
  • u is initial velocity in metres per second.
  • v is final velocity in metres per second.
  • a is acceleration in metres per second squared.
  • t is elapsed time in seconds.

Formula reference

Four kinematic equations

Velocity–timev = u + at

Displacement–times = ut + ½at²

Velocity–displacementv² = u² + 2as

Average-velocity forms = ½(u + v)t

Equation selection

How to choose the correct equation

Select an equation that contains the variable you want to calculate and the values you already know.

  • Use v = u + at when displacement is not required.
  • Use s = ut + ½at² when final velocity is not known.
  • Use v² = u² + 2as when time is not known.
  • Use s = ½(u + v)t when acceleration is not required.

Worked example

Calculate final velocity

An object has an initial velocity of 5 m/s, acceleration of 2 m/s², and moves for 4 seconds.

  1. Choose v = u + at.
  2. Substitute v = 5 + (2 × 4).
  3. Simplify v = 5 + 8.
  4. Final velocity is 13 m/s.

Worked example

Calculate displacement

An object starts at 5 m/s, accelerates at 2 m/s², and moves for 4 seconds.

  1. Choose s = ut + ½at².
  2. Substitute s = (5 × 4) + ½(2)(4²).
  3. Calculate s = 20 + 16.
  4. Displacement is 36 m.

Direction and signs

Positive and negative values

Velocity, acceleration, and displacement can be positive or negative depending on the selected direction. Use one direction as positive and keep that sign convention throughout the calculation.

Time must remain positive because it represents elapsed duration.

Validity

When not to use SUVAT equations

These equations assume constant acceleration. They should not be used directly when acceleration changes continuously with time or position.

For variable acceleration, calculus, numerical methods, or motion graphs may be required.

Related tools

Use the Acceleration Calculator for direct velocity-change calculations.

Use the Displacement Calculator to compare initial and final positions.

Use the Average Velocity Calculator to calculate displacement per unit time.

Use the Free Fall Calculator for vertical motion under gravity.

Questions and answers

Calculator FAQ

What are kinematic equations used for?

Kinematic equations are used to calculate relationships between displacement, velocity, acceleration, and time for objects moving with constant acceleration.

When can kinematic equations be applied?

They can be applied when acceleration remains constant and the required motion variables are known.

What are the SI units used in kinematic equations?

Common SI units include meters for displacement, meters per second for velocity, meters per second squared for acceleration, and seconds for time.

Why are kinematic equations important in physics?

Kinematic equations help scientists and engineers predict motion behavior, analyze experiments, and design systems involving acceleration and movement.