Gravitational Potential Energy Calculator
Calculate gravitational potential energy calculator calculate potential energy PE = m * g * h in Joules, kJ, kcal, and ft-lbf from mass m, height h, and gravity g (9.80665 m/s²). Accurate physics formulas and unit conversions for engineers, students & technicians.
Calculate Gravitational Potential Energy (PE = m · g · h)
Enter your physical parameters below to compute verified potential energy metrics.
Calculation Results
Calculated using verified physical methodology: Gravitational Potential Energy: PE = m \cdot g \cdot h
\text{Impact Velocity upon Freefall: } v = \sqrt{2 \cdot g \cdot h}
Quick Summary
The Gravitational Potential Energy Calculator evaluates stored mechanical energy ($PE = m \cdot g \cdot h$) from mass ($m$), height ($h$), and gravity ($g$) in Joules (J), Kilojoules (kJ), kcal, Imperial $\text{ft}\cdot\text{lbf}$, and freefall velocity.
Formula Explanation
Gravitational Potential Energy: PE = m \cdot g \cdot h
\text{Impact Velocity upon Freefall: } v = \sqrt{2 \cdot g \cdot h}
How It Works
The Gravitational Potential Energy Calculator multiplies mass ($m$ in kg) by gravity ($g = 9.80665\text{ m/s}^2$) and height ($h$ in meters). It outputs potential energy ($PE$) in Joules, kJ, kcal, Imperial $\text{ft}\cdot\text{lbf}$, Watt-Hours (Wh), and maximum impact velocity ($v = \sqrt{2gh}$) upon freefall.
Step-by-Step Worked Example
Practical Problem: Calculate the gravitational potential energy $PE$ of a $m = 50.0\text{ kg}$ boulder elevated to height $h = 20.0\text{ meters}$ above ground level on Earth ($g = 9.80665\text{ m/s}^2$).
- Step 1: Identify Input Parameters: Mass $m = 50.0\text{ kg}$, Height $h = 20.0\text{ m}$, $g = 9.80665\text{ m/s}^2$.
- Step 2: Apply the Gravitational Potential Energy Formula ($PE = m \cdot g \cdot h$): $PE = 50.0 \times 9.80665 \times 20.0$.
- Step 3: Execute Multiplication for Joules & Kilojoules: $PE = 9,806.65\text{ Joules (J)} = 9.80665\text{ Kilojoules (kJ)}$.
- Step 4: Calculate Maximum Freefall Impact Velocity ($v = \sqrt{2gh}$): $v = \sqrt{2 \times 9.80665 \times 20.0} = \sqrt{392.266} = 19.8057\text{ m/s} = 71.30\text{ km/h}$.
- Step 5: Convert Units to Foot-Pounds & Kilocalories: Imperial Foot-Pounds: $9,806.65 \times 0.737562 = 7,233.02\text{ ft}\cdot\text{lbf}$. Kilocalories: $\9.80665 / 4.184 = 2.344\text{ kcal}$. Watt-Hours: $\9,806.65 / 3,600 = 2.724\text{ Wh}$.
Real-World Calculation Examples
Scenario 1: 50 kg Boulder on 20m Cliff
Parameters: $m = 50.0\text{ kg}$, $h = 20.0\text{ m}$, $g = 9.81\text{ m/s}^2$
Result: $PE = 9.807\text{ kJ}$ ($9,806.65\text{ J}$, $19.81\text{ m/s}$ freefall speed). Cliff boulder potential.
Scenario 2: Hydroelectric Dam Reservoir Water (1,000,000 kg @ 50m)
Parameters: $m = 1,000,000.0\text{ kg}$ ($1,000\text{ m}^3$), $h = 50.0\text{ m}$, $g = 9.81\text{ m/s}^2$
Result: $PE = 490.33\text{ MJ}$ ($490,332.5\text{ kJ}$, 136.2 kWh). Hydroelectric dam potential energy.
Scenario 3: Skydiver in Aircraft (80 kg @ 4,000m)
Parameters: $m = 80.0\text{ kg}$, $h = 4,000.0\text{ m}$, $g = 9.81\text{ m/s}^2$
Result: $PE = 3.138\text{ MJ}$ ($3,138.13\text{ kJ}$, 750 kcal). Skydiver potential energy.
Scenario 4: Lunar Rover on Moon (500 kg @ 10m, g = 1.62 m/s²)
Parameters: $m = 500.0\text{ kg}$, $h = 10.0\text{ m}$, $g = 1.62\text{ m/s}^2$
Result: $PE = 8.100\text{ kJ}$ ($8,100.00\text{ J}$, $5.69\text{ m/s}$ impact). Lunar gravity potential.
Key Benefits of Using This Calculator
Conservation of Energy & Impact Speed
Calculates equivalent freefall impact velocity ($v = \sqrt{2gh}$) assuming zero air resistance.
Multi-Planet Gravity Compatibility
Supports Earth ($9.81\text{ m/s}^2$), Moon ($1.62\text{ m/s}^2$), Mars ($3.71\text{ m/s}^2$), and custom gravity values.
Multi-Unit Readouts
Outputs potential energy in Joules, Kilojoules (kJ), Megajoules (MJ), Imperial $\text{ft}\cdot\text{lbf}$, and Wh.
100% Free & Client-Side
Executes locally in your browser with zero latency or web server transmission.
Frequently Asked Questions (FAQ)
What is gravitational potential energy?
Gravitational potential energy (PE) is the stored energy an object possesses due to its position in a gravitational field relative to a reference height datum (PE = m * g * h).
What is the formula for gravitational potential energy?
PE = m * g * h, where m is mass in kg, g is gravitational acceleration (9.80665 m/s² on Earth), and h is height in meters.
What is the SI unit of potential energy?
Joule (J), defined as 1 kg*m²/s² = 1 N*m.
How does potential energy convert to kinetic energy during freefall?
By Conservation of Mechanical Energy: as height h decreases, gravitational PE decreases and converts 100% into kinetic energy (KE = 1/2*m*v²), so 1/2*m*v² = m*g*h => v = sqrt(2*g*h).
What is Universal Gravitational Potential Energy formula for astronomical distances?
PE = -G * M * m / r, where G is Gravitational Constant, M is planet mass, m is object mass, and r is distance from planet center.
Why is height datum arbitrary in potential energy?
Only DIFFERENCES in potential energy (Delta PE = m*g*Delta h) have physical significance; ground level, sea level, or floor level can be chosen as h = 0.
How hydroelectric dams generate electrical power using potential energy?
Water stored behind a high dam possesses gravitational potential energy PE = m*g*h; releasing water through penstocks converts PE into kinetic energy to spin turbines and generators.
What is the gravity g on Moon and Mars?
Moon g = ~1.62 m/s² (16.5% of Earth); Mars g = ~3.71 m/s² (37.8% of Earth); Jupiter g = ~24.79 m/s² (253% of Earth).
How converts Joules to Kilocalories?
Divide Joules by 4,184 (1 kcal = 4,184 Joules).
Is gravitational potential energy a conservative force field?
Yes! Gravity is a conservative force, meaning work done lifting an object depends ONLY on initial and final heights, completely independent of path taken.