Potential Energy
Calculate gravitational potential energy from mass and height. Analyze stored energy and energy conversions.
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Why: Understanding potential energy helps you make better, data-driven decisions.
How: Enter Mass (m), Height (h), Potential Energy to calculate results.
Run the calculator when you are ready.
Potential Energy Calculator
PE = mgh • Elastic ½kx² • Energy Conservation
Sample Scenarios — Click to Load
Input Parameters
Mass
Height
Gravity
For educational and informational purposes only. Verify with a qualified professional.
📋 Key Takeaways
- • Gravitational PE PE = mgh — stored energy due to height; reference point matters
- • Elastic PE PE = ½kx² — energy stored in springs
- • PE + KE = constant (no friction) — conservation of mechanical energy
- • Equivalent velocity v = √(2gh) — speed if object is dropped from height h
💡 Did You Know?
📖 How Potential Energy Calculation Works
Potential energy is stored energy due to position. Gravitational PE = mgh; elastic PE = ½kx².
Step 1: Convert to SI
Mass in kg, height in m, g in m/s². Use g = 9.81 for Earth.
Step 2: Apply PE = mgh
PE = mass × 9.81 × height. Result in Joules.
Step 3: Derived Values
Equivalent velocity v = √(2PE/m). If dropped, this is impact speed.
🎯 Expert Tips
💡 Reference Point
PE is relative. Choose ground, table, or any reference. Only ΔPE matters physically.
💡 mgh Limits
PE = mgh works near Earth. For satellites use PE = -GMm/r.
💡 Energy Conservation
PE_top = KE_bottom for falling objects. v = √(2gh) from rest.
💡 Hydroelectric
Power = η × ρ × g × h × Q. Dam height and flow rate determine output.
⚖️ PE Comparison
| Object | Mass | Height | PE (J) |
|---|---|---|---|
| Apple | 0.1 kg | 2.5 m | 2.45 |
| Person | 70 kg | 3 m | 2,060 |
| Coaster | 800 kg | 50 m | 392,400 |
| Skydiver | 80 kg | 4000 m | 3.14M |
❓ FAQ
Can PE be negative?
Yes. PE is relative to reference. Below reference = negative PE. Only ΔPE matters.
What happens when object falls?
PE converts to KE. At ground, PE=0, all energy is KE. v = √(2gh).
PE vs elastic PE?
Gravitational PE = mgh. Elastic PE = ½kx² for springs. Both are stored energy.
Why mgh for Earth only?
Assumes constant g. For large heights use PE = -GMm/r.
How does PE relate to work?
Work done against gravity = ΔPE. Lifting stores PE.
PE without motion?
Yes. PE is stored; object at rest at height has PE but zero KE.
📊 PE by the Numbers
📚 Sources
⚠️ Disclaimer: Theoretical values from PE = mgh and PE = ½kx². Real-world factors (friction, air resistance) affect results. For high altitude use PE = -GMm/r.
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