Weight / Force Calculator

GCSE PHYSICS: Formula for Gravity, Mass {amp} Weight

Weight/Force Mass Gravity Calculator

Weight/Force is the gravity on an object, the formula is:
W = m × g

Where:

  W: Weight/Force, in N
m: Mass of the object, in kg
g: Gravity, in m/s^2


GCSE Physics

The questions on this page test your ability to use the formula:

Weight = Mass × Gravity

You may also wish to learn the formula as:

W = mg


Question 1

The strength of gravity at the Earth’s surface is 10 newtons per kilogram. Calculate the weight of a car with a mass of 1500 kg.


Question 2

The strength of gravity on the Moon is 1.6 newtons per kilogram.

If an astronaut’s mass is 80 kg on Earth, what would it be on the Moon?


Question 3

The surface gravity of Jupiter is about 26 newtons per kilogram.

What would be the weight of a probe of mass 50 kg at Jupiter’s surface?


How to Calculate Weight from Mass

The weight of an object is defined as the force of gravity on the object and may be calculated as the mass times the acceleration of gravity, w = mg. Since the weight is a force, its SI unit is the newton.

For an object in free fall, so that gravity is the only force acting on it, then the expression for weight follows from Newton’s second law.

You might well ask, as many do, «Why do you multiply the mass times the freefall acceleration of gravity when the mass is sitting at rest on the table?». The value of g allows you to determine the net gravity force if it were in freefall, and that net gravity force is the weight. Another approach is to consider «g» to be the measure of the intensity of the gravity field in Newtons/kg at your location. You can view the weight as a measure of the mass in kg times the intensity of the gravity field, 9.8 Newtons/kg under standard conditions.

Data can be entered into any of the boxes below. Then click outside the box to update the other quantities.

At the Earth’s surface, where g=9.8 m/s2 :

The kilogram is the SI unit of mass and it is the almost universally used standard mass unit. The associated SI unit of force and weight is the Newton, with 1 kilogram weighing 9.8 Newtons under standard conditions on the Earth’s surface. However, in the US common units, the pound is the unit of force (and therefore weight).The pound is the widely used unit for commerce. The use of the pound force constrains the mass unit to an inconveniently large measuring unit called a «slug». The use of this unit is discouraged, and the use of exclusively SI units for all scientific work is strongly encouraged.

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Science {amp}gt;{amp}gt; Physics for KidsWhat is mass?

Mass is a measurement of how much matter is in an object. Mass is a combination of the total number of atoms, the density of the atoms, and the type of atoms in an object.

How to Measure Mass

Mass is usually measured in kilograms which is abbreviated as kg.

In physics there are different ways of determining the quantity of mass. Two of the most commonly used are inertial mass and gravitational mass.

  • Inertial mass — Inertial mass is determined by how much the object resists acceleration. For example, if you push two objects under the same conditions with the same amount of force, the object with the lower mass will accelerate faster.
  • Gravitational mass — Gravitational mass is a measurement of how much gravity an object exerts on other objects. It can also be the measurement of how much gravity an object experiences from another object.

When scientists want to express mass in terms of atoms and molecules they use the atomic mass unit which is abbreviated «u». One atomic mass unit is equal to 1/12 of the mass of carbon-12.

What is the difference between mass and weight?

Weight is different from mass. Weight is the measure of the force of gravity on an object. The mass of an object will never change, but the weight of an item can change based on its location. For example, you may weigh 100 pounds on Earth, but in outer space you would be weightless. However, you will always have the same mass on Earth as you have in outer space.

Measuring Weight

In the United States we usually measure weight in pounds, but in physics when we are describing weight as a force, it is generally measured in Newtons which is abbreviated as «N».

Converting Mass to Weight

Since gravity is fairly consistent on Earth, weight will be consistent as well. This allows us to use a formula to convert weight into mass or mass into weight. The formula is:

force = mass * acceleration
or

f = ma

In this equation force is equal to the weight. The acceleration is the acceleration caused by gravity «g» which is 9.8 m/s2.

Now we can substitute weight for mass and 9.8 m/s2 for acceleration to get the formula:

weight = mass * g
weight = mass * 9.8 m/s2

Example:

What is the weight of a 50 kg mass object?

weight = 50 kg * 9.8 m/s2
weight = 490 N

Is mass the same as size?

No, mass is different than size or volume. This is because the type of atoms or molecules as well as their density helps to determine the mass. For example, a balloon filled with helium will have much less mass than a similar sized item made of solid gold.

The Law of Conservation of Mass

The law of conservation of mass states that the mass of a closed system must remain constant over time. This means that although changes are being made to the objects in a system, the overall mass of the system must remain the same.

Interesting Facts about Mass and Weight

  • The word «mass» comes from the Greek word «maza» meaning «lump of dough.»
  • Scientists estimate that the total mass of the universe is between 1052kg and 1053 kg.
  • 1000kg is equal to a metric tonne.
  • Greek philosopherPlato said that weight was the natural tendency of objects to seek their kin.
  • The gravity of Earth can vary as much as 0.5% depending on where you are on Earth.
  • If you weigh 100 pounds on Earth you would weigh 37.7 pounds on Mars and 236.4 pounds on Jupiter.

Activities

Take a ten question quiz about this page.
Go here to test your knowledge with a crossword puzzle about motion.

More Physics Subjects on Motion, Work, and Energy

Science {amp}gt;{amp}gt; Physics for Kids

Figure out the gravitational acceleration.

In other words, figure out

g

. On the surface of the earth,

g

is 9.8 m/s

2

. Elsewhere in the universe, the acceleration of gravity changes.

[4]

Your teacher should tell you, or the problem should indicate, where the gravity is acting from so that you know.

  • The gravitational acceleration on the moon is different from the gravitational acceleration on the earth. Acceleration due to gravity on the moon is about 1.622 m/s2,[5] or about 1/6 of the acceleration that it is here on earth. That’s why you weigh 1/6 of your earth-weight on the moon.
  • The gravitational acceleration on the sun is different from the gravitational acceleration on the earth and moon. Acceleration due to gravity on the sun is about 274.0 m/s2,[6] or about 28 times the acceleration that it is here on earth. That’s why you would weigh 28 times your earth-weight on the sun (if you could survive!).

Weight

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Weight Equation

Computer drawing of kids page link This page is intended for college, high school, or middle school students.
For younger students, a simpler explanation of the information on this page is
available on the
Kids Page.


Computer drawing of an airliner with the weight equation.{amp}#xD;{amp}#xA; Weight equals mass time gravitational acceleration (W = m g)

Weight is the force
generated by the gravitational attraction of the earth on any object.
Weight is fundamentally
different from the aerodynamic forces,lift and drag.
Aerodynamic forces are mechanical forces and the object has to be
in physical contact with the air which generates the force. The
gravitational force is a field force; the source of the force does
not have to be in physical contact with the object.

The nature of the gravitational force has been studied by
scientists for many years and is still being investigated by
theoretical physicists. For an object the size of an airplane flying
near the earth, the descriptions given three hundred years ago by Sir
Isaac Newton work quite well. Newton published his theory of
gravitation with his laws of motion in
1686. The gravitational force, F, between two particles equals a
universal constant, G, times the product of the mass of the particles, m1 and m2,
divided by the square of the distance, d, between the particles.

F = G * m1 * m2 / d^2

If you have a lot of particles acting on a single particle, you
have to add up the contribution of all the individual particles. For
objects near the earth, the sum of the mass of all the particles is
simply the mass of the earth and the distance is then measured from
the center of the earth. On the surface of the earth the distance is
about 4000 miles. Scientists have combined the universal
gravitational constant, the mass of the earth, and the square of the
radius of the earth to form the gravitational acceleration, g
. On the surface of the earth, its value is 9.8 meters per
square second or 32.2 feet per square second.

g = G * m earth / (d earth)^2

The weight W, or
gravitational force, is then just the mass of an object times the
gravitational acceleration.

W = m * g

Since the gravitational constant (g) depends on the square of the
distance from the center of the earth, the
weight of an object decreases with altitude.

Let’s do a
test problem to see how much the weight of an airplane changes
with altitude. If an airplane is
flying at 35000 feet (about 7 miles) the distance to the center of
the earth is about 4007 miles. We can calculate the ratio of the
gravitational constant to the value at the surface of the
earth as the square of (4000/4007) which equals
.9983*.9983 = .9965. If the airplane weighs 10000 pounds on the surface of the
earth, it weighs 9965 pounds at 35000 feet; it has lost 35 pounds, a
very small amount compared to 10000 pounds.

Let’s do another problem and compute the weight of
the Space Shuttle in low earth orbit. On the ground, the orbiter
weighs about 250,000 pounds. In orbit, the shuttle is about 200 miles above
the surface of the earth. As before, the gravitational constant ratio is
the square of (4000/4200) which equals .9523*.9523 = .907. On orbit, the shuttle
weighs 250,000 * .907 = 226,757 pounds. Notice: the weight is not
zero. The shuttle is not weightless in orbit
. «Weightlessness» is
caused by the speed of the shuttle in orbit. The shuttle is
pulled towards the earth because of gravity. But the high orbital speed,
tangent to the surface of the earth, causes the fall towards the surface to
be exactly matched by the curvature of the earth away from the shuttle.
In essence, the shuttle
is constantly falling all around the earth.


You can view a short
movie
of «Orville and Wilbur Wright» discussing the weight force
and how it affected the flight of their aircraft. The movie file can
be saved to your computer and viewed as a Podcast on your podcast player.


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What is weight?

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