Potential Energy Calculator
PE (J)
4900
How it works
Gravitational potential energy (GPE) is the energy stored in an object due to its height above a reference point: PE = m × g × h, where m is mass, g is gravitational acceleration (9.81 m/s²), and h is height. This energy is recoverable as kinetic energy when the object falls.
**Choosing a reference point** The reference height (h = 0) is arbitrary — only differences in PE matter. For a ball thrown upward, the ground is a natural reference. For a hydroelectric dam, the turbine elevation is the reference. The choice affects sign but not the energy difference between two states.
**Elastic potential energy** Springs and deformed materials store elastic PE: PE = ½ × k × x², where k is the spring constant (N/m) and x is displacement from equilibrium. The squared displacement means a spring compressed twice as far stores four times the energy. Car suspension springs, rubber bands, and trampolines store and release elastic PE.
**Chemical and other potential energies** PE extends beyond gravity and springs: chemical bonds store energy released in combustion, nuclear bonds store energy released in fission/fusion, electric fields store energy in charged systems. The general principle is the same — potential energy is work done against a conservative force, recoverable without loss.
**Conservation of mechanical energy** In frictionless systems, total mechanical energy (KE + PE) is constant. A pendulum swings from maximum height (all PE) to minimum height (maximum KE) and back. Real systems lose energy to friction and air resistance — conservation holds for the total including heat generated.
Frequently Asked Questions
- PE = m × g × h. A 200,000-liter (200 m³) water tower with average height of 25 m: mass = 200,000 kg. PE = 200,000 × 9.81 × 25 = 49,050,000 J ≈ 49 MJ = 13.6 kWh. As electricity this is minimal, but as hydraulic pressure (flow potential), it provides continuous pressure to thousands of homes. Pumped hydro storage works the same way at massive scale — Dinorwig in Wales stores 9 GWh by pumping 7 million m³ of water 500 m uphill.
- Elastic PE is stored in compressed or stretched elastic materials: PE_elastic = ½kx², where k is spring stiffness (N/m) and x is deformation. The energy source is mechanical work done against the restoring force. Gravitational PE (mgh) comes from work done against gravity. Both are conservative — energy is fully recoverable without loss (in ideal systems). A compressed spring stores more energy for a given volume than an elevated mass in most practical scenarios. Bows, trampolines, rubber bands, and pneumatic accumulators all store elastic PE.
- Stable equilibrium corresponds to a potential energy minimum — displaced objects return to their original position. Unstable equilibrium corresponds to a PE maximum — any displacement causes the object to move away. A ball at the bottom of a bowl (stable) vs. balanced on top of a hill (unstable). Buckling analysis of columns uses PE: the buckled shape has lower total PE than the straight shape once load exceeds the critical (Euler buckling) load. Structural stability analysis is fundamentally an energy problem — finding conditions where PE is minimized.
- Battery energy is electrochemical potential energy — stored in the chemical bonds of the electrode materials and electrolyte. Capacity is rated in Wh or Ah (Ah × voltage = Wh). A 100 Ah, 12V lead-acid battery: 1200 Wh = 4.32 MJ = m × g × h equivalent: 4,320,000 / (9.81 × 1000) ≈ 440 m height for 1000 kg of water. Lithium-ion energy density (~250 Wh/kg) is far higher than lead-acid (~35 Wh/kg), explaining the shift to lithium for EVs and portable electronics.