Acceleration Calculator
Calculate acceleration of any moving object based on initial and final speed. You can also do reverse calculation and determine final speed or initial speed or time taken given the acceleration.
Enter Initial Speed, Final Speed and Time Taken in hours, minutes or seconds to calculate Linear Acceleration.
What is Acceleration?
- Acceleration is defined as the Change of Velocity over a period of time (Rate of change of velocity).
- Velocity is same as Speed but has both magnitude (speed value) and direction.
- There are two main kinds of acceleration namely Linear Acceleration and Angular Acceleration
- Linear Acceleration applies to objects moving linearly in a straight path. The SI unit of Acceleration is meters per sec squared (m/s2)
- Angular Acceleration comes into play when an object is moving in a circular path or angular path.
- Angular Acceleration has two components - Tangential and Radial Acceleration.
- Tangential Acceleration is Rate of Change of Linear Velocity when an object moves in a circular path.
- Radial Acceleration is rate of change of Angular Velocity of an object in circular path moving towards centre. It is measured in radians.
- In a circular motion, an object tries to accelerate to the centre of the circle due to what is known as Centripetal force. Therefore, Radial Acceleration is also referred to as Centripetal Acceleration
- Unit of Radial or Centripetal Acceleration is radians per second squared (r/s2)
What is the formula to calculate Acceleration?
- Average Acceleration = (Final Speed - Initial Speed) / Time taken in secs
- It is also expressed as Change in Velocity / Change in Time
(a = Δv / Δt) - If 'v' is final speed, 'u' is initial speed and 't' is elapsed time in seconds, then
a = v - u / t - Alternately, expressed as v = u + at
- For example, if initial speed is 40 meters/second and final speed is 300 meters/second and duration is 5 minutes, then acceleration is equal to
a = (v - u) / t in secs, which works out as
a = (300 - 40) / (5 * 60) = 0.86667 m/s2
Units of Acceleration
Given Velocity in m/s or Acceleration in m/s2 which are SI units, we can calculate Acceleration in different units using the formula given below.
Acceleration in Kilometers per Hour Per Second (km/hr/s)
Acceleration in Miles per Hour per second (mi/hr/s)
Acceleration in feet per second squared (ft/s2)
Acceleration in inches per minute per second (in/min/s )
Acceleration in meters per hour per second (m/hr/s)
Acceleration in knots per sec (kn/s)
Acceleration in kilometers per minute per second (km/min/s)
Acceleration in kilometers per sec squared (km/s²)
Acceleration in miles per minute per second (mi/min/s)
Acceleration in miles per second squared (mi/s2)
To convert m/s2 to km/hr/s, multiply meters per sec squared by 3.6
a (in km/hr/s) = m/s2 * 3.6
Alternately, we can convert the speed to km/hr/s and calculate as follows:
Acceleration in km/hr/s = (Final Speed in m/s * 3.6 - Initial Speed in m/s * 3.6) / Time in Secs
For example, if acceleration is 120 m/s2, then the same in km/hr/sec is equal to 3.6 * 120 = 432 km/hr/s
To convert m/s2 to mi/hr/s, multiply meters per sec squared by 0.447
a (in mi/hr/s)= m/s2 * 0.447
Alternately, we can convert the speed to mi/hr/s and calculate as follows:
Acceleration in mi/hr/s = (Final Speed * 0.447 - Initial Speed * 0.447) / Time in Secs
For example, if acceleration is 150 m/s2, then the same in mi/hr/s is equal to 0.447 * 150 = 67.05 mi/hr/s
To convert m/s2 to ft/s2, multiply meters per sec squared by 3.281
a (in ft/s2) = m/s2 * 3.281
Alternately, we can convert the speed to ft/s2 and calculate as follows:
Acceleration in ft/s2 = (Final Speed * 3.281 - Initial Speed * 3.281) / Time in Secs
For example, if acceleration is 111.5 m/s2, then the same in ft/s2 is equal to 3.281 * 111.5 = 365.8315 ft/s2
To convert m/s2 to in/min/s, multiply meters per sec squared by 2362.2
a (in inch/min/s) = m/s2 * 2362.20
Alternately, we can convert the speed to in/min/s and calculate as follows:
Acceleration in in/min/s = (Final Speed * 2362.2 - Initial Speed * 2362.2) / Time in Secs
For example, if acceleration is 19.33 m/s2, then the same in in/min/s is equal to 19.33 * 2362.2 = 45661.326 in/min/s
To convert m/s2 to m/hr/s, multiply meters per sec squared by 3600
a (in meter/hr/s) = m/s2 * 3600
Alternately, we can convert the speed to m/hr/s and calculate as follows:
Acceleration in m/hr/s = (Final Speed * 3600 - Initial Speed * 3600) / Time in Secs
For example, if acceleration is 156.7 m/s2, then the same in m/hr/s is equal to 156.7 * 3600 = 5641207 m/hr/s
To convert m/s2 to kn/s, multiply meters per sec squared by 1.943844
a (in kn/s) = m/s2 * 1.943844
Alternately, we can convert the speed to kn/s and calculate as follows:
Acceleration in kn/s = (Final Speed * 1.943844 - Initial Speed * 1.943844) / Time in Secs
For example, if acceleration is 65.3 m/s2, then the same in kn/s is equal to 65.3 * 1.943844 = 126.933 kn/s
To convert m/s2 to km/min/s, multiply meters per sec squared by 0.06
a (in km/min/s) = m/s2 * 0.06
Alternately, we can convert the speed to km/min/s and calculate as follows:
Acceleration in km/min/s = (Final Speed * 0.06 - Initial Speed * 0.06) / Time in Secs
For example, if acceleration is 0.547 m/s2, then the same in km/min/s is equal to 0.547 * 0.06 = 0.03282 km/min/s
To convert m/s2 to km/s², multiply meters per sec squared by 0.001
a (in km/s2) = m/s2 * 0.001
Alternately, we can convert the speed to km/s² and calculate as follows:
Acceleration in km/s² = (Final Speed * 0.001 - Initial Speed * 0.001) / Time in Secs
For example, if acceleration is 9748.89 m/s2, then the same in km/s² is equal to 9748.89 * 0.001 = 9.74889 km/s²
To convert m/s2 to mi/min/s, multiply meters per sec squared by 0.0372822715
a (in mi/min/s) = m/s2 * 0.0372822715
Alternately, we can convert the speed to mi/min/s and calculate as follows:
Acceleration in mi/min/s = (Final Speed * 0.0372822715 - Initial Speed * 0.0372822715) / Time in Secs
For example, if acceleration is 657.2 m/s2, then the same in mi/min/s is equal to 657.2 * 0.0372822715 = 24.5019 mi/min/s
To convert m/s2 to mi/s2, multiply meters per sec squared by 0.0006213712
a (in mi/s2) = m/s2 * 0.0006213712
Alternately, we can convert the speed to mi/s2 and calculate as follows:
Acceleration in mi/s2 = (Final Speed * 0.0006213712 - Initial Speed * 0.0006213712) / Time in Secs
For example, if acceleration is 103 m/s2, then the same in mi/s2 is equal to 103 * 0.0006213712 = 0.064001 mi/s2
How to derive the First Equation of Motion ( v = u + at)?
- The first equation of motion was given by Sir Issac Newton
- There are 3 equations of motion. This is the first equation
- This equation gives the relationship between velocity, acceleration and time.
- When a body at an initial velocity 'u' moves at a constant acceleration 'a' in a time period from 0 to 't' secs, then the final velocity of the body is expressed as
v = u + at
- Acceleration is defined as the rate of change of velocity.
Expressing Acceleration:
a = dv / dt
dv- change in velocity
dt- change in time
Simplifying, it further , we get
a = v-u/t-0
and then,
at = v-u
v = u + at
Frequently Asked Questions on Acceleration Calculator
They are not the same though both deal with Rate of Change of Linear Velocity.
Linear Acceleration is Rate of Change of Velocity of an object moving in a linear path
Linear Acceleration = Change in Linear Velocity / Time.
Tangential Acceleration is Range of Change of Linear Velocity of an object moving in a circular path
Tangential Acceleration = Angular Acceleration * Radius of the Circle
where Angular Acceleration is change in angular velocity / Time Taken
The unit of both Linear Acceleration and Tangential Acceleration is m/sv2
Both are components of Acceleration of an object moving in a circular path.
The object has a linear acceleration which is acting tangential to the circular path which is termed as Tangential Acceleration
The object in motion is also subjected to a centripetal force which pulls it towards the centre. This is also called Radial Acceleration or Centripetal Acceleration.
The SI Unit of Tangential Acceleration is m/s2 (meters per sec squared) The SI Unit of Radial Acceleration is r/s2 (radians per sec squared)
Since Acceleration is defined as Change in Velocity over time, an object is said to have 0 acceleration if it is moving at a constant speed over a period of time.
If a car is travelling at 60 kms without any change of speed over the measured period of time, it has zero acceleration.
Yes, Acceleration can be negative. If the final speed is lower than the initial speed during a specific time period, then the acceleration is -ve.
It is also called de-acceleration or deceleration or retardation.
For eg, a car moving at 60 kms/hour slows down to 10 kms/hour within 20 secs,
then the acceleration is 10-60/20 = -50/20= -2.5 kms/hr/sec
In addition, if an object changes direction from its original path, then the acceleration becomes -ve when compared to its original direction
In general parlance, they are used interchangeably and mean the same.
There are other sources who mention subtle differences between the two.
Uniform Acceleration
In uniform acceleration, the rate of change of acceleration is fixed but acceleration value itself may increase or decrease proportionately with time.
For eg, an object accelerating by 10 m/s2 every 15 mins is said to have uniform acceleration.
0 mins - 0 m/s2
15 mins - 10 m/s2
30 mins - 20 m/s2
45 mins - 30 m/s2
60 mins - 40 m/s2
If we plot time in X Axis and Acceleration in Y Axis, it will be like a 60 degree line or a -60 degree line for negative acceleration
Constant Acceleration
Here, the acceleration value is the same. It does not change with time. It is a fixed value.
Example - An object in a free fall has a constant acceleration of 9.81m/s2 which is the gravitational force acting on it. So all bodies in free fall are subjected to a constant acceleration.
If you plot time in X Axis and acceleration in Y Axis, it will be a line parallel to X Axis for constant acceleration.
It can be considered as a subset of Uniform acceleration.
which means every Constant acceleration is Uniform Acceleration
