Our Potential Energy Calculator helps students, engineers, and enthusiasts calculate the stored energy of an object due to its height and mass. Using the formula:
$$PE = m \times g \times h$$
📘 Formula Derivation
Potential Energy is derived from the work done against gravity. Work = Force × Distance. Force due to gravity = \( F = m \times g \). Distance = height (h). So, \[ PE = F \times h = (m \times g) \times h \] which simplifies to: \[ PE = m \times g \times h \]
This tool not only gives results in Joules but also provides unit conversions, energy equivalents, kinetic energy simulations, and planetary gravity variations. It is designed for both learning and practical applications in physics and engineering.
🔹 Features of the Potential Energy Calculator
1. Standard PE Calculation
Enter mass (m), height (h), and gravity (g) to calculate potential energy:
$$PE = m \times g \times h$$
2. Unit Conversion Output
Results are automatically converted into:
- Kilojoules (kJ)
- Calories (cal)
- Foot-pounds (ft·lb)
3. Energy Equivalents
To help visualize results, the calculator translates energy into real-life equivalents, such as:
- Lifting an apple by a few meters 🍎
- Raising a book onto a shelf 📚
- Lifting gym weights 🏋️
- Powering a light bulb 💡
4. Energy Conversion to Kinetic Energy
When dropped, potential energy converts to kinetic energy. The relationship is:
$$PE = KE = \tfrac{1}{2} m v^2$$
The impact velocity is calculated as:
$$v = \sqrt{2gh}$$
5. Variable Gravity Selection
Choose gravitational acceleration for different planets:
- 🌍 Earth: \( g = 9.81 \, m/s^2 \)
- 🌙 Moon: \( g = 1.62 \, m/s^2 \)
- 🔴 Mars: \( g = 3.71 \, m/s^2 \)
- 🟠 Jupiter: \( g = 24.79 \, m/s^2 \)
- ✏️ Custom gravity input
6. Formula Derivation (Step-by-Step)
Show Derivation
Potential energy is derived from the work-energy principle:
Work = Force × Distance
Gravitational Force: $$F = m \times g$$
Distance moved = height (h)
Therefore: $$PE = F \times h = (m \times g) \times h$$
Final formula: $$PE = m \times g \times h$$
📘 How to Use the Potential Energy Calculator
- Select your calculation mode (PE, mass, or height).
- Enter the known values (mass, height, or PE).
- Choose your unit system (Metric or Imperial).
- Pick a gravity preset (Earth, Moon, Mars, Jupiter) or enter a custom value.
- Click Calculate to view results with unit conversions, equivalents, and kinetic energy output.
🧮 Example Calculation
Mass (m): 5 kg
Height (h): 10 m
Gravity (g): 9.81 m/s²
Formula: $$PE = m \times g \times h$$
Substitution: $$PE = 5 \times 9.81 \times 10 = 490.5 \, J$$
Output:
• 490.5 J
• 0.49 kJ
• 117.3 cal
• 361.5 ft·lb
• Equivalent: lifting a heavy book onto a shelf 📚
• Impact velocity: ~14 m/s when dropped
⚡ Applications of Potential Energy
- Physics Education – Learn concepts of energy conservation.
- Engineering – Estimate stored energy in structures or machinery.
- Astronomy – Understand energy differences under various planetary gravities.
- Daily Life – Relating energy values to simple activities.
❓ FAQ – Potential Energy Calculator
Q1. What is potential energy?
Potential energy is the stored energy of an object due to its position in a gravitational field.
Q2. Can I use imperial units?
Yes. Enter mass in pounds (lb) and height in feet (ft), and the calculator will convert them.
Q3. Does the calculator support different planets?
Yes. You can select Earth, Moon, Mars, or Jupiter, or set your own gravity value.
Q4. How is potential energy related to kinetic energy?
When an object falls, its potential energy converts into kinetic energy until it hits the ground.