Constant-Acceleration Kinematics Calculator
Choose a formula, enter known values, and calculate instantly. Use SI units for best results (meters, seconds).
What is kinematics?
Kinematics is the branch of mechanics that describes motion without focusing on the forces causing it. In plain language, it answers questions like: How far did something move? How fast is it going? and How long did the motion take? This is essential in physics, engineering, sports science, robotics, and vehicle safety analysis.
This kinematics calculator is built around constant acceleration motion in one dimension. That means acceleration does not change over time, and the motion is tracked along a straight line.
Variables used in this calculator
- s = displacement (meters, m)
- u = initial velocity (m/s)
- v = final velocity (m/s)
- a = acceleration (m/s2)
- t = time (seconds, s)
Core equations (SUVAT)
These are the standard equations for motion with constant acceleration:
- v = u + at
- s = ut + 1/2 at2
- a = (v - u)/t
- t = (v - u)/a
- s = ((u + v)/2)t
- s = (v2 - u2)/(2a)
How to use this kinematics calculator
- Pick the quantity you want to solve for from the dropdown.
- Enter the known values in the generated input fields.
- Click Calculate to see the result and formula used.
- Click Reset to clear values and start over.
Tip: Keep units consistent. If you enter distance in meters and time in seconds, velocity will be in m/s and acceleration in m/s2.
Worked examples
Example 1: Final velocity
A cyclist starts at 3 m/s and accelerates at 1.2 m/s2 for 5 s. Using v = u + at:
v = 3 + (1.2 × 5) = 9 m/s
Example 2: Braking displacement
A car slows from 22 m/s to 0 m/s at -4 m/s2. Use s = (v2 - u2)/(2a):
s = (0 - 484)/(-8) = 60.5 m
So the stopping distance is 60.5 meters (ignoring reaction time and road conditions).
Common mistakes to avoid
- Mixing units (e.g., km/h with m/s).
- Sign errors when acceleration is negative (deceleration).
- Using constant-acceleration formulas for changing acceleration.
- Forgetting direction in one-dimensional motion.
Unit conversion quick reference
| Quantity | From | To SI |
|---|---|---|
| Speed | km/h | multiply by 0.27778 to get m/s |
| Speed | mph | multiply by 0.44704 to get m/s |
| Distance | km | multiply by 1000 to get m |
| Time | minutes | multiply by 60 to get s |
When not to use this tool
This calculator is not ideal if acceleration changes continuously (for example, rocket flight with varying mass/thrust, or drag-dominated high-speed motion). In those cases, calculus-based models or numerical simulations are better.
FAQ
Can I use negative values?
Yes. Negative velocity or acceleration can represent direction, depending on your coordinate setup.
What does displacement mean?
Displacement is the change in position from start to finish. It includes direction, unlike total path length.
Is this the same as a projectile calculator?
Not exactly. Projectile motion is two-dimensional (horizontal + vertical components). This tool handles one-dimensional constant-acceleration motion.