Energy Calculator
Calculate energy calculator calculate total mechanical energy E = KE + PE from mass m, velocity v, and height h. Accurate physics formulas and unit conversions for engineers, students & technicians.
Calculate Total Mechanical Energy
Enter your physical parameters below to compute verified energy metrics.
Calculation Results
Calculated using verified physical methodology: Total Mechanical Energy: E = KE + PE = \1 / 2m v^2 + m \cdot g \cdot h
Conversion Identity: 1\text{ J} = 0.000947817\text{ BTU} = 0.000239006\text{ kcal}
Quick Summary
The Energy Calculator computes total mechanical energy ($E = KE + PE = \1 / 2mv^2 + mgh$) by summing kinetic energy and gravitational potential energy across SI and Imperial units (Joules, kJ, MJ, BTU, and kWh).
Formula Explanation
Total Mechanical Energy: E = KE + PE = \1 / 2m v^2 + m \cdot g \cdot h
Conversion Identity: 1\text{ J} = 0.000947817\text{ BTU} = 0.000239006\text{ kcal}
How It Works
The Energy Calculator computes kinetic energy ($KE = 0.5 \cdot m \cdot v^2$) and potential energy ($PE = m \cdot g \cdot h$). It sums them into total mechanical energy ($E_{total}$), outputting metrics in Joules, kJ, MJ, Imperial BTU, and electrical kWh.
Step-by-Step Worked Example
Practical Problem: Calculate total mechanical energy for a 10.0 kg object moving at $20.0\text{ m/s}$ at an elevation height of $15.0\text{ meters}$.
- Step 1: Identify Input Values: Mass $m = 10.0\text{ kg}$, Velocity $v = 20.0\text{ m/s}$, Height $h = 15.0\text{ m}$, $g = 9.81\text{ m/s}^2$.
- Step 2: Calculate Kinetic Energy ($KE$): $KE = 0.5 \times 10.0 \times (20.0)^2 = 5.0 \times 400.0 = 2,000.00\text{ Joules}$.
- Step 3: Calculate Potential Energy ($PE$): $PE = 10.0 \times 9.81 \times 15.0 = 1,471.50\text{ Joules}$.
- Step 4: Sum Total Mechanical Energy ($E_{total}$): $E_{total} = 2,000.00 + 1,471.50 = 3,471.50\text{ Joules}$.
- Step 5: Convert and Interpret Imperial & Electrical Units: Total Energy $E = 3,471.50\text{ J} = 3.472\text{ kJ}$. Imperial BTU: $3,471.5 \times 0.000947817 = 3.290\text{ BTU}$. Electrical kWh: $\3,471.5 / 3,600,000 = 0.000964\text{ kWh}$.
Real-World Calculation Examples
Scenario 1: Roller Coaster Peak & Dip Motion
Parameters: $m = 500\text{ kg}$, $v = 20.0\text{ m/s}$, $h = 15.0\text{ m}$
Result: $E = 173,575.00\text{ J}$ ($173.58\text{ kJ}$). Combined mechanical energy.
Scenario 2: Projectile Cannonball Flight
Parameters: $m = 5.0\text{ kg}$, $v = 100.0\text{ m/s}$, $h = 50.0\text{ m}$
Result: $E = 27,452.50\text{ J}$ ($27.45\text{ kJ}$). Cannonball total mechanical energy.
Scenario 3: Hydroelectric Dam Water Storage Drop
Parameters: $m = 1,000\text{ kg}$ (1 m³ water), $v = 0\text{ m/s}$, $h = 100.0\text{ m}$
Result: $E = 980,665.00\text{ J}$ ($980.67\text{ kJ}$). Potential energy head for power generation.
Scenario 4: High-Speed Vehicle Crash Test
Parameters: $m = 1,500\text{ kg}$, $v = 30.0\text{ m/s}$ (108 km/h), $h = 0\text{ m}$
Result: $E = 675,000.00\text{ J}$ ($675.00\text{ kJ}$). Pure kinetic energy crash impact.
Key Benefits of Using This Calculator
Combined KE & PE Breakdown
Provides simultaneous calculation of Kinetic Energy ($KE$) and Potential Energy ($PE$).
Conservation of Energy Support
Verifies total mechanical energy conservation ($E_{total} = KE + PE$).
Multi-Unit Readouts
Outputs energy in Joules, kJ, MJ, Imperial BTU, and electrical kWh.
100% Free & Client-Side
Executes locally in your browser with zero latency or web server transmission.
Frequently Asked Questions (FAQ)
What is mechanical energy?
Mechanical energy is the sum of kinetic energy (energy of motion) and potential energy (stored energy of position): E = KE + PE.
What is the Law of Conservation of Energy?
The Law of Conservation of Energy states that energy cannot be created or destroyed, only transformed from one form to another (E_initial = E_final).
What is kinetic energy vs potential energy?
Kinetic energy KE = 0.5 * m * v² is possessed due to motion; gravitational potential energy PE = m * g * h is possessed due to height position.
What is the SI unit of energy?
The SI unit of energy is the Joule (J), defined as 1 kg·m²/s².
How converts Joules to BTU and kWh?
Multiply Joules by 0.000947817 for BTU; divide Joules by 3,600,000 for kWh (e.g. 3.6 MJ = 1 kWh = 3,412 BTU).
What is Einstein's mass-energy equivalence formula?
E = m * c², stating that rest mass m contains total rest energy E equal to mass times speed of light squared (c = 3 x 10^8 m/s).
How does air resistance affect mechanical energy conservation?
Non-conservative forces like air drag dissipate mechanical energy into thermal heat energy, reducing mechanical E_total over time.
What is elastic potential energy?
Elastic potential energy PE_elastic = 0.5 * k * x² is energy stored in a compressed or stretched spring of stiffness constant k.
What is 1 food Calorie (kcal) in Joules?
1 food Calorie (1 kcal = 1,000 cal) equals 4,184 Joules (4.184 kJ).
How is energy related to power?
Energy is total work capability (J); power is the rate of energy consumption or generation over time: P = E / t.