Calculator Inputs
Formula Used
This calculator supports four important potential energy formulas.
- Gravitational: U = mgh
- Elastic spring: U = 1/2 kx²
- Charge and voltage: U = qV
- Point charges: U = kq₁q₂/r
All inputs are converted to SI units before calculation. The result is then converted into the selected output unit.
How to Use This Calculator
- Select the potential energy type.
- Enter the required values for that formula.
- Choose matching units for each input.
- Select the final energy unit.
- Set decimal precision if needed.
- Press the calculate button.
- Review the result, formula, steps, and equivalent units.
- Download the CSV or PDF report.
Example Data Table
| Case | Formula | Sample Inputs | Approximate Result |
|---|---|---|---|
| Raised object | U = mgh | m = 5 kg, g = 9.80665 m/s², h = 10 m | 490.3325 J |
| Compressed spring | U = 1/2 kx² | k = 250 N/m, x = 0.2 m | 5 J |
| Charge in voltage | U = qV | q = 2 uC, V = 12 V | 2.4E-5 J |
| Two point charges | U = kq₁q₂/r | q₁ = 3 uC, q₂ = -1 uC, r = 0.05 m | -0.5393 J |
Potential Energy Formula Calculator Guide
What Potential Energy Means
Potential energy is stored energy. It appears when position, shape, or electric condition can create work later. This calculator helps compare common classroom and engineering cases. It supports gravitational energy near Earth, elastic energy in springs, charge energy in a voltage field, and interaction energy between point charges.
Gravitational Potential Energy
Gravitational potential energy depends on mass, gravity, and height. A heavier object stores more energy at the same level. A higher position also stores more energy. The value can be positive or negative if your chosen reference height is above or below zero. For normal school problems, ground is often the zero point.
Elastic Potential Energy
Elastic potential energy depends on stiffness and displacement. A spring with a large spring constant stores energy faster. Doubling the stretch or compression makes energy four times larger. That square term is important. It means small measurement errors in displacement can strongly change the answer.
Electric Potential Energy
Electric potential energy can be found in two ways. The charge and voltage method uses U equals qV. It is useful for circuits, particles, capacitors, and field work. The point charge method uses separation distance. It shows whether two charges store positive or negative interaction energy. Like charges give positive energy. Opposite charges give negative energy.
Unit Conversion and Reports
Unit conversion is a major source of mistakes. This page converts mass, distance, spring constant, charge, voltage, and final energy. You can enter grams, pounds, centimeters, inches, microcoulombs, kilovolts, and other common choices. The internal calculation uses SI units. Results can then be displayed as joules, kilojoules, calories, electron volts, watt hours, or foot pounds.
Checking Your Work
The step summary is useful for checking work. It shows converted inputs, selected formula, raw joules, and the final unit. Use the notes box to record the reference level, spring direction, sign convention, or test case. Exporting results helps save lab reports, homework checks, or design comparisons.
Real World Limits
Potential energy is not always the same as usable energy. Friction, heat, sound, air drag, and material losses can reduce real output. Use the result as an ideal physics estimate unless your system includes efficiency factors. For safety work, compare the value with standards, impact limits, and verified measurements. Always verify unusual inputs with a teacher, engineer, or measured experiment before making important design decisions today.
FAQs
What is potential energy?
Potential energy is stored energy caused by position, shape, charge, or a field. It can become motion, heat, sound, or other energy forms when conditions change.
Which formula should I choose?
Use U = mgh for height, U = 1/2 kx² for springs, U = qV for charge in voltage, and U = kq₁q₂/r for two point charges.
Why can electric potential energy be negative?
Electric potential energy depends on charge signs. Opposite charges can give negative energy. This shows an attractive interaction relative to the chosen zero reference.
Can height be negative?
Yes. Height can be negative if the chosen zero level is above the object. The result then becomes negative under the same sign convention.
Why does spring displacement get squared?
Spring energy grows with the square of displacement. Doubling stretch or compression creates four times the stored energy when the spring constant stays the same.
What units are used internally?
The calculator converts values into SI units before calculation. It uses kilograms, meters, newtons per meter, coulombs, volts, and joules internally.
Is this calculator suitable for lab reports?
It can help prepare checks and summaries. Always include your measured values, uncertainty, reference level, and teacher or lab instructions in formal reports.
Why are CSV and PDF downloads included?
CSV is useful for spreadsheets. PDF is useful for sharing a readable result summary with formulas, inputs, notes, and final converted energy.