Electric potential tells you how much electric energy per unit charge exists at a point in space. This Electric Potential Calculator computes V using V = kQ/r for a point charge and converts common units so you can get a correct answer fast.
Enter a charge and distance, choose units, and read the potential in volts. It also shows the intermediate values so you can verify the result.
What Electric Potential Means
Electric potential (V) is the work (energy transfer) per unit charge needed to move a test charge from a reference point to a given location. It’s a scalar quantity, meaning it has magnitude but no direction.
Engineers use potential to simplify many problems because energy changes are often easier to compute than forces.
Core Formula for the Electric Potential Calculator
For a point charge, the electric potential at distance r is:
V = kQ / r
- V is electric potential in volts (V)
- Q is source charge in coulombs (C)
- r is distance from the charge in meters (m)
- k is Coulomb’s constant: k = 8.9875517923 × 109 N·m²/C²
Variables and Units (What You Should Enter)
The calculator accepts the most common real-world units:
- Charge: coulombs (C) by default, with optional microcoulombs (µC) and nanocoulombs (nC)
- Distance: meters (m) by default, with optional centimeters (cm) and millimeters (mm)
Internally, it converts your inputs to SI units (C and m), applies V = kQ/r, then converts the result to volts (V).
Important Notes About Reference Points
Electric potential depends on the chosen zero reference. For a single point charge, a common convention is to set V = 0 at infinity. With that convention, the formula above is standard.
If you are working with circuits or bounded regions, your textbook may use a different reference point, but the calculator’s point-charge model still matches the usual physics convention.
How to Use the Electric Potential Calculator
- Enter the charge value and select its unit.
- Enter the distance from the charge and select its unit.
- Click Calculate to compute electric potential in volts.
- If you make a mistake, click Reset and try again.
The calculator also checks for invalid inputs like negative distance or a distance of zero (which would cause division by zero).
Practical Examples (Real-Life Use)
Example 1: Estimating Potential Around a Charged Atom
Suppose a small charge of Q = 1.0 nC is located at a point. At a distance of r = 0.50 m, the potential is:
V = (8.9875517923×109) × (1.0×10-9) / 0.50 ≈ 17.98 V
This shows how quickly potential changes as you move closer to (or farther from) a charge.
Example 2: Comparing Potentials at Two Distances
Let Q = 5.0 µC. Compare potential at r = 2.0 cm and r = 4.0 cm.
- Because V ∝ 1/r, doubling the distance halves the potential.
- So the potential at 4.0 cm is half the potential at 2.0 cm.
That inverse relationship is one of the main reasons potential is so useful in physics and engineering.
Common Mistakes to Avoid
- Using distance = 0: the formula would divide by zero. Real charges also have size, so you cannot treat them as perfect point charges at extremely small distances.
- Mixing units: always confirm whether your input is in C vs µC or m vs cm.
- Assuming direction: electric potential is a scalar. Direction belongs to electric field, not potential.
Frequently Asked Questions
What is the difference between electric potential and electric field?
Electric potential (V) measures energy per unit charge at a point and is a scalar value. Electric field (E) describes the force per unit charge and has direction. For a point charge, the field relates to potential by the spatial change of V.
Can electric potential be negative?
Yes. Electric potential becomes negative when the source charge Q is negative under the common reference convention V = 0 at infinity. A negative V means a test positive charge would have lower potential energy compared to infinity, not that anything is “broken.”
Why does electric potential follow 1/r?
For a point charge, the work needed to bring a charge from infinity depends on how the Coulomb force spreads out in space. As distance increases, the influence weakens, and the energy per unit charge decreases proportionally to 1/r, giving V = kQ/r.
What units should I use for the Electric Potential Calculator?
Use coulombs for charge and meters for distance for the standard SI formula. If your values are in microcoulombs or nanocoulombs, or centimeters and millimeters, the calculator converts them automatically. The output is in volts (V).
How is this calculator limited?
This calculator models electric potential for a single point charge using V = kQ/r. It does not compute potential from multiple charges, conductors with complex shapes, or time-varying fields. For those cases, you need superposition or more advanced models and boundary conditions.