Acceleration Calculator

Created by Dominik Czernia, PhD candidate
Last updated: Jul 01, 2022

Use our acceleration calculator if you need to know how to find acceleration using different variables such as velocity, time, distance traveled, or mass and force. The tool consists of three formulae for acceleration in physics, which you can select in the first box of the calculator.

The following article presents concise information explaining, e.g., what acceleration is and how to calculate acceleration. Furthermore, we show solutions to the below popular problems:

  1. How to find acceleration with velocity and distance;
  2. How to find acceleration with velocity and time; and
  3. How to find time with acceleration and distance.

The acceleration equation is strictly related to the velocity. We have prepared a separate tool for the latter physical quantity. You can find it under this average velocity calculator link.

Acceleration formula in physics

The acceleration measures how velocity changes over time. With this basic definition, you should be able to tell what the acceleration formula is:

a=ΔvΔta = \frac{\Delta v}{\Delta t}

where:

  • aa - The acceleration;
  • Δv\Delta v - The velocity change; and
  • Δt\Delta t - The time change.

If the change in velocity is not constant, then you should use derivatives instead of finite change (but that's a completely different story). The above equation is a simple average acceleration formula.

The second option in the acceleration calculator helps you if you need to know how to find acceleration with velocity and distance dd:

a=2dv0×tt2a = 2\frac{d - v_0 \times t}{t^2}

where, this time, v0v_0 is the initial velocity.

Finally, let's see what the equation for acceleration is from the perspective of Newton's second law:

a=Fma = \frac{F}{m}

where:

  • FF - The net force acting on an object; and
  • mm - The mass of the object.

From the practical point of view, acceleration plays a vital role in fuel consumption, which you can estimate with our fuel efficiency calculator.

How to find time with acceleration and distance

This constant acceleration calculator can make calculations in any direction you want. For example:

  1. The initial speed is 10 m/s10 \text{ m/s}.
  2. The distance is 100 m100 \text{ m}.
  3. The acceleration is 1 m/s21 \text{ m/s}^2
  4. Input all the above values in the corresponding acceleration calculator field in the mode "Distance traveled", and you'll find that time equals 7.32 s7.32 \text{ s}.

What is the acceleration formula we used in that case? It arises from one of the quadratic equation solutions with respect to tt based on the acceleration formula with distance:

t=v0+v02+2×a×dat = \frac{-v_0 + \sqrt{v_0^2 + 2\times a \times d}}{a}

All the above considerations are about linear motion. The story is entirely different if you want to include the rotational aspect. You can, for example, calculate rotational kinetic energy of an object that is not moving at all, just rotating.

Dominik Czernia, PhD candidate
Given
Speed difference
Speed difference
Initial speed
ft/s
Final speed
ft/s
Time
sec
Acceleration
ft/s²
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