Electric Potential (Voltage) Calculator

Enter the source charge and observation distance to instantly calculate electric potential, field strength, potential energy, and more.

Created by Luis GonzalezLast updated: May 9, 2026

How to Use This Calculator

1
Enter the Source Charge (Q)
Input the magnitude of the point charge in coulombs (C). Use scientific notation for small charges, e.g., '1e-9' for 1 nanocoulomb. Negative values will result in negative potential.
2
Specify the Distance (r)
Enter the radial distance in meters (m) from the point charge to the observation point. This value must be greater than zero.
3
Review Electrical Properties
The calculator will instantly display the electric potential (voltage), electric field magnitude, potential energy, and electron-volt energy at the specified point.

Example Calculation

An electrical engineer is analyzing the electric potential around a 1 nanocoulomb (1e-9 C) point charge at a distance of 0.05 meters.

Charge (Q) (C)

1e-9

Distance (r) (m)

0.05

Results

179.75 V

Tips

Potential is a Scalar Quantity

Unlike electric field (which is a vector with direction), electric potential is a scalar quantity. This simplifies calculations for multiple charges, as you can simply add their individual potentials.

Reference Point for Potential

Electric potential is always relative. By convention, the potential at an infinite distance from a point charge is considered zero. All other potentials are measured relative to this reference.

Voltage and Energy Relationship

A potential of 1 Volt means that 1 Joule of energy is required to move 1 Coulomb of charge from the zero-potential reference point to that location. For individual electrons, 1 electron-volt (eV) is the energy gained by an electron moving through 1 Volt.

Calculating Electric Potential and Field Properties for Point Charges

The Electric Potential (Voltage) Calculator determines the electric potential (voltage) at any given distance from a point charge, a fundamental concept in electrical engineering and physics. By inputting the charge magnitude and distance, this tool instantly computes the potential in volts, along with the electric field magnitude, potential energy, and energy per electron-volt. Understanding electric potential is crucial for designing circuits, analyzing electrostatic interactions, and comprehending energy dynamics in 2025.

Why Electric Potential is Fundamental to Electrical Systems

Electric potential, or voltage, is a cornerstone concept in electrical engineering because it quantifies the "push" or "pull" that drives electric current. It represents the potential energy per unit charge at a specific point in an electric field, indicating the work that can be done if a charge moves from that point. In practical terms, voltage differences (potential differences) are what make batteries work, power grids transmit energy, and electronic circuits function. Without understanding electric potential, it would be impossible to design, analyze, or troubleshoot any electrical system.

Deriving Electric Potential from a Point Charge

The Electric Potential (Voltage) Calculator computes the electric potential (V) using a simplified form of Coulomb's Law, specifically tailored for potential rather than force. The potential is defined as the work required per unit charge to move a test charge from infinity to a point near a source charge.

The formula for electric potential (V) from a point charge is:

V = K × Q / r

Where:

V is the electric potential in Volts (V).
K is Coulomb's constant (approximately 8.9875 × 10^9 N·m²/C²).
Q is the source point charge in coulombs (C).
r is the distance from the point charge in meters (m).

💡 To calculate the energy costs of common household appliances that rely on electric potential, our Water Heater Energy Cost Calculator can help you budget effectively.

Analyzing Electric Potential: A Practical Example

Consider an electrical engineer examining the electric potential around a 1 nanocoulomb (1e-9 C) point charge at a distance of 0.05 meters (5 cm).

Identify the charge (Q): Q = 1e-9 C.
Determine the distance (r): r = 0.05 m.
Apply Coulomb's constant (K): K = 8.9875 × 10^9 N·m²/C².
Calculate the electric potential (V): V = (8.9875 × 10^9) × (1 × 10^-9) / 0.05 V = 8.9875 / 0.05 V = 179.75 V

The electric potential at 0.05 meters from this 1 nanocoulomb charge is 179.75 Volts. This means that 179.75 Joules of energy would be required to bring 1 Coulomb of positive charge from infinity to this point.

💡 For analyzing more complex circuit configurations, such as balancing resistors in a bridge, our Wheatstone Bridge Calculator can provide precise measurements of unknown resistance.

Voltage in Practical Electrical Systems

Electric potential, or voltage, is the driving force for current in all practical electrical systems, from the micro-scale of integrated circuits to the macro-scale of power transmission. Residential wiring typically operates at 120V or 240V AC, providing sufficient potential difference to power household appliances. Industrial settings often utilize higher voltages, such as 480V AC, for heavy machinery. In power transmission, voltages can reach hundreds of thousands of volts (e.g., 765 kV) to minimize current and reduce resistive losses over long distances. The safe handling and effective utilization of these varying voltage levels are paramount in electrical engineering, requiring careful design to prevent insulation breakdown and ensure efficient energy delivery.

Electric Potential from Continuous Charge Distributions

While the point charge formula V = kQ/r is straightforward, calculating electric potential from continuous charge distributions (like charged lines, planes, or spheres) requires more advanced mathematical techniques, primarily integration. For a uniformly charged sphere, the potential outside the sphere is identical to that of a point charge located at its center. However, inside the sphere, the potential varies differently. For a charged line, the potential depends logarithmically on distance, and for an infinite charged plane, the potential changes linearly with distance. These variants highlight that while the fundamental concept of potential remains, the specific mathematical approach must adapt to the geometry of the charge distribution. The principle of superposition, however, still applies: the total potential at any point is the scalar sum of the potentials due to each infinitesimal charge element.

Frequently Asked Questions

What is electric potential or voltage?

Electric potential, commonly known as voltage, is a scalar quantity representing the amount of potential energy per unit of electric charge at a given point in an electric field. Measured in Volts (V), it quantifies the work required to move a unit positive charge from a reference point (often infinity) to that specific point against the electric field. It's the 'pressure' that drives electric current in a circuit, with higher potential differences leading to stronger currents.

How does charge and distance affect electric potential?

Electric potential is directly proportional to the magnitude of the source charge and inversely proportional to the distance from it. This means that a larger charge creates a higher potential at any given distance, and the potential decreases as you move further away from the charge. Unlike electric field strength, which decreases by the square of the distance, electric potential decreases linearly with distance, making its fall-off less rapid.

What is an electron-volt (eV) and when is it used?

An electron-volt (eV) is a unit of energy commonly used in atomic, nuclear, and particle physics. It represents the kinetic energy gained by a single electron when it accelerates through an electric potential difference of one volt. One electron-volt is equivalent to approximately 1.602 × 10^-19 Joules. It's particularly useful when dealing with the energies of electrons and other subatomic particles, as Joules would result in extremely small, inconvenient numbers.