Kinematics Calculator (SUVAT)
Enter any three SUVAT variables to solve for the remaining two. Supports displacement, velocity, acceleration, and time.
What are kinematics equations?
Kinematics is the branch of physics that describes motion without considering the forces that cause it. The four kinematic equations relate five variables: displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t). Given any three of these five values, you can calculate the remaining two.
These equations assume constant (uniform) acceleration, which covers many real-world scenarios: objects in free fall (constant gravitational acceleration), vehicles accelerating or braking at a steady rate, and objects sliding on surfaces with constant friction. For non-constant acceleration, calculus-based methods are needed.
The four equations
- v = u + at — Final velocity from initial velocity, acceleration, and time.
- s = ut + (1/2)at squared — Displacement from initial velocity, time, and acceleration.
- v squared = u squared + 2as — Final velocity from initial velocity, acceleration, and displacement (no time needed).
- s = (u + v)/2 * t — Displacement from average velocity and time.
How to use this tool
Enter any three of the five kinematic variables and the calculator solves for the remaining two. Select which variable to solve for, or let the tool auto-detect based on which fields are filled. Results include both the numerical answer and the equation used.
Free fall as a special case
Free fall is kinematics with a = g (approximately 9.81 m/s squared downward). A dropped object (u = 0) falls a distance s = (1/2)gt squared. After 1 second: 4.9m. After 2 seconds: 19.6m. After 3 seconds: 44.1m. The velocity increases linearly: 9.8 m/s after 1 second, 19.6 m/s after 2 seconds, and so on (ignoring air resistance).
Frequently asked questions
Do the equations work for objects moving upward?
Yes. Use a positive initial velocity for upward motion and negative acceleration (gravity pulling down). The equations automatically handle the object slowing down, stopping at the peak, and falling back. The peak height occurs when v = 0, and the total flight time is twice the time to reach the peak (for symmetric trajectories).
What happens when acceleration is not constant?
These equations only apply when acceleration is constant. For variable acceleration (like a rocket burning fuel, or an object encountering increasing air resistance), you need to use calculus — specifically, integrate the acceleration function over time. Numerical methods can also approximate the motion in small time steps.