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Kinematic Equations Calculator

Solve one-dimensional constant-acceleration motion problems. Enter any supported set of three known values for u, v, a, t, and s to calculate the missing values.

kinematic-equations

Enter any three known values for constant-acceleration one-dimensional motion. Leave the unknowns blank.

Solved values
—
Initial velocity u—
Final velocity v—
Acceleration a—
Time t—
Displacement s—
Equation used—

What kinematic equations solve

Kinematic equations describe one-dimensional motion with constant acceleration. OpenStax presents these relationships in its motion equations for constant acceleration section. The calculator uses the standard symbols u for initial velocity, v for final velocity, a for acceleration, t for time, and s for displacement.

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

Worked example

A car starts at 5 m/s, accelerates at 2 m/s² for 6 s. u = 5 m/s a = 2 m/s² t = 6 s v = u + at = 5 + 2(6) = 17 m/s s = ut + ½at² = 5(6) + ½(2)(6²) = 66 m

Important limitation

This calculator assumes straight-line motion with constant acceleration. It is not for changing acceleration, curved paths, air resistance, or full projectile-motion problems unless the horizontal and vertical directions are handled separately.

Common questions

  • The common constant-acceleration equations are v = u + at, s = ut + 1/2at^2, v^2 = u^2 + 2as, and s = ((u+v)/2)t.
  • u means initial velocity.
  • v means final velocity.
  • s means displacement, not total distance traveled.
  • Use them when acceleration is constant and motion is one-dimensional.
  • Yes. Negative acceleration means acceleration acts in the negative direction based on your sign convention.
  • No. Displacement can be positive, negative, or zero depending on direction.
  • It can help if you split projectile motion into horizontal and vertical components, but it is not a full projectile calculator.