How do you calculate gravitational potential energy?

To calculate gravitational potential energy: (1) Measure the mass of the object in kilograms. (2) Determine the height above your reference point in meters. (3) Use g = 9.80665 m/s² for Earth (or a different value for other planets). (4) Multiply: PE = m × g × h. For example, a 10 kg object at 5 m height has PE = 10 × 9.81 × 5 = 490.3 joules.

What is the formula for potential energy?

There are three common potential energy formulas: (1) Gravitational: PE = mgh, where m is mass, g is gravitational acceleration, and h is height. (2) Elastic: PE = ½kx², where k is the spring constant and x is displacement from equilibrium. (3) Electric: PE = kq₁q₂/r, where k is Coulomb's constant, q₁ and q₂ are charges, and r is distance between them.

Can potential energy be negative?

Yes, electric potential energy can be negative when two opposite charges attract each other. Negative PE means the system is in a bound state — you would need to add energy to separate the charges. Gravitational PE is typically positive when measured above a reference point, but can be negative if measured from a higher reference (e.g., in orbital mechanics, where PE = -GMm/r).

What is the difference between potential and kinetic energy?

Potential energy is stored energy due to position or configuration, while kinetic energy is energy of motion (KE = ½mv²). They are interconvertible: when a ball is held at height, it has PE. When dropped, PE converts to KE as it falls. At the bottom, all PE has become KE. The total mechanical energy (KE + PE) remains constant in an isolated system.

How does gravity affect potential energy on different planets?

Gravitational PE = mgh depends directly on the local gravitational acceleration. On the Moon (g = 1.62 m/s²), the same object at the same height has only 16.5% of the PE it would have on Earth. On Jupiter (g = 24.79 m/s²), it would have 2.53 times more PE. This calculator includes presets for Earth, Moon, Mars, Jupiter, Venus, and Saturn.

What is elastic potential energy?

Elastic potential energy is the energy stored in a spring or elastic material when it is stretched or compressed from its natural length. The formula is PE = ½kx², where k is the spring constant (in N/m) and x is the displacement from equilibrium (in meters). The energy depends on the square of displacement, so doubling the compression quadruples the stored energy.

How do you calculate the impact velocity from potential energy?

Using conservation of energy, if an object falls from height h with no air resistance, all gravitational PE converts to kinetic energy: mgh = ½mv². Solving for velocity: v = √(2gh). Notice that mass cancels out — all objects fall at the same speed regardless of mass (in a vacuum). For example, dropping from 10 m on Earth: v = √(2 × 9.81 × 10) = 14.0 m/s.

Potential Energy Calculator

PE = mgh — energy from height in a gravity field

Solve for

Mass

Height

Gravitational Acceleration

Result unit

Planet / Body

Preset

Gravitational Potential Energy

6,864.7J

All Values

PE = mgh — all values in SI base units

Mass

70.0000 kg

Gravity

9.8066 m/s²

Height

10.0000 m

6864.65 J

Impact velocity

14.0047 m/s

If dropped from this height, the object would reach 14.005 m/s (31.328 mph) at ground level.

Based on conservation of energy: v = √(2gh), ignoring air resistance.

Step-by-Step Solution

Calculation walkthrough with your values

1.Formula: PE = m × g × h

2.PE = 70.0000 × 9.8066 × 10.0000

3.PE = 6864.65 J

Energy Equivalences

What 6,864.65 J looks like in the real world

Food calories

1.6407 kcal

Watt-hours

1.9068 Wh

60W lightbulb

1.9068 minutes

Phone charges

0.171616 charges

Lift 1 kg to

700.00 m height

Energy Unit Conversions

Result expressed in all supported energy units

J6,864.65

kJ6.865

MJ0.006865

cal1,640.69

kcal1.641

Wh1.907

kWh0.001907

eV4.285e+22

ft-lbf5,063.11

BTU6.506

How the Potential Energy Calculator Works

Three types of potential energy with all solve modes

Potential energy is the energy stored in an object due to its position, configuration, or state. Unlike kinetic energy (energy of motion), potential energy is "stored" and can be released to do work. This calculator handles three fundamental types: gravitational, elastic, and electric potential energy.

Gravitational PE

PE = mgh

Mass × gravity × height

Elastic PE

PE = ½kx²

Spring constant × displacement²

Electric PE

PE = kq₁q₂/r

Coulomb’s law for charges

Example — Person on a diving board (70 kg at 3 m)

Mass

person

Gravity

9.807

Earth

m/s²

Height

diving board

2,059

70 × 9.807 × 3

J ≈ 2.06 kJ

What Is Potential Energy?

Understanding stored energy in physics

Potential energy is the energy an object has because of its position relative to other objects, its internal stress, or its electric charge. The concept was introduced by 19th-century Scottish engineer William Rankine. Unlike kinetic energy, potential energy is not about motion but about the capacity to do work.

Types of Potential Energy

Gravitational — energy from height in a gravitational field (PE = mgh)

Elastic — energy stored in a stretched or compressed spring (PE = ½kx²)

Electric — energy between electric charges (PE = kq&sub1;q&sub2;/r)

Chemical — energy stored in chemical bonds (e.g., food, fuel)

Nuclear — energy stored in atomic nuclei (E = mc²)

The law of conservation of energy states that energy cannot be created or destroyed — only converted between forms. When a ball falls, gravitational PE converts to kinetic energy. The total mechanical energy (KE + PE) remains constant in an isolated system.

Gravitational Acceleration by Celestial Body

Surface gravity values used in PE = mgh calculations

Body	g (m/s²)	Relative to Earth	PE of 1 kg at 1 m
Sun	274.00	27.94x	274.00 J
Jupiter	24.79	2.53x	24.79 J
Neptune	11.15	1.14x	11.15 J
Saturn	10.44	1.06x	10.44 J
Earth	9.81	1.00x	9.81 J
Venus	8.87	0.90x	8.87 J
Uranus	8.69	0.89x	8.69 J
Mars	3.72	0.38x	3.72 J
Mercury	3.70	0.38x	3.70 J
Moon	1.62	0.17x	1.62 J
Pluto	0.62	0.06x	0.62 J

Common Mistakes to Avoid

Frequent errors in potential energy calculations

Confusing height reference points

Gravitational PE depends on the reference point (datum) you choose. A ball on a table has PE relative to the floor, but zero PE relative to the table. Always be clear about your reference height. This calculator uses the input height directly as the height above datum.

Mixing unit systems

PE = mgh requires consistent units. Using kilograms with feet, or pounds with meters, gives wrong results. This calculator handles conversions automatically, but when computing by hand, convert everything to SI (kg, m, m/s²) first.

Using g = 10 instead of 9.80665

While g ≈ 10 m/s² is convenient for rough estimates, it introduces a 2% error. For precise work, use g = 9.80665 m/s² (the standard value) or the exact local value. The error compounds with large masses or heights.

Forgetting PE can be negative

Gravitational PE is always positive (above datum), but electric PE between opposite charges is negative. A negative PE means the system is bound — you must add energy to separate the charges. Do not assume all PE values should be positive.

Real-World Potential Energy Values

Reference values for common objects and scenarios

Scenario	Mass	Height	PE
Apple on a table	0.2 kg	0.8 m	1.57 J
Book on a shelf	1 kg	1.5 m	14.7 J
Person on diving board	70 kg	3 m	2.06 kJ
Roller coaster at peak	500 kg	30 m	147 kJ
Skier at top of slope	80 kg	200 m	157 kJ
Water behind Hoover Dam	1,000 kg	221 m	2.17 MJ
Boulder on a cliff	5,000 kg	100 m	4.90 MJ
ISS in orbit	420,000 kg	408 km	1.68 TJ

Frequently Asked Questions

Common questions and detailed answers

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Last updated Apr 11, 2026

Potential Energy Calculator

All Values

Step-by-Step Solution

Energy Equivalences

Energy Unit Conversions

How the Potential Energy Calculator Works

What Is Potential Energy?

Gravitational Acceleration by Celestial Body

Common Mistakes to Avoid

Real-World Potential Energy Values

Frequently Asked Questions

Embed Potential Energy Calculator

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