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Instantaneous Velocity Calculator

Instantaneous Velocity Calculator

Select the value and fetch in the required parameters. The calculator will take instants to calculate it along with instantaneous velocity for certain displacement and time.


Initial Displacement (x₁)


Final Displacement(x₂)


Initial Time Taken (t₁)


Final Time Taken (t₂)


Instantaneous Velocity (V)


Instantaneous Velocity Calculator (Time Function)

Enter the Function x(t)

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An online instantaneous velocity calculator allows you to calculate instantaneous velocity corresponding to the instantaneous rate of change of velocity formula. Yes, calculating instantaneous velocity becomes efficient with this tool as it eliminates the chance of error of manual calculations.

This post will assist you to understand how to find instantaneous velocity and all the facts you need to know about it. So, let’s begin with its basic definition in physics! Also, try this velocity calculator for physics through which you can easily calculate the velocity of a moving object.

What is instantaneous velocity in physics?

In physics change in the distance over time at a specific point is known as instantaneous velocity and it defines the speed of an object that is moving on the road at any specific point of its path. Usually, we call it simple velocity and its magnitude is known as instantaneous speed. Furthermore, it is a vector quantity and we can also say that it is the average velocity that is present between any two points on any path in a particular limited time or at any specific moment. For convenience, the online instantaneous speed calculator helps you to calculate the speed of an object at a certain instant of time.

Mathematical Representation:

For its mathematical representation we will suppose two points on any road. Points will be represented by “x”. Now assume that a car is moving among these two points in particular time duration “t”. The simple average velocity of moving car between these two points will be represented by:

“v=x(t2) −x(t1) t2−t1v–=x(t2) −x(t1) t2−t1” in particular time “t”

The instantaneous velocity at any point on the road will be as follows:

“t1=tt1=t and t2=t+Δtt2=t+Δt”

Now we will put these values in the equation of average velocity and take the limit as follows:


Finally, we will have the final representation of instantaneous velocity by physics in numerical form as follows:

“v(t)=limΔt→0x(t+Δt) −x(t)Δt=dx(t)dt.v(t)=limΔt→0x(t+Δt)−x(t)Δt=dx(t)dt”

On the basis of the above explanation, we can say that the instantaneous velocity of any moving object is the limit of the average velocity and the rate at which position of any object changes. Its value will be small always.

What is the formula for instantaneous velocity?

Sometime in case of a moving car we are interested to calculate instantaneous velocity to find out its speed at any specific instant of time. This can be determined in a simple way by applying formula as follows:

Instantaneous velocity formula: Vint=limΔt→0Δx/Δt=dx/dt.

Above explained instantaneous velocity equation can be further simplified as follows:



  • Δt = a very small portion of time or time interval.
  • Vi= instantaneous velocity of any moving object.
  • s = displacement.
  • t = time.

Though we can find it by formulas the use of instantaneous velocity calculator is another option for the verification of answers.

Unit of Instantaneous Velocity:

According to the international system of units its unit is the combination of: unit of distance / unit of speed. Hence:
SI unit: ds/dt = m/s = ms-1.

Instantaneous Velocity Example:

If you are going somewhere on a car, then its speed meter is showing you the instantaneous velocity. Therefore, we can say that it is the current speed of any moving object. Moreover, if the car has uniform velocity, then its instantaneous velocity will be similar to its standard velocity.

Take another example of a cyclist who participated in a race and moving forward. While cycling his velocities are changing continuously. At one specific moment if wish to calculate his velocity it will be known as instantaneous velocity. For calculating the instantaneous velocity of cyclist we can use the following two approaches:

  1. Application of Instantaneous Velocity formula =limΔt→0Δx/Δt=dx/dt.
  2. Use of instantaneous velocity calculator to avoid manual calculations.

About Instantaneous Velocity Calculator:

The instantaneous velocity calculator helps you to find instantaneous velocity according to the instantaneous velocity formula of physics. This calculator not only helps to calculate instantaneous velocity, but also initial displacement, final displacement, initial time taken, and final time taken.

How to find instantaneous velocity With This Calculator for Instantaneous Velocity:

You can readily find the instantaneous velocity with this calculator, all you need to stick to the mentioned steps:


This instantaneous velocity calculator provided you with the five input fields, these are:

  • Initial Displacement
  • Final Displacement
  • Initial Time Taken
  • Final Time Taken
  • Instantaneous Velocity

You just have to plug-in values into any above four fields to calculate the fifth one!


  • Once you put the values into any four fields, hit the calculate button, the results can either be instantaneous velocity, initial displacement, final displacement, initial time taken, and final time taken.

Difference between Instantaneous Speed and Instantaneous Velocity:

Instantaneous Speed:

  • Instantaneous speed is said to be as the magnitude of instantaneous velocity
  • It is said to be as a scalar quantity
  • Formula of instantaneous speed is : Speed (i) = ds/dt

Instantaneous Velocity:

  • Instantaneous velocity is said to be as the change in position taking place at small change in time
  • It is said to be as the vector quantity
  • Formula of instantaneous velocity is : Vint=limΔt→0Δx/Δt=dx/dt

How to Calculate instantaneous velocity (manually)?

Assume a particle that is moving forward on a straight line for 3 seconds. Its position x is defined as:5² + 2t + 4? What will be its instantaneous velocity?

In the above question:

  • x =5t² + 2t + 4.

We will simply apply the instantaneous velocity formula that is: Vi=dx/dtVi=dx/dt

In the next step, we will be substituting the value of function x in the instantaneous velocity equation.

  • Vi=ddt5t2+2t+4Vi=ddt5t2+2t+4
  • Vi=10t+2Vi=10t+2

Now we will put the value of t= 3

  • Vi=10×3+2Vi=10×3+2
  • Vi=32ms−1Vint=32ms−1
  • Vi = 32ms or 132ms−1.

Note: Finding instantaneous velocity might be very tricky as it is a constant velocity of any moving object at any particular time period. It exists for a very short period of time and then changes. On the other hand, to avoid the risk of mistake in its calculation online instantaneous velocity calculator is the best option.

FAQ’s (Instantaneous Velocity):

Can instantaneous velocity be measured directly?

No, remember that instantaneous velocity can never be measured because there is no single way to do anything instantaneously. Remember that all the measurements take some amount of time to perform.

How to find instantaneous velocity of a function?

Physics study depicts that instantaneous velocity is indicated as to as a continuous function of time & even gives the velocity at any point in time during a particle’s motion. To compute the instantaneous velocity at a specific time, simply, you have to take the derivative of the position function, that provides you with the functional form of instantaneous velocity v(t).

What is the difference between instantaneous velocity and average velocity?

In the term of physics, the instantaneous velocity is indicated as the specific rate of change of displacement (or position) corresponding to time at a single point (x,t) – and when it comes to average velocity, it is said to be as the average rate of change of displacement (or position) according to time over an interval.

Is instantaneous velocity the same as acceleration?

No, both are different as when an object distance (s) changes with time, its velocity is said to be as the rate at which the distance is changing according t to time, while its acceleration is indicated as the rate at which the velocity is changing corresponding to time.

If an object has the instantaneous velocity of 40 miles per hour, then what is its instantaneous velocity?

Simply, the instantaneous speed of this object is said to be as 40 miles per hour.

How are instantaneous velocity and instantaneous speed related?

Yes, they are related as instantaneous speed is said to be as the magnitude of the instantaneous velocity.

Does a car’s speedometer show instantaneous speed?

The speedometer of a car is something that depicts the information about the instantaneous speed of your car. Yes, it shows your speed at a particular instant in time.

How do you find the instantaneous velocity at t = 2 for the position function #s(t) = t^3 +8t^2-t#?

Well, the instantaneous velocity is stated as #(ds)/dt#:

Since #s(t)=t^3+8t^2-t#, #(ds)/dt=3t^2+16t-1#.

At #t=2#, #[(ds)/dt]_(t=2)=3*2^2+16*2-1=43#.

We have the position as the function #s(t)=t^3+8t^2-t#.

Velocity is the rate of change of position over time, so its the derivative of the function.


So at #t=2#, the velocity is,







It is imperative to understand, instantaneous speed depends on distance, and when it comes to instantaneous velocity, it depends on displacement, and when the time interval is small these two quantities are effectively the same (and they even have the same magnitude).This instantaneous velocity calculator helps its users to understand how to calculate velocity at any specific instant and also solve the physics equations in no time.


From the source of phys.libretexts – Instantaneous Velocity and Speed – Calculating Instantaneous Velocity and Finding Velocity from a Position-Versus-Time Graph

From the source of wikihow – A simple guide on How to Calculate Instantaneous Velocity – Sample Problems

From the source of sciencestruck – instantaneous velocity in physics – formula for an instantaneous velocity – Different examples of instantaneous velocity

From the source of physics.stackexchange – Instantaneous velocity related question and answer for active researchers, academics and students of physics.