Gravitational Acceleration Calculator

Select Calculation Type: Mass of the field source (kg) : Distance between masses (m) : Gravitational Acceleration (m/s²) :

Calculation Steps:

What Gravitational Acceleration?

Gravitational acceleration, often denoted as g, is a fundamental concept in physics that describes the acceleration experienced by an object due to the force of gravity. It is the rate at which an object near the Earth’s surface gains velocity as it falls freely under the influence of gravity. Gravitational acceleration is a vector quantity, meaning it has both magnitude and direction. Near the surface of the Earth, gravitational acceleration is directed towards the center of the Earth.

Gravitational Acceleration Formula :

The formula for gravitational acceleration is given by Newton’s law of universal gravitation, which was first formulated by Sir Isaac Newton in the 17th century. This law states that the force of gravity between two objects is inversely proportional to the square of the distance between their centers and directly proportional to the product of their masses. The formula for gravitational acceleration can be derived from Newton’s law by considering the force acting on an object of mass m near the Earth’s surface:

F = m⋅g

Here, $F$ is the force of gravity, $m$ is the mass of the object, and $g$ is the gravitational acceleration. Rearranging this equation to solve for $g$ gives:

g = F / m

In the case of an object near the Earth’s surface, the force of gravity can be expressed using Newton’s law:

Here, $G$ is the gravitational constant (approximately ), $M$ is the mass of the Earth, $m$ is the mass of the object, and $r$ is the distance between the centers of the Earth and the object. Substituting this expression for $F$ into the equation for $g$ , we get:

g = G⋅M / $r²$

The standard value for the acceleration due to gravity on the surface of the Earth is approximately . This value can vary slightly depending on location (due to differences in altitude and latitude) and is often rounded to for simplicity in calculations.

So, the acceleration that an object experiences as an effect of gravity is known as gravitational acceleration. The formula for gravitational acceleration is g = G⋅M / r², where G is the gravitational constant, M is the mass of the Earth, and r is the distance from the center of the Earth to the object. The standard value for gravitational acceleration on the surface of the Earth is approximately 9.8 m/s².

Units in Gravitational Acceleration Calculator :

The units of gravitational acceleration depend on the system of units being used. In the International System of Units (SI), gravitational acceleration is typically measured in meters per second squared (). This unit represents the acceleration gained by an object per second as it falls freely under the influence of gravity

In other systems of units, such as the Imperial system, gravitational acceleration can be expressed in feet per second squared ( $s²$ ). To convert from SI units to Imperial units, the conversion factor is approximately $\approx 3.281 s²$ .

It’s essential to be consistent with units in calculations to ensure accurate and meaningful results. When using the formula g = G⋅M / $r²$ for gravitational acceleration, make sure that the mass ( $M$ ) is in kilograms, the gravitational constant ( $G$ ) is in , and the distance ( $r$ ) is in meters.

How an Gravitational Acceleration Calculator Works: A Step-by-Step Example

Question:

Calculate the gravitational acceleration at a location where the distance from the center of the Earth is . Given that the mass of the Earth ( $M$ ) is $kg$ and the gravitational constant ( $G$ ) is .

Solution:

The formula for gravitational acceleration ( $g$ ) remains the same:

g = G⋅M / $r²$

Substituting the updated values:

g = (

Calculating this expression gives the value of $g$ , the gravitational acceleration at the given location.

g = (

g = -0.00000000000330180752m/s²

g = -3.3018 x 10¹² m/s²

Therefore, with the updated values, the gravitational acceleration at this location is approximately -3.3018 x 10¹² m/s².