Kinematics Equation Solver (SUVAT)

Enter any three known values to compute the remaining kinematics variables. Includes step-by-step derivations and a velocity–position graph.

Inputs (SI units)
Results
s
u
v
a
t
Steps (Derivation)
Graphs
t
v–s shows velocity vs displacement. Use v–t and s–t for time-based views.
Comparisons
Color u a tend send
Notes
  • Equations: v = u + a t; s = u t + ½ a t²; s = v t − ½ a t²; v² = u² + 2 a s; s = (u+v)/2 · t.
  • Provide any 3 variables to solve remaining unknowns. Time is assumed non-negative; the solver selects physically meaningful roots where applicable.
  • All calculations run locally in your browser.
FAQ

Which variables can be negative?
Velocities and acceleration can be positive or negative depending on direction; time is taken as ≥ 0.

Why are there two possible solutions?
Quadratic equations (e.g., s = u t + ½ a t²) can produce two times. The tool reports the non-negative solution; if both are valid you’ll see a note in steps.

What about variable acceleration?
These equations assume constant acceleration. For variable a(t), use calculus or numerical integration.

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About This Tool & Methodology

Solves kinematics equations (SUVAT) under constant acceleration using SI units. Computes unknowns from provided variables and shows relationships between them.

Learning Outcomes

  • Connect displacement, velocity, acceleration, and time.
  • Practice consistent units and conversions.
  • Test scenarios to build intuition (e.g., zero initial velocity).

Authorship

  • Author: Anish Nath — Follow on X
  • Last updated: 2025-11-19

Trust & Privacy

  • All calculations run locally.