Potential Energy Calculator
Calculate gravitational potential energy PE = m g h.
Quadratic Equation Solver (ax² + bx + c = 0)
About Potential Energy Calculator
The Gravitational, Elastic & Electrostatic Potential Energy ($U$) Calculator computes stored energy for elevated masses ($U = mgh$), compressed springs ($U = \frac{1}{2}kx^2$), planetary gravitation ($U = -G \frac{M m}{r}$), and point charges ($U = k_e \frac{q_1 q_2}{r}$).
How to Use Potential Energy Calculator
Step 1
Select Potential Energy Type (Gravitational, Spring / Hooke's, or Celestial).
Step 2
Enter mass and height (or spring constant $k$ and displacement $x$).
Step 3
Review computed potential energy and maximum free-fall velocity.
Step 4
Click "Copy Energy Value".
Practical Use Cases for Potential Energy Calculator
Hydroelectric Pumped Storage & Gravity Battery Sizing
Calculate megawatt-hours (MWh) of electrical energy stored in elevated water reservoirs or gravity battery hoist masses.
Mechanical Spring & Automotive Suspension Design
Compute stored strain energy in compression coil springs and determine required spring rates ($k$) for vehicle shock absorbers.
Input & Output Examples
Calculating Gravitational PE of 500kg Mass at 20m Height
Mass ($m$): `500 kg`, Height ($h$): `20 m`, Gravity ($g$): `9.80665 m/s²`
Potential Energy ($U$): `98,066.5 Joules (98.07 kJ)` | kWh Equivalent: `0.0272 kWh` | Impact Velocity from Drop: `19.81 m/s`
Key Features & Performance
- ✓Potential Energy Equations: Gravitational Near Earth ($mgh$), Celestial Gravitational ($-GMm/r$), Spring / Elastic Strain ($\frac{1}{2}kx^2$), Electrostatic ($k q_1 q_2 / r$).
- ✓Free Fall Velocity Predictor: computes velocity upon ground impact assuming 100% kinetic energy conversion ($v = \sqrt{2gh}$).
- ✓Unit conversions: Joules (J), Kilojoules (kJ), Watt-hours (Wh), Foot-pounds (ft-lbf), Kilocalories.
- ✓100% Client-Side memory execution.
- ✓1-Click Copy potential energy specs.
Key Terminology & Definitions
Potential Energy ($U$)
Stored energy an object possesses relative to other objects due to its spatial position, internal mechanical stress, or electric charge.
Spring Constant ($k$)
A measure of the stiffness of a spring in Newtons per meter (N/m), defined in Hooke's law as $F = -kx$.