How to use the kinematics calculator
- Choose meters or feet for the labels.
- Fill in any three of the five boxes: displacement (s), starting velocity (u), final velocity (v), acceleration (a) and time (t). Leave the other two blank.
- Use a negative number for motion in the opposite direction, or for slowing down.
- Read the two unknown values. If two solutions fit, both are shown in a table.
Formula
v = u + a t
s = u t + a t^2 / 2
v^2 = u^2 + 2 a s
s = (u + v) t / 2
These are the equations of motion with constant acceleration. Any three known values give a system the others must satisfy, and the page picks the equations that solve for the two unknowns. Time is never negative.
From rest at 2 m/s2 for 5 seconds
Starting from rest (u = 0) with acceleration 2 for 5 seconds, v = 0 + 2 x 5 = 10 and s = 0.5 x 2 x 25 = 25. If u = 10 and v = 30 over 4 seconds, a = (30 - 10) / 4 = 5 and s = (10 + 30) x 4 / 2 = 80.
Two answers can fit. A ball thrown upward at 20 with acceleration -10 passes a height of 15 twice: at t = 1 with v = 10 on the way up, and at t = 3 with v = -10 on the way down. The page shows both.
Signs and direction
Pick a positive direction and keep to it. If up is positive, gravity is a negative acceleration, and an object thrown up has a positive starting velocity. A negative displacement means the object ended below where it started.
If the numbers describe something that cannot happen, such as a thrown ball that never reaches the height you gave, the page says so instead of showing a result.
Limits of the model
Everything here assumes straight-line motion with the same acceleration the whole time. Air drag, changing force and rotation are not modeled. For a launch at an angle, use the Projectile Motion Calculator, and for repeated swinging, the Pendulum Period Calculator. The Unit Converter changes units first.
Assumptions and limits
- Acceleration is constant and motion is along one straight line.
- Exactly three values must be filled in.
- Time must be greater than zero when you enter it.
- Only solutions with a time that is zero or more are shown.
Frequently asked questions
What are the kinematic equations?
They are four equations that link displacement, starting velocity, final velocity, acceleration and time for motion with constant acceleration. Knowing any three values lets you find the other two.
Why does the page show two answers?
Some inputs fit two motions, for example a ball passing the same height going up and coming down. Both are valid, so the table lists them.
Why must I fill in exactly three values?
Three values fix the motion. With fewer there are many answers, and with more the extra values could disagree with each other.
How do I handle slowing down?
Use a negative acceleration if the positive direction is the direction of motion. A car at 20 meters per second braking at 5 meters per second squared has a = -5.