Enter Values
Formula Used
Gravitational potential energy: PE = m × g × h
Elastic potential energy: PE = 1/2 × k × x²
Electric potential energy: PE = kₑ × q₁ × q₂ / r
Total potential energy: PE total = gravitational PE + elastic PE + electric PE
Here, m is mass, g is gravity, h is height, k is spring constant, x is displacement, q is charge, and r is distance.
How to Use This Calculator
- Select the calculation type.
- Enter the values needed for that energy model.
- Choose the correct units beside each input.
- Press Calculate to view the result above the form.
- Use CSV or PDF download buttons to save the report.
Example Data Table
| Case | Mass | Gravity | Height | Potential Energy |
|---|---|---|---|---|
| Book on shelf | 2 kg | 9.80665 m/s² | 1.5 m | 29.42 J |
| Crate lifted | 50 kg | 9.80665 m/s² | 3 m | 1471 J |
| Spring compressed | Not needed | Not needed | 0.2 m displacement | 4 J when k = 200 N/m |
Understanding Potential Energy
Potential energy is stored energy. It appears when position, shape, or electric separation can do work. In basic mechanics, the most common case is gravitational potential energy. A raised object can fall. Its stored energy depends on mass, local gravity, and height above a chosen reference. That reference can be the floor, a table, ground level, or any useful zero line.
Main Calculation Ideas
This calculator handles several practical forms. For a height problem, it uses mass, gravity, and vertical height. For a spring problem, it uses spring constant and compression or stretch. For an electric charge pair, it uses charge size and separation distance. Each input is converted into standard units before calculation. That helps reduce mistakes when values come from mixed unit systems.
Why Reference Level Matters
Potential energy is often measured as a change. The absolute zero point is selected by the user. If height is measured from the floor, the floor has zero gravitational potential energy. If height is measured from a shelf, the shelf becomes zero. The energy difference is what affects motion, safety, storage, and design.
Using Results Wisely
Results are shown in joules and common converted units. The tool also estimates an equivalent fall speed when mass is available. This speed assumes stored gravitational energy becomes motion without losses. Real systems lose energy through air drag, friction, heat, and sound. For engineering checks, add a safety margin and verify assumptions.
Physics Study Benefits
Potential energy connects force, motion, work, and conservation of energy. It helps explain roller coasters, cranes, springs, batteries, and charged particles. A clear calculation sheet makes homework and lab reports easier. The export options let you save values for records, comparison, or later review. Always enter positive magnitudes and match the height direction to your selected reference. Small unit errors can create very large energy errors.
Advanced Inputs
The advanced fields support realistic checks. You may include a height change, custom gravity, spring displacement, charge distance, and conversion preferences. The calculator separates each energy type before adding the total. This makes the answer easier to audit. It also shows intermediate steps, so teachers, students, and technicians can see how every displayed value was produced during final review.
FAQs
What is potential energy?
Potential energy is stored energy due to position, shape, or charge separation. It can become kinetic energy when a system moves or changes.
What is the main gravitational formula?
The main formula is PE = mgh. It multiplies mass, local gravity, and height above the selected reference level.
Which gravity value should I use?
Use 9.80665 m/s² for standard Earth gravity. Use a local or experimental value when your problem gives one.
Can height be negative?
Yes. A negative height can show position below your chosen reference level. The sign depends on your coordinate setup.
What does elastic potential energy mean?
Elastic potential energy is stored in a stretched or compressed spring. It depends on spring constant and displacement squared.
Why is electric potential energy sometimes negative?
Electric potential energy depends on charge signs. Opposite charges give a negative value, while like charges give a positive value.
Does the calculator include friction?
No. The formulas are ideal models. Real systems may lose energy through friction, heat, sound, air resistance, or deformation.
What does equivalent speed mean?
Equivalent speed estimates motion if stored energy becomes kinetic energy. It assumes no losses and requires a valid mass value.