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Kinematics Calculator

Free web tool: Kinematics Calculator

Kinematics Calculator

Solve for any kinematic variable using the equations of motion.

Displacement (d)

30 m

Equation Used

d = v₀t + ½at²

Kinematic Equations

  • v = v₀ + at
  • d = v₀t + (1/2)at²
  • v² = v₀² + 2ad
  • d = (v + v₀)/2 × t

About Kinematics Calculator

The Kinematics Calculator solves for any one of the five standard kinematic variables — displacement (d), initial velocity (v₀), final velocity (v), acceleration (a), and time (t) — using the equations of uniform linear motion. Select the variable you want to find, enter the known four values, and the result appears instantly along with the specific equation that was applied. This covers the core SUVAT equations used in classical mechanics.

Physics students, engineering candidates preparing for exams, and anyone working through projectile motion or vehicle dynamics problems will find this tool immediately useful. The calculator picks the appropriate kinematic equation automatically: v = v₀ + at for final velocity, d = v₀t + ½at² for displacement, a = (v − v₀) / t for acceleration, and the quadratic formula for time when acceleration is non-zero. Error messages appear clearly when a valid solution does not exist, such as when the discriminant is negative.

Everything runs inside your browser with no server communication. Input values are parsed from the numeric fields, the solver function applies the correct equation, and the result is rendered in real time. The tool also shows the equation used for each calculation, making it transparent and educational. All five kinematic units are displayed (m, m/s, m/s², s) to keep track of dimensions.

Key Features

  • Solves for any of 5 kinematic variables: displacement (d), initial velocity (v₀), final velocity (v), acceleration (a), time (t)
  • Automatically selects the correct kinematic equation based on the unknown variable selected
  • Displays the equation used (e.g. d = v₀t + ½at²) alongside the numerical result
  • Handles the quadratic time formula t = (−v₀ + √(v₀² + 2ad)) / a when acceleration is nonzero
  • Clear error messages for invalid inputs such as zero acceleration when solving for time with zero initial velocity
  • Consistent SI units throughout: meters, m/s, m/s², and seconds
  • 100% client-side processing — no server, no account needed, works offline
  • Dark mode support and responsive layout for desktop, tablet, and mobile

Frequently Asked Questions

What kinematic equations does this calculator use?

The calculator uses the four standard SUVAT equations: v = v₀ + at, d = v₀t + ½at², v² = v₀² + 2ad (rearranged), and d = (v + v₀)/2 × t. It selects the equation that isolates the unknown variable using only the four provided known values.

How do I solve for displacement (d)?

Select "Displacement (d)" from the Solve For dropdown. Enter the initial velocity (v₀), acceleration (a), and time (t). The calculator applies d = v₀t + ½at² and returns the displacement in meters.

Can the calculator find time (t) when acceleration is zero?

Yes. When a = 0 and v₀ is nonzero, the calculator uses t = d / v₀. If both acceleration and initial velocity are zero, the system is indeterminate and an error message is shown.

What happens when the discriminant is negative while solving for time?

A negative discriminant (v₀² + 2ad < 0) means there is no real solution for time given those inputs. The calculator displays a "No real solution" error message rather than returning a complex number.

Does the calculator work for deceleration (negative acceleration)?

Yes. Enter a negative value for acceleration. The equations handle negative a correctly — for example, a braking vehicle decelerating from 20 m/s to rest can be solved by entering v = 0, v₀ = 20, and a negative a value.

What units does the calculator use?

All calculations use SI units: displacement in meters (m), velocities in meters per second (m/s), acceleration in meters per second squared (m/s²), and time in seconds (s). Convert your inputs to these units before entering them.

Can I use this calculator for projectile motion problems?

Yes, for the vertical and horizontal components separately. For the vertical component set a = −9.8 m/s² (gravity) and solve for height, time of flight, or vertical velocity. For the horizontal component set a = 0 and solve for range or time.

Why does the calculator only show one equation?

With 5 variables and one unknown, only one independent kinematic equation is needed to solve the problem. The calculator shows the equation that directly gives the unknown from the four known values, avoiding redundant steps.