Gravitational Potential Energy
Calculates Ep=m·g·h in joules from mass, height and gravitational acceleration.
—
Gravitational potential energy: Ep = m·g·h
Lift a body against gravity and it banks energy. That stored amount is the gravitational potential energy, Ep = m·g·h, measured in joules, with mass in kg, gravity g ≈ 9.81 m/s² near Earth's surface, and height in meters from whatever reference you pick. Put a 2 kg book on a 5 m shelf and it holds Ep ≈ 98 J relative to the floor. Let it fall and those 98 J show up as kinetic energy when it lands. Notice the result hangs on the reference you chose. The zero level is up to you, so what actually matters physically is the difference, ΔEp. When there's no friction and the system is conservative, Ec + Ep = constant, which is where mechanical energy conservation comes from.
Applications
It shows up in hydroelectric plants, where Itaipu's ~14 GW comes from turning the Ep of dammed water into electricity, and in pumped-storage hydropower. A roller coaster's first climb sets the energy budget the rest of the ride has to spend. The same idea drives free-fall problems, pile drivers, and gravitational batteries that hoist heavy weights to release the energy later.
FAQ
Does g change with location? It does. You get about 9.78 m/s² at the equator and 9.83 m/s² at the poles, a consequence of how the Earth spins and how it's shaped. For everyday problems, 9.81 m/s² is close enough.
What is the reference height? You decide where h = 0, whether that's the floor, sea level, or a table top. The physical results only depend on differences in Ep, never the absolute value.
Is mgh valid at any altitude? Only while the height stays small next to Earth's radius. Once you're dealing with satellites or space, switch to the general form Ep = -G·M·m/r.
Related Tools
Energy per Elevator Trip
Calculate the potential energy spent to raise a load, E = m·g·h, from the unbalanced mass m (net load after the counterweight, kg), gravity g and the lift height h (m). The result, in joules, is the minimum theoretical energy to hoist the load — a basis for estimating the elevator's electrical consumption and the energy-regeneration potential. Modern elevators with regenerative drives recover part of this energy on descent (when the counterweight descends with a light car), feeding it back to the grid. Actual consumption is higher, divided by the efficiency. Enter the unbalanced mass and the lift height.
Potential Energy Calculator
Compute gravitational potential energy PE = m g h with mass (kg), g and height (m).
Optimum Reflux Ratio
Compute a distillation column's operating reflux ratio, R = factor · Rmin, multiplying the minimum reflux by a factor (typically 1.1 to 1.5). There is a classic economic trade-off: a low reflux (near minimum) requires many plates (more column investment); a high reflux requires fewer plates but much more energy in the reboiler and condenser (more operating cost). The optimum balances the two. Enter the minimum reflux and the factor.
Kinetic Energy Calculator
Compute kinetic energy KE = ½ m v² from mass (kg) and velocity (m/s). Result in joules.
Spring Elastic Energy
Calculates the elastic energy stored in a spring E=0.5·k·x² in joules from constant and deformation.
Arc Flash Incident Energy (Lee Method)
Computes arc flash incident energy by the Ralph Lee method, E = 5.12×10⁵ × V × I_bf × t ÷ d², with voltage in kV, bolted fault current in kA, fault clearing time in seconds and working distance in millimetres. Lee's method models an open-air arc as an ideal radiant heat source, ignoring the energy an enclosure reflects back; IEEE 1584 therefore keeps it only as the legacy model, recommended for open-air arcs and for voltages above 15 kV where the empirical equations do not apply. The result in cal/cm² sets the PPE category: 1.2 cal/cm² is the second-degree burn threshold and the value that bounds the arc flash boundary. The cal/cm² form is adopted (the J/cm² variant uses 2.142×10⁶ and is 4.184 times larger). Enter the voltage, the fault current, the clearing time and the working distance.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.