Electric Potential Energy Calculator
Energy of a charge at an electric potential: U = q · V.
Inputs
Drag the handle (or focus it and press ↑/↓) to reorder. Scientific notation such as 1.6e-19 is accepted. Pick any unit; conversion is automatic. Use a negative q for negative charge. Pick any unit; conversion is automatic.
Results
Enter values and press Calculate. Your answer will appear here.
Potential energy vs. potential
For a fixed charge, U rises in direct proportion to V, and doubling q doubles U. The solid line is your charge, the dashed lines are half and double it, and the dot is your result.
What is being calculated
Reference values
| Potential V (for a charge of 1 e) | Energy U | In electronvolts |
|---|
One electronvolt is the energy of one elementary charge at one volt.
Typical potential differences (approximate)
| Source | V |
|---|---|
| AA battery | ≈ 1.5 V |
| Car battery | ≈ 12 V |
| Mains outlet (RMS) | ≈ 120 V or 230 V |
| Static shock from a doorknob | ≈ several kV |
| Medical X-ray tube | ≈ 30 to 150 kV |
| Lightning (cloud to ground) | ≈ 10⁸ V |
Constants used
| Constant | Value |
|---|---|
| Elementary charge e | 1.602176634×10⁻¹⁹ C |
| 1 electronvolt | 1.602176634×10⁻¹⁹ J |
| Coulomb constant k | 8.9875517923×10⁹ N·m²/C² |
| Electron mass | 9.1093837×10⁻³¹ kg |
Unit conversions
| Quantity | Conversion |
|---|---|
| Charge | 1 C = 1,000 mC = 10⁶ µC = 10⁹ nC · 1 e = 1.602×10⁻¹⁹ C |
| Potential | 1 kV = 1,000 V · 1 MV = 10⁶ V |
| Energy | 1 kJ = 1,000 J · 1 eV = 1.602×10⁻¹⁹ J · 1 MeV = 1.602×10⁻¹³ J · 1 kWh = 3.6×10⁶ J |
| Distance | 1 cm = 0.01 m · 1 mm = 10⁻³ m · 1 nm = 10⁻⁹ m |
Formula
- U: electric potential energy (J)
- q: charge (C), positive or negative
- V: electric potential at the charge’s position (V), relative to a zero reference
Example: q = 2 µC at V = 100 V. U = 2×10⁻⁶ C × 100 V = 2×10⁻⁴ J = 200 µJ.
For a charge moved between two points, the change in energy is ΔU = q·ΔV. For a point charge Q the potential is V = k·Q / r, so the energy of charge q at distance r is U = k·q·Q / r (zero at infinity); Advanced mode uses this when you pick the point-charge input. Rearranged: q = U / V and V = U / q. The sign matters: like charges (qQ > 0) give positive U and repel, opposite charges give negative U and attract. If you add a particle mass, the speed v = √(2|U| / m) assumes all of |U| becomes kinetic energy and is valid well below the speed of light.
References
- Wikipedia, Electric potential energy: U = q·V and the point-charge case
- OpenStax University Physics Vol. 2, Electric Potential Energy: derivation and examples
- NIST, Fundamental Physical Constants: e, k and particle masses
How to Use This Tool
- Pick a preset, or enter the charge q and its unit (use a negative value for negative charge).
- Enter the electric potential V and its unit.
- In Advanced, solve for q or V from a known energy, find V from a point charge Q and a distance, or add a mass to get the speed.
- Click Calculate.
- Read U in the highlighted result, in joules and electronvolts, and check the chart.
What This Tool Offers
- Basic and Advanced modes on one calculation engine
- Charge, potential and energy unit conversion, including elementary charge and electronvolts
- Energy in joules, eV and kWh with sign explained
- Solve for q or V, potential from a point charge, and speed from a mass (Advanced)
- Energy-vs-potential chart and labelled two-plate diagram
- Reorderable inputs, presets and a mobile-friendly layout
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| U | Electric potential energy | J |
| q | Charge | C |
| V | Electric potential (voltage) | V |
What it means
The electric potential energy U of a charge q located in an electric potential V is given by U = q·V. This represents the work required to bring the charge from infinity (where V = 0) to its present position. The potential energy is a scalar quantity and can be positive or negative depending on the signs of q and V. In circuits, the potential energy of charges is converted to other forms, such as heat in a resistor or kinetic energy in a motor. This concept is used to analyse energy transfer in electrochemical cells and capacitors. For a system of multiple charges, the total potential energy is the sum over all pairs. Understanding U helps in analysing conservation of energy in electrical systems. Example: A charge of 2µC placed at a point where the potential is 100V has potential energy U = 2e-6 * 100 = 2×10⁻⁴ J. If released, it would gain kinetic energy equal to this amount (assuming no losses).
Worked example
Electric Potential Energy – Practical Example
Real‑World| Parameter | Value |
|---|---|
| q | 2 µC = 2×10⁻⁶ C |
| V | 50 V |
| Formula | U = q·V |
Common mistakes
- Charge q: The test charge experiencing the potential.
- Voltage V: The electric potential at the charge’s location.
- Units: q in coulombs, V in volts → U in joules.
- Reference: Potential energy is defined relative to a reference (usually infinity).
- Sign: Positive charge gains energy when moving from low to high potential.
Applications
Electric potential energy U = q·V represents the energy a charge possesses due to its position in an electric field. This concept is essential for understanding the energy stored in capacitors, the operation of electron beams, and the behaviour of charged particles in electric fields. Engineers use it to design cathode ray tubes, particle accelerators, and electrostatic precipitators. By calculating the potential energy, they can determine the work required to move charges, which is crucial for energy conversion and transport. This formula bridges the gap between electrostatics and energy, enabling practical applications.
- Design of cathode ray tubes and electron microscopes
- Particle accelerator and mass spectrometer design
- Electrostatic precipitators for air pollution control
- Energy storage in capacitors and batteries
- Educational understanding of electric potential
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