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Acceleration Calculator

Use this acceleration calculator to solve constant acceleration (uniformly accelerated motion) problems in physics. It calculates acceleration, time, initial/final velocity, displacement, distance, average velocity, and average speed. The calculator also draws position vs. time and velocity vs. time graphs.

Tip: Select which 3 parameters you know (e.g., time + initial velocity + final velocity), enter values with units, then click Calculate. Use dot “.” as decimal separator.

How to use the acceleration calculator

  1. Choose the known parameters from the dropdown.
  2. Enter the highlighted (yellow) values.
  3. Select the correct units for each input.
  4. Click Calculate to compute all remaining values and generate graphs.

Kinematics formulas (SUVAT) used by this calculator

The equations below are valid when acceleration is constant. Here, v0 is initial velocity, v (or vf) is final velocity, a is acceleration, t is time, and Δx is displacement.

Displacement Δx = v0t + 1/2 a t2
Velocity v = v0 + at
Velocity (no time) v2 = v02 + 2aΔx
Average Velocity vavg = (Δx) / t
Average Speed average speed = distance / time

Acceleration formula: a = (vf − v0) / t

Acceleration calculator showing kinematics inputs and velocity-time and position-time graphs

Step-by-step solution (which equation to use)

This calculator solves constant acceleration (SUVAT) problems. Choose the set of known values, then follow the matching steps below.

Symbols: Δx = displacement, v0 = initial velocity, vf = final velocity, a = acceleration, t = time.

Known: Time + Initial Velocity + Final Velocity

  1. Compute acceleration: a = (vf − v0) / t
  2. Compute displacement: Δx = v0t + ½at²
  3. Average velocity: vavg = Δx / t
  4. Distance & average speed account for direction change (turning point) when applicable.

Known: Acceleration + Initial Velocity + Final Velocity

  1. Compute time: t = (vf − v0) / a
  2. Compute displacement: Δx = v0t + ½at²
  3. Average velocity: vavg = Δx / t
  4. Average speed uses distance / time (distance may differ from |Δx| if direction changes).

Known: Time + Acceleration + Final Velocity

  1. Compute initial velocity: v0 = vf − at
  2. Compute displacement: Δx = v0t + ½at²
  3. Average velocity: vavg = Δx / t

Known: Time + Acceleration + Initial Velocity

  1. Compute final velocity: vf = v0 + at
  2. Compute displacement: Δx = v0t + ½at²
  3. Average velocity: vavg = Δx / t

Known: Time + Initial Velocity + Displacement

  1. Compute acceleration: a = (Δx − v0t) / (½t²)
  2. Compute final velocity: vf = v0 + at
  3. Average velocity: vavg = Δx / t

Known: Time + Final Velocity + Displacement

  1. Compute acceleration: a = (Δx − vft) / (−½t²)
  2. Compute initial velocity: v0 = vf − at
  3. Average velocity: vavg = Δx / t

Known: Acceleration + Initial Velocity + Displacement

This case solves for time using a quadratic derived from Δx = v0t + ½at²:

  1. Rewrite: ½at² + v0t − Δx = 0
  2. Solve: t = (−v0 ± √(v0² + 2aΔx)) / a
  3. If both times are positive, there are two valid solutions (your page already supports two-solution selection).
  4. Then compute: vf = v0 + at

Known: Acceleration + Final Velocity + Displacement

This case solves for time using Δx = vft − ½at²:

  1. Rewrite: −½at² + vft − Δx = 0
  2. Solve (two solutions may exist): t = (vf ± √(vf² − 2aΔx)) / a
  3. Then compute: v0 = vf − at

Calculate acceleration, velocity, time and distance

KNOWN PARAMETERS
INPUT PARAMETERS
Displacement (Δx)
Initial Velocity (V0)
Final Velocity (Vf)
Elapsed Time (t)
Constant Acceleration (a)

Note: Use dot "." as decimal separator.

 


Results

RESULTS
Parameter Solution Unit
Displacement
Distance
Initial Velocity
Final Velocity
Average Velocity
Average Speed
Constant Acceleration
Time

Note: Default rounding is 5 decimal places.

How to interpret the graphs

  • Velocity vs time is a straight line for constant acceleration. The slope equals a.
  • Position vs time is a curve (parabola). Its curvature depends on a.
  • If the velocity line crosses zero, the object changes direction; this is why distance can be larger than |Δx|.

About the graphs: The calculator plots position vs. time and velocity vs. time using your input values and the constant-acceleration equations. These plots help you visually verify the motion model.

Definitions

Average Speed: Total distance traveled divided by the time elapsed.

Average Velocity: Displacement divided by the time elapsed.

Displacement: Change in position of an object from the starting point (can be negative). Displacement may not equal the total distance traveled.

Distance: Scalar length of the path traveled, always non‑negative.

Worked example

Suppose a car increases speed from 5 m/s to 25 m/s in 4 s.

  • Acceleration: a = (25 − 5) / 4 = 5 m/s²
  • Displacement: Δx = v0t + ½at² = 5·4 + ½·5·16 = 20 + 40 = 60 m
  • Average velocity: vavg = Δx / t = 60 / 4 = 15 m/s

You can verify this by selecting Time + Initial Velocity + Final Velocity in the calculator and entering v0=5, vf=25, t=4 with units m/s and s.

Frequently Asked Questions

How do you calculate acceleration?

If acceleration is constant, use a = (vf − v0) / t. This calculator also supports other SUVAT combinations (e.g., displacement + acceleration + initial velocity).

What is the unit of acceleration?

The SI unit is m/s², but you can select other units (cm/s², ft/s², miles/h², etc.).

Can acceleration be negative?

Yes. Negative acceleration often indicates deceleration or acceleration in the opposite direction of motion.

When are these formulas valid?

These kinematics (SUVAT) equations are valid when acceleration is constant. If acceleration changes with time (non‑uniform acceleration), the results may not represent the real motion.

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