Kinetic Energy (½mv²) | Potential Energy (mgh) | Mechanical Energy (KE + PE)
Result
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📝 Step-by-step solution
Select energy type and enter values
💡 KE = ½ × mass × velocity² | PE = mass × gravity (9.81) × height | Energy in Joules | g = 9.81 m/s²
📖 How to Use This Energy Calculator
1
Select energy type - Choose Kinetic Energy (KE), Potential Energy (PE), or Mechanical Energy (KE+PE).
2
Enter the required values - For KE: mass and velocity. For PE: mass and height. For Mechanical: mass, velocity, and height.
3
Click "Calculate Energy" - Get your result with a complete step-by-step solution.
⚡ Understanding Energy in Physics
Energy is the capacity to do work. It exists in many forms, but two fundamental types in mechanics are kinetic energy (energy of motion) and potential energy (stored energy due to position or configuration). The SI unit for energy is the Joule (J).
The Law of Conservation of Energy states that energy cannot be created or destroyed, only transformed from one form to another. In a closed system, total mechanical energy (KE + PE) remains constant if only conservative forces (like gravity) act.
📊 Energy Formulas
Kinetic Energy (KE): KE = ½ × m × v²
Where: m = mass (kg), v = velocity (m/s)
Potential Energy (PE): PE = m × g × h
Where: m = mass (kg), g = gravity (9.81 m/s²), h = height (m)
Mechanical Energy (ME): ME = KE + PE = ½mv² + mgh
🔬 Real-World Examples
Roller Coaster: Maximum PE at the top → converts to KE as it goes down
Pendulum: Energy oscillates between KE and PE
Hydroelectric Dam: Water's PE converts to KE to spin turbines
Car Braking: KE converts to heat energy (thermal)
Bouncing Ball: PE at height → KE at impact
💡 Typical Energy Values
1 Joule (J): Energy to lift a small apple 1 meter
1 Kilojoule (kJ) = 1000 J: Energy in a bite of food
1 Calorie (food) = 4184 J: Energy in food
1 kWh = 3.6 × 10⁶ J: Household electricity unit
Car at 60 mph (1000 kg): KE ≈ 180,000 J
❓ Frequently Asked Questions (FAQ)
What is the difference between kinetic and potential energy?
Kinetic energy is the energy of motion (moving object). Potential energy is stored energy based on position (height) or configuration (spring compression). They can convert between each other.
Why is gravity 9.81 m/s²?
Gravity on Earth's surface is approximately 9.81 m/s². This value varies slightly by location (9.76-9.83 m/s²). Other planets have different gravitational accelerations (Moon: 1.62 m/s², Mars: 3.71 m/s²).
What is the law of conservation of mechanical energy?
In the absence of non-conservative forces (like friction or air resistance), total mechanical energy (KE + PE) remains constant. Energy changes form between kinetic and potential but total stays the same.
Can energy be negative?
Kinetic energy is always positive (depends on v²). Potential energy can be negative if we choose a reference point (e.g., below ground level). Total energy in a bound system (like Earth-Moon) is negative.
What is the difference between energy and power?
Energy is the capacity to do work (measured in Joules). Power is the rate at which energy is used or transferred (measured in Watts = Joules/second). Power = Energy ÷ Time.
How does mass affect kinetic energy?
Kinetic energy is directly proportional to mass. Doubling mass doubles KE (at same velocity). Velocity has a greater effect because KE depends on v² - doubling velocity quadruples KE.