Example data table
| Scenario | Inputs | Initial energy (J) |
|---|---|---|
| Gravitational | m = 10 kg, g = 9.81 m/s², h = 5 m, h₀ = 0 m | 490.5 |
| Spring | k = 800 N/m, x = 0.12 m | 5.76 |
| Electric | q = 250 μC, V = 12 V | 0.003 |
These examples match the formulas shown below.
Formula used
- Gravitational: E = m × g × (h − h₀)
- Spring: E = ½ × k × x²
- Electric: E = q × V
Efficiency output is E_available = E × (efficiency/100).
How to use this calculator
- Select the energy source you want to model.
- Enter inputs in any supported unit system.
- Set a reference height for meaningful comparisons.
- Choose an efficiency if losses reduce usable energy.
- Click Calculate to view conversions and export options.
What initial potential energy means
Initial potential energy is stored energy at a system’s starting state. This calculator covers three models: gravitational energy from height, spring energy from deformation, and electric energy from charge at a voltage. Results appear in joules and key equivalents for clear reporting.
Gravitational energy with reference height
For gravitational setups, the calculator uses E = m·g·(h − h₀). The reference height h₀ matters because only the height difference changes energy. Example: m = 10 kg, g = 9.81 m/s², h = 5 m, and h₀ = 0 m gives E = 490.5 J. If h₀ increases to 2 m, Δh becomes 3 m and energy becomes 294.3 J.
Gravity presets for different environments
Gravity can be set to standard 9.80665 m/s² or presets like Moon 1.62 m/s² and Mars 3.71 m/s². Using the same 10 kg mass and Δh = 5 m, energy is about 81.0 J on the Moon and 185.5 J on Mars. A custom g option helps model elevators, test rigs, or simulated gravity values.
Spring energy from compression or stretch
Spring energy is computed with E = ½·k·x², where k is stiffness and x is displacement from equilibrium. Because x is squared, doubling displacement increases energy four times. Example: k = 800 N/m and x = 0.12 m yields 5.76 J. Increasing x to 0.24 m raises energy to 23.04 J, assuming the spring remains in its linear range.
Electric energy from charge and voltage
The electric model uses E = q·V. With q = 250 μC and V = 12 V, energy is 0.003 J. This is small compared with many mechanical examples, but it becomes meaningful at larger charge, higher voltage, or repeated pulses. The sign of q affects the sign of E, which can be useful in bookkeeping calculations.
Conversions that add context
Joules are converted to kJ, Wh, calories, eV, and a TNT equivalent. For example, 490.5 J equals about 0.136 Wh, 117.3 cal, and roughly 3.06×10²¹ eV. These views help you relate mechanical storage to electrical consumption, food energy units, and small particle-scale energies.
Efficiency and rounding for realistic outputs
Real systems lose energy to friction, damping, and heat. The calculator applies an efficiency factor to show “available energy” as E×(eff/100). If 490.5 J is stored and efficiency is 80%, the usable value is 392.4 J. Use the CSV and PDF exports to share results with teammates quickly. Significant-digit rounding keeps reports consistent for lab notes, estimates, or teaching examples.
FAQs
1) Why can gravitational energy be negative?
If h is below the reference height h₀, then (h − h₀) is negative. The sign reflects your chosen reference level, not “bad energy.” Only changes in height relative to the reference affect the value.
2) Which gravity option should I use?
Use Standard or Earth for everyday problems. Use Moon or Mars for those environments. Choose Custom when you have a measured or specified g value from a test rig, simulation, or special scenario.
3) Does spring energy work for both compression and extension?
Yes. The calculator uses x², so compression and extension of the same magnitude store the same energy in an ideal linear spring. Just enter the displacement size from equilibrium.
4) Why is my electric energy very small?
Energy from E = q·V depends on charge in coulombs. Microcoulombs are tiny amounts of charge, so the energy can be small even at moderate voltage. Increase q, V, or use repeated events to compare totals.
5) What does the efficiency setting change?
Efficiency scales the stored energy to an “available” value: E_available = E × (eff/100). It helps model losses such as friction, damping, heating, or conversion inefficiencies in real systems.
6) When should I increase rounding digits?
Use more significant digits when inputs are precise or when you need consistent reports across conversions. Use fewer digits for quick estimates, classroom demonstrations, or when input measurements are approximate.