Potential energy is stored energy based on an object's position or configuration — gravitational potential energy (PE = mgh) depends on height above a reference point, elastic potential energy (PE = ½kx²) depends on spring compression or extension, and electric potential energy depends on charge separation. These forms of stored energy convert to kinetic energy when released: a 70 kg person standing on a 10-meter diving platform has PE = 70 × 9.81 × 10 = 6,867 joules of gravitational potential energy, which converts entirely to kinetic energy (and ultimately to thermal energy and sound) upon hitting the water. Our potential energy calculator computes gravitational PE from mass, height, and gravitational acceleration, elastic PE from spring constant and displacement, and electric PE from charges and distance. It handles unit conversions between joules, calories, electron-volts, and foot-pounds, making it useful for physics problems, engineering design, and energy analysis.
Gravitational potential energy
Gravitational PE = mgh, where m is mass (kg), g is gravitational acceleration (9.81 m/s² on Earth), and h is height above the reference point (meters). The reference point is arbitrary — what matters is the change in height. A 1,000 kg car at the top of a 50-meter hill has PE = 1,000 × 9.81 × 50 = 490,500 J (490.5 kJ) relative to the bottom. This energy converts to kinetic energy as the car descends — at the bottom (assuming no friction), it reaches v = √(2gh) = √(2 × 9.81 × 50) = 31.3 m/s (70 mph). Hydroelectric dams exploit this principle: water falling through a height (head) drives turbines. The Hoover Dam's 180-meter head generates enormous energy per cubic meter of water: PE = 1,000 × 9.81 × 180 = 1,765,800 J per m³.
Elastic potential energy in springs
Elastic PE = ½kx², where k is the spring constant (N/m or lb/in) and x is the displacement from equilibrium. This relationship is quadratic — doubling the compression quadruples the stored energy. A spring with k = 500 N/m compressed 0.1 m stores PE = ½ × 500 × 0.01 = 2.5 J. A car suspension spring (k ≈ 25,000 N/m) compressed 5 cm by hitting a bump stores PE = ½ × 25,000 × 0.0025 = 31.25 J per spring. Bows and crossbows store elastic PE — a compound bow with k ≈ 2,500 N/m at 0.7m draw stores approximately 612 J, enough to launch an arrow at 90+ m/s. The spring constant determines the force-displacement relationship: F = kx (Hooke's law) — a stiffer spring requires more force to compress but stores more energy per unit displacement.
Conservation of energy and practical applications
The conservation of energy principle states that total energy (kinetic + potential) remains constant in an isolated system (ignoring friction and air resistance). At the top of a roller coaster hill, energy is mostly potential; at the bottom, it is mostly kinetic. This principle enables simple calculations: a ball dropped from 5 meters reaches v = √(2 × 9.81 × 5) = 9.9 m/s at ground level regardless of mass. With friction, some energy converts to heat — a real roller coaster at the bottom of a 30-meter drop reaches approximately 85-90% of the theoretical speed due to friction and air resistance losses. In engineering, potential energy analysis is critical for: sizing pumps (must overcome gravitational PE of water being lifted), designing safety systems (energy absorbed by crash barriers), and energy storage (pumped hydro stores energy as gravitational PE by pumping water uphill during low-demand periods).