Calculate gravitational potential energy \(U_g=mg(h-h_{\mathrm{ref}})\) and apply conservation of mechanical energy to solve for speed, height, or mass with a custom reference height.
Enter the known values, then click “Calculate”.
Gravitational Potential Energy and Conservation of Mechanical Energy
Physics Classical Mechanics • Work Energy and Power
Frequently Asked Questions
What is gravitational potential energy near Earth's surface?
It is U = mg(h - href), where m is mass, g is gravitational field strength, h is height, and href is the chosen zero-potential reference height.
Does the reference height matter?
The numerical value of potential energy depends on the reference height, but energy differences are what affect motion.
What is conservation of mechanical energy?
It is the principle that K + U remains constant when only conservative forces act. For gravity-only motion, K1 + U1 = K2 + U2.
How is non-conservative work included?
Use K1 + U1 + Wnc = K2 + U2. Positive Wnc adds mechanical energy, while negative Wnc removes mechanical energy.
How do I find speed at the bottom of a frictionless hill?
Compute K2 = K1 + U1 - U2, then use v2 = sqrt(2K2/m).
Why can the calculator say a final height is impossible?
If the requested final height requires more potential energy than the system has, the computed final kinetic energy becomes negative, which is physically impossible.
Can gravitational potential energy be negative?
Yes. It is negative when the object is below the selected reference height.
Does mass cancel in conservation of energy?
In many frictionless height-speed problems, mass cancels because every energy term contains m. It does not necessarily cancel when a fixed non-conservative work value is included.
What units should I use?
Use kilograms for mass, meters for height, meters per second for speed, meters per second squared for gravity, and joules for energy in SI input.