Gravitational Potential Energy
This page contains calculators for working out the force of gravity on or near the Earth’s surface. The formula is given as
well as calculators with the equation rearranged to make mass (kg) and height (m) the subject. Examples are also given
in each case.
Potential energy is the stored energy of an object due to its position or state. For example, it we lift something up it now
has greater potential energy. This is obvious if you have ever dropped something on your foot. The higher and heavier
an object is the more potential it has to hurt when dropped, i.e. it possesses more energy.
The equations used here use g (sometimes known as “little g”) and is the Earth’s gravitational field strength -- the force of
gravity felt by objects on or near the surface of the Earth. Its value and units are 9.81 ms
-2
.
When using the calculators enter all figures without commas. For example, enter 2,400 as 2400.
Calculate gravitational potential energy
The equation for gravitational potential energy is given on the right.
Example: A person with a mass of 75 kg climbs a ladder to a height of
8 m. What is the resulting potential energy of the person at the top of
the ladder?
In this case we simply enter the mass and height into the calculator and
click Calculate, to show that the answer is 5886 J.
The same equation is sometimes shown in different ways, such as PE
= mgh, PE
grav
= mgh, GPE = mgh, or U = mgh.
Where:
E
p
=
gravitational potential energy (J)
m = mass (kg)
g =
gravitational field strength
(
9.81 ms
-2
)
h = height (m)
Gravitational Potential Energy Calculator
Quick Facts
Weight isn’t the same as mass.
Weight is due to the pull of gravity.
In space your weight can be zero,
but your mass remains the same.
The equation for
gravitational potential
energy in joules (J)
is:
Calculate mass from potential energy and height
Where:
m = mass (kg)
E
p
=
gravitational potential energy (J)
g =
gravitational field strength
(
9.81 ms
-2
)
h = height (m)
The equation for mass
from
potential energy
and height is:
The equation for mass is given above right.
Example: A crane lifts an object to a height of 25 m and in doing so
expends 12000 J of energy. What is the mass of the object?
Again, we simply enter the energy and height into the calculator and
click Calculate, to show that the answer is 48.9297 kg.
Calculate height from potential energy and mass
Where:
h = height (m)
E
p
=
gravitational potential energy (J)
m = mass (kg)
g =
gravitational field strength
(
9.81 ms
-2
)
The equation for height
from
potential energy
and mass is:
The equation for mass is given above right.
Example: Just before jumping from an aeroplane a skydiver has a
potential energy of 3 million joules (J). The mass of the skydiver is
80 kg. What height did the skydiver jump from?
We simply enter the energy and mass into the calculator and click
Calculate, to show that the answer is 3822.63 meters (m).
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Gravitational Potential Energy
This page contains calculators for working out the force of gravity
on or near the Earth’s surface. The formula is given as well as
calculators with the equation rearranged to make mass (kg) and
height (m) the subject. Examples are also given in each case.
Potential energy is the stored energy of an object due to its
position or state. For example, it we lift something up it now has
greater potential energy. This is obvious if you have ever dropped
something on your foot. The higher and heavier an object is the
more potential it has to hurt when dropped, i.e. it possesses more
energy.
The equations used here use g (sometimes known as “little g”)
and is the Earth’s gravitational field strength -- the force of gravity
felt by objects on or near the surface of the Earth. Its value and
units are 9.81 ms
-2
.
When using the calculators enter all figures without commas. For
example, enter 2,400 as 2400.
Gravitational Potential Energy
Calculator
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Calculate gravitational potential energy
The equation for gravitational potential energy is given below.
Example: A person with a mass of 75 kg climbs a ladder to a
height of 8 m. What is the resulting potential energy of the person
at the top of the ladder?
In this case we simply enter the mass and height into the
calculator and click Calculate, to show that the answer is 5886 J.
The same equation is sometimes shown in different ways, such
as PE = mgh, PE
grav
= mgh, GPE = mgh, or U = mgh.
Where:
E
p
=
gravitational potential energy (J)
m = mass (kg)
g =
gravitational field strength
(
9.81 ms
-2
)
h = height (m)
The equation for
gravitational potential
energy in joules (J)
is:
Calculate mass from potential energy and height
The equation for mass is given above below.
Example: A crane lifts an object to a height of 25 m and in doing
so expends 12000 J of energy. What is the mass of the object?
Again, we simply enter the energy and height into the calculator
and click Calculate, to show that the answer is 48.9297 kg.
Where:
m = mass (kg)
E
p
=
gravitational potential energy (J)
g =
gravitational field strength
(
9.81 ms
-2
)
h = height (m)
The equation for mass
from
potential energy
and height is:
Calculate height from potential energy and mass
The equation for mass is given above below.
Example: Just before jumping from an aeroplane a skydiver has
a potential energy of 3 million joules (J). The mass of the
skydiver is 80 kg. What height did the skydiver jump from?
We simply enter the energy and mass into the calculator and
click Calculate, to show that the answer is 3822.63 meters (m).
Where:
h = height (m)
E
p
=
gravitational potential energy (J)
m = mass (kg)
g =
gravitational field strength
(
9.81 ms
-2
)
The equation for height
from
potential energy
and mass is:
