Calculate potential energy, mass, height, or gravitational acceleration using PE = m × g × h. Free online mechanics calculator for physics and engineering with multiple unit support.
Calculate potential energy using PE = m × g × h
Copy the code below to embed this calculator on your website
Potential energy is one of the most fundamental concepts in physics, representing the energy stored in an object due to its position in a gravitational field. Whether you're studying mechanics, engineering, or understanding how energy transforms, knowing how to calculate potential energy is essential. Our Potential Energy Calculator makes it easy to calculate potential energy, mass, height, or gravitational acceleration using the fundamental formula: PE = m × g × h.
Gravitational potential energy is the energy an object possesses because of its position relative to a reference point (usually Earth's surface). When you lift an object, you're doing work against gravity, storing energy that can be released when the object falls. This stored energy increases with mass, gravitational acceleration, and height - the higher and heavier an object, the more potential energy it has.
Our Potential Energy Calculator is designed for simplicity and accuracy. Follow these steps to get your calculation:
The calculator uses the fundamental potential energy formula: PE = m × g × h
You can rearrange this formula to solve for any variable:
The potential energy formula is one of the most important equations in mechanics:
PE = m × g × h
Where: PE = potential energy, m = mass, g = gravitational acceleration, h = height
Potential energy is stored energy that depends on an object's position or configuration. Gravitational potential energy specifically refers to the energy stored due to an object's position in a gravitational field:
Standard Earth gravity (9.80665 m/s²) is the average gravitational acceleration at Earth's surface. It varies slightly by location (latitude, altitude), but for most practical calculations, this standard value provides excellent accuracy. The calculator allows you to use standard gravity or enter a custom value for calculations on other planets, moons, or specific locations.
Potential energy calculations are used in countless real-world scenarios across various fields:
Our calculator supports various units for energy, mass, acceleration, and distance:
Tip: The calculator automatically handles all unit conversions, so you can input values in any supported unit and get results in your preferred unit.
A 5 kg object is lifted to a height of 10 meters above the ground. What is its potential energy?
m = 5 kg, g = 9.80665 m/s², h = 10 m
PE = m × g × h = 5 kg × 9.80665 m/s² × 10 m = 490.33 J
The object has 490.33 Joules of potential energy stored
An object with a mass of 2 kg has 1000 J of potential energy. How high is it above the reference point?
PE = 1000 J, m = 2 kg, g = 9.80665 m/s²
h = PE / (m × g) = 1000 J / (2 kg × 9.80665 m/s²) = 50.97 m
The object is approximately 51 meters above the reference point
A box has 500 J of potential energy when raised to a height of 5 meters. What is its mass?
PE = 500 J, h = 5 m, g = 9.80665 m/s²
m = PE / (g × h) = 500 J / (9.80665 m/s² × 5 m) = 10.2 kg
The box has a mass of approximately 10.2 kilograms
An object with mass 10 kg is at a height of 20 m on the Moon, where gravity is 1.625 m/s². What is its potential energy?
m = 10 kg, g = 1.625 m/s² (Moon), h = 20 m
PE = m × g × h = 10 kg × 1.625 m/s² × 20 m = 325 J
On the Moon, the object has 325 J of potential energy (less than on Earth due to lower gravity)
A 1000 kg car is at the top of a 50 m hill. If all its potential energy converts to kinetic energy at the bottom, what speed would it reach (ignoring friction)?
First calculate PE: PE = 1000 kg × 9.80665 m/s² × 50 m = 490,333 J
Using KE = ½mv² and PE = KE: v = √(2PE/m) = √(2 × 490333 / 1000) = 31.3 m/s (112.7 km/h)
The car would reach approximately 113 km/h at the bottom (in an ideal frictionless scenario)
Understanding the relationship between potential and kinetic energy is fundamental:
This energy transformation is the basis for understanding many mechanical systems, from simple pendulums to complex machinery.
Gravitational acceleration varies by location. Here are some common values:
The calculator allows you to enter custom gravitational acceleration values for calculations on different planets or in different gravitational environments.
Understanding potential energy has practical applications in daily life:
Potential energy is stored energy due to an object's position in a gravitational field. It's calculated using PE = m × g × h, where m is mass, g is gravitational acceleration (9.80665 m/s² on Earth), and h is height above a reference point. The formula shows that potential energy increases with mass, gravity, and height.
Potential energy is always relative to a chosen reference point (usually ground level where h = 0). The reference point defines where potential energy is zero. All potential energy values are measured relative to this point, so changing the reference point changes the absolute value but not the energy differences between positions.
Yes, potential energy can be negative if the reference point is chosen such that the object is below it. For example, if ground level is the reference point (h = 0) and an object is in a hole, its height would be negative, giving negative potential energy. The sign indicates position relative to the reference point.
Potential energy and kinetic energy are different forms of mechanical energy that can convert into each other. When an object falls, potential energy decreases while kinetic energy increases. In ideal systems (no friction), total mechanical energy (PE + KE) remains constant. This is the principle of conservation of mechanical energy.
Gravitational acceleration (g) directly multiplies the potential energy. Higher gravity means more potential energy for the same mass and height. On planets with stronger gravity (like Jupiter), objects have more potential energy. On planets with weaker gravity (like the Moon), objects have less potential energy for the same mass and height.
When an object falls, its height decreases, so potential energy decreases. This lost potential energy converts to kinetic energy (energy of motion). If there's no air resistance or friction, all the potential energy converts to kinetic energy. The object's speed increases as it falls, reaching maximum speed (and maximum KE) at the lowest point.
Standard Earth gravity is the average gravitational acceleration at Earth's surface. Actual gravity varies slightly by location (latitude, altitude, local geology), but the standard value (9.80665 m/s²) provides excellent accuracy for most calculations. It's an internationally accepted standard that simplifies calculations while maintaining precision.
Use the same formula PE = m × g × h, but use the gravitational acceleration of that planet. Uncheck 'Use standard Earth gravity' in the calculator and enter the planet's gravitational acceleration (e.g., 1.625 m/s² for the Moon, 3.711 m/s² for Mars). The calculator will use your custom value for all calculations.
Use consistent SI units for best results: Joules (J) for energy, kilograms (kg) for mass, meters per second squared (m/s²) for acceleration, and meters (m) for height. However, the calculator supports many units and automatically converts between them, so you can use any compatible units (e.g., calories, pounds, feet) and get results in your preferred units.
Understanding potential energy and the relationship between mass, gravity, height, and stored energy is fundamental to mechanics and physics. Our Potential Energy Calculator simplifies these calculations, making it easy to solve problems involving gravitational potential energy, energy storage, and energy transformations.
Whether you're studying energy conservation, designing systems that store or use potential energy, or understanding everyday phenomena like objects on hills, this calculator provides accurate results with support for multiple units and standard or custom gravitational acceleration. Ready to explore more mechanics concepts? Check out our other calculators like the Velocity Calculator for motion calculations, or use our Gravitational Force Calculator for understanding gravitational forces that create potential energy.
Get instant results with our optimized calculation engine
Precise calculations you can trust for any project
Works perfectly on all devices and screen sizes